Mathematical formulation of quantum mechanics

Mathematical formulation of quantum mechanics

The mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. Such are distinguished from mathematical formalisms for theories developed prior to the early 1900s by the use of abstract mathematical structures, such as...

• bra-ket notation
  Bra-ket notation
  Bra-ket notation is a standard notation for describing quantum states in the theory of quantum mechanics composed of angle brackets and vertical bars. It can also be used to denote abstract vectors and linear functionals in mathematics...
  
  
• canonical commutation relation
  Canonical commutation relation
  In physics, the canonical commutation relation is the relation between canonical conjugate quantities , for example:[x,p_x] = i\hbar...
  
  
• complete set of commuting observables
  Complete set of commuting observables
  In quantum mechanics, a complete set of commuting observables is a set of commuting operators whose eigenvalues completely specify the state of a system ....
  
  
• Heisenberg picture
  Heisenberg picture
  In physics, the Heisenberg picture is a formulation of quantum mechanics in which the operators incorporate a dependency on time, but the state vectors are time-independent. It stands in contrast to the Schrödinger picture in which the operators are constant and the states evolve in time...
  
  
• Hilbert space
  Hilbert space
  The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions...
  
  
• Measurement in quantum mechanics
  Measurement in quantum mechanics
  The framework of quantum mechanics requires a careful definition of measurement. The issue of measurement lies at the heart of the problem of the interpretation of quantum mechanics, for which there is currently no consensus....
  
  
• quantum field theory
  Quantum field theory
  Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...
  
  
• quantum logic
  Quantum logic
  In quantum mechanics, quantum logic is a set of rules for reasoning about propositions which takes the principles of quantum theory into account...
  
  
• quantum operation
  Quantum operation
  In quantum mechanics, a quantum operation is a mathematical formalism used to describe a broad class of transformations that a quantum mechanical system can undergo. This was first discussed as a general stochastic transformation for a density matrix by George Sudarshan...
  
  
• Schrödinger picture
  Schrödinger picture
  In physics, the Schrödinger picture is a formulation of quantum mechanics in which the state vectors evolve in time, but the operators are constant. This differs from the Heisenberg picture which keeps the states constant while the observables evolve in time...
  
  
• semiclassical
  Semiclassical
  Semiclassical may refer to:* In Physics: a theory in which one part of a system is described quantum-mechanically whereas the other is treated classically, e.g....
  
  
• statistical ensemble
• wavefunction
  Wavefunction
  Not to be confused with the related concept of the Wave equationA wave function or wavefunction is a probability amplitude in quantum mechanics describing the quantum state of a particle and how it behaves. Typically, its values are complex numbers and, for a single particle, it is a function of...
  
  
• wave-particle duality
• Wightman axioms
  Wightman axioms
  In physics the Wightman axioms are an attempt at a mathematically rigorous formulation of quantum field theory. Arthur Wightman formulated the axioms in the early 1950s but they were first published only in 1964, after Haag-Ruelle scattering theory affirmed their significance.The axioms exist in...
  
  
• WKB approximation
  WKB approximation
  In mathematical physics, the WKB approximation or WKB method is a method for finding approximate solutions to linear partial differential equations with spatially varying coefficients...
  
  

Schrödinger equation

Schrödinger equation

The Schrödinger equation was formulated in 1926 by Austrian physicist Erwin Schrödinger. Used in physics , it is an equation that describes how the quantum state of a physical system changes in time....

• quantum mechanics
  Quantum mechanics
  Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
  
  , matrix mechanics
  Matrix mechanics
  Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925.Matrix mechanics was the first conceptually autonomous and logically consistent formulation of quantum mechanics. It extended the Bohr Model by describing how the quantum jumps...
  
  , Hamiltonian (quantum mechanics)
  Hamiltonian (quantum mechanics)
  In quantum mechanics, the Hamiltonian H, also Ȟ or Ĥ, is the operator corresponding to the total energy of the system. Its spectrum is the set of possible outcomes when one measures the total energy of a system...
  
  
• particle in a box
  Particle in a box
  In quantum mechanics, the particle in a box model describes a particle free to move in a small space surrounded by impenetrable barriers. The model is mainly used as a hypothetical example to illustrate the differences between classical and quantum systems...
  
  
• particle in a ring
  Particle in a ring
  In quantum mechanics, the case of a particle in a one-dimensional ring is similar to the particle in a box. The Schrödinger equation for a free particle which is restricted to a ring is...
  
  
• particle in a spherically symmetric potential
• quantum harmonic oscillator
  Quantum harmonic oscillator
  The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary potential can be approximated as a harmonic potential at the vicinity of a stable equilibrium point, it is one of the most important model systems in quantum mechanics...
  
  
• hydrogen atom
  Hydrogen atom
  A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positively-charged proton and a single negatively-charged electron bound to the nucleus by the Coulomb force...
  
  
• ring wave guide
• particle in a one-dimensional lattice (periodic potential)
  Particle in a one-dimensional lattice (periodic potential)
  In quantum mechanics, the particle in a one-dimensional lattice is a problem that occurs in the model of a periodic crystal lattice. The potential is caused by ions in the periodic structure of the crystal creating an electromagnetic field so electrons are subject to a regular potential inside...
  
  

Symmetry

Symmetry

Symmetry generally conveys two primary meanings. The first is an imprecise sense of harmonious or aesthetically pleasing proportionality and balance; such that it reflects beauty or perfection...

• identical particles
  Identical particles
  Identical particles, or indistinguishable particles, are particles that cannot be distinguished from one another, even in principle. Species of identical particles include elementary particles such as electrons, and, with some clauses, composite particles such as atoms and molecules.There are two...
  
  
• angular momentum
  Angular momentum
  In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...
  
  
  • angular momentum operator
    Angular momentum operator
    In quantum mechanics, the angular momentum operator is an operator analogous to classical angular momentum. The angular momentum operator plays a central role in the theory of atomic physics and other quantum problems involving rotational symmetry...
    
    
• rotational invariance
  Rotational invariance
  In mathematics, a function defined on an inner product space is said to have rotational invariance if its value does not change when arbitrary rotations are applied to its argument...
  
  
  • rotational symmetry
    Rotational symmetry
    Generally speaking, an object with rotational symmetry is an object that looks the same after a certain amount of rotation. An object may have more than one rotational symmetry; for instance, if reflections or turning it over are not counted, the triskelion appearing on the Isle of Man's flag has...
    
    
  • rotation operator
• translational symmetry
  Translational symmetry
  In geometry, a translation "slides" an object by a a: Ta = p + a.In physics and mathematics, continuous translational symmetry is the invariance of a system of equations under any translation...
  
  
• Lorentz symmetry
• Parity transformation
• Noether's theorem
  Noether's theorem
  Noether's theorem states that any differentiable symmetry of the action of a physical system has a corresponding conservation law. The theorem was proved by German mathematician Emmy Noether in 1915 and published in 1918...
  
  
• Noether charge
• spin (physics)
  Spin (physics)
  In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
  
  
  • isospin
    Isospin
    In physics, and specifically, particle physics, isospin is a quantum number related to the strong interaction. This term was derived from isotopic spin, but the term is confusing as two isotopes of a nucleus have different numbers of nucleons; in contrast, rotations of isospin maintain the number...
    
    
• Pauli matrices
  Pauli matrices
  The Pauli matrices are a set of three 2 × 2 complex matrices which are Hermitian and unitary. Usually indicated by the Greek letter "sigma" , they are occasionally denoted with a "tau" when used in connection with isospin symmetries...
  
  
• scale invariance
  Scale invariance
  In physics and mathematics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor...
  
  
• spontaneous symmetry breaking
  Spontaneous symmetry breaking
  Spontaneous symmetry breaking is the process by which a system described in a theoretically symmetrical way ends up in an apparently asymmetric state....
  
  
• supersymmetry breaking
  Supersymmetry breaking
  In particle physics, supersymmetry breaking is the process to obtain a seemingly non-supersymmetric physics from a supersymmetric theory which is a necessary step to reconcile supersymmetry with actual experiments. It is an example of spontaneous symmetry breaking...
  
  

Quantum states

• quantum number
  Quantum number
  Quantum numbers describe values of conserved quantities in the dynamics of the quantum system. Perhaps the most peculiar aspect of quantum mechanics is the quantization of observable quantities. This is distinguished from classical mechanics where the values can range continuously...
  
  
• Pauli exclusion principle
  Pauli exclusion principle
  The Pauli exclusion principle is the quantum mechanical principle that no two identical fermions may occupy the same quantum state simultaneously. A more rigorous statement is that the total wave function for two identical fermions is anti-symmetric with respect to exchange of the particles...
  
  
• quantum indeterminacy
  Quantum indeterminacy
  Quantum indeterminacy is the apparent necessary incompleteness in the description of a physical system, that has become one of the characteristics of the standard description of quantum physics...
  
  
• uncertainty principle
  Uncertainty principle
  In quantum mechanics, the Heisenberg uncertainty principle states a fundamental limit on the accuracy with which certain pairs of physical properties of a particle, such as position and momentum, can be simultaneously known...
  
  
• wavefunction collapse
  Wavefunction collapse
  In quantum mechanics, wave function collapse is the phenomenon in which a wave function—initially in a superposition of several different possible eigenstates—appears to reduce to a single one of those states after interaction with an observer...
  
  
• zero-point energy
  Zero-point energy
  Zero-point energy is the lowest possible energy that a quantum mechanical physical system may have; it is the energy of its ground state. All quantum mechanical systems undergo fluctuations even in their ground state and have an associated zero-point energy, a consequence of their wave-like nature...
  
  
• bound state
  Bound state
  In physics, a bound state describes a system where a particle is subject to a potential such that the particle has a tendency to remain localised in one or more regions of space...
  
  
• coherent state
  Coherent state
  In quantum mechanics a coherent state is a specific kind of quantum state of the quantum harmonic oscillator whose dynamics most closely resembles the oscillating behaviour of a classical harmonic oscillator...
  
  
  • squeezed coherent state
• density state
• Fock state
  Fock state
  A Fock state , in quantum mechanics, is any element of a Fock space with a well-defined number of particles . These states are named after the Soviet physicist, V. A. Fock.-Definition:...
  
  , Fock space
  Fock space
  The Fock space is an algebraic system used in quantum mechanics to describe quantum states with a variable or unknown number of particles. It is named after V. A...
  
  
• vacuum state
  Vacuum state
  In quantum field theory, the vacuum state is the quantum state with the lowest possible energy. Generally, it contains no physical particles...
  
  
• quasinormal mode
  Quasinormal mode
  -Wave Mechanics:Quasinormal modes are the modes of energy dissipation of aperturbed object or field. A familiar example is theperturbation of a wine glass with a knife: the glass begins to...
  
  
• no cloning theorem
  No cloning theorem
  The no-cloning theorem is a result of quantum mechanics that forbids the creation of identical copies of an arbitrary unknown quantum state. It was stated by Wootters, Zurek, and Dieks in 1982, and has profound implications in quantum computing and related fields.The state of one system can be...
  
  
• quantum entanglement
  Quantum entanglement
  Quantum entanglement occurs when electrons, molecules even as large as "buckyballs", photons, etc., interact physically and then become separated; the type of interaction is such that each resulting member of a pair is properly described by the same quantum mechanical description , which is...
  
  

Dirac equation

Dirac equation

The Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928. It provided a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity, and...

• spinor
  Spinor
  In mathematics and physics, in particular in the theory of the orthogonal groups , spinors are elements of a complex vector space introduced to expand the notion of spatial vector. Unlike tensors, the space of spinors cannot be built up in a unique and natural way from spatial vectors...
  
  , spinor group, spinor bundle
• Dirac sea
  Dirac sea
  The Dirac sea is a theoretical model of the vacuum as an infinite sea of particles with negative energy. It was first postulated by the British physicist Paul Dirac in 1930 to explain the anomalous negative-energy quantum states predicted by the Dirac equation for relativistic electrons...
  
  
• Spin foam
  Spin foam
  In physics, a spin foam is a topological structure made out of two-dimensional faces that represents one of the configurations that must be summed to obtain a Feynman's path integral description of quantum gravity...
  
  
• Poincaré group
  Poincaré group
  In physics and mathematics, the Poincaré group, named after Henri Poincaré, is the group of isometries of Minkowski spacetime.-Simple explanation:...
  
  
• gamma matrices
• Dirac adjoint
• Wigner's classification
  Wigner's classification
  In mathematics and theoretical physics, Wigner's classificationis a classification of the nonnegative energy irreducible unitary representations of the Poincaré group, which have sharp mass eigenvalues...
  
  
• anyon
  Anyon
  In physics, an anyon is a type of particle that occurs only in two-dimensional systems. It is a generalization of the fermion and boson concept.-From theory to reality:...
  
  

Interpretations of quantum mechanics

• Copenhagen interpretation
  Copenhagen interpretation
  The Copenhagen interpretation is one of the earliest and most commonly taught interpretations of quantum mechanics. It holds that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta,...
  
  
• locality principle
• Bell's theorem
  Bell's theorem
  In theoretical physics, Bell's theorem is a no-go theorem, loosely stating that:The theorem has great importance for physics and the philosophy of science, as it implies that quantum physics must necessarily violate either the principle of locality or counterfactual definiteness...
  
  
  • Bell test loopholes
• CHSH inequality
  CHSH inequality
  In physics, the CHSH Bell test is an application of Bell's theorem, intended to distinguish between the entanglement hypothesis of quantum mechanics and local hidden variable theories. CHSH stands for John Clauser, Michael Horne, Abner Shimony and Richard Holt, who described it in a much-cited...
  
  
• Wigner–d'Espagnat inequality
• hidden variable theory
  Hidden variable theory
  Historically, in physics, hidden variable theories were espoused by some physicists who argued that quantum mechanics is incomplete. These theories argue against the orthodox interpretation of quantum mechanics, which is the Copenhagen Interpretation...
  
  
• path integral formulation
  Path integral formulation
  The path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action principle of classical mechanics...
  
  , quantum action
• Bohm interpretation
  Bohm interpretation
  The de Broglie–Bohm theory, also called the pilot-wave theory, Bohmian mechanics, and the causal interpretation, is an interpretation of quantum theory. In addition to a wavefunction on the space of all possible configurations, it also includes an actual configuration, even in situations where...
  
  
• many-worlds interpretation
  Many-worlds interpretation
  The many-worlds interpretation is an interpretation of quantum mechanics that asserts the objective reality of the universal wavefunction, but denies the actuality of wavefunction collapse. Many-worlds implies that all possible alternative histories and futures are real, each representing an...
  
  
• Tsirelson's bound
  Tsirelson's bound
  Tsirelson's bound, also known as Tsirelson's inequality, or in another transliteration, Cirel'son's inequality, is an inequality that imposed an upper limit to quantum mechanical correlations between distant events...
  
  

Quantum field theory

Quantum field theory

Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...

• Feynman diagram
  Feynman diagram
  Feynman diagrams are a pictorial representation scheme for the mathematical expressions governing the behavior of subatomic particles, first developed by the Nobel Prize-winning American physicist Richard Feynman, and first introduced in 1948...
  
  
  • One-loop Feynman diagram
    One-loop Feynman diagram
    In physics, a one-loop Feynman diagram is a connected Feynman diagram with only one cycle . Such a diagram can be obtained from a connected tree diagram by taking two external lines of the same type and joining them together into an edge....
    
    
  • tree diagram
    Tree diagram
    The term tree diagram refers to a specific type of diagram that has a unique network topology. It can be seen as a specific type of network diagram, which in turn can be seen as a special kind of cluster diagram.-Applications:...
    
    
• Schwinger's quantum action principle
• Propagator
  Propagator
  In quantum mechanics and quantum field theory, the propagator gives the probability amplitude for a particle to travel from one place to another in a given time, or to travel with a certain energy and momentum. Propagators are used to represent the contribution of virtual particles on the internal...
  
  
• Annihilation operator
• S matrix
  S matrix
  In physics, the scattering matrix relates the initial state and the final state of a physical system undergoing a scattering process...
  
  
• Standard model
  Standard model (basic details)
  This is a detailed description of the standard model of particle physics. It describes how the leptons, quarks, gauge bosons and the Higgs particle fit together...
  
  
• Local quantum physics
• Nonlocal
• Effective field theory
  Effective field theory
  In physics, an effective field theory is, as any effective theory, an approximate theory, that includes appropriate degrees of freedom to describe physical phenomena occurring at a chosen length scale, while ignoring substructure and degrees of freedom at shorter distances .-The renormalization...
  
  
• Correlation function (quantum field theory)
  Correlation function (quantum field theory)
  In quantum field theory, the matrix element computed by inserting a product of operators between two states, usually the vacuum states, is called a correlation function....
  
  
• Renormalizable
• Cutoff
  Cutoff
  In theoretical physics, cutoff is an arbitrary maximal or minimal value of energy, momentum, or length, used in order that objects with larger or smaller values than these physical quantities are ignored in some calculation...
  
  
• Infrared divergence
  Infrared divergence
  In physics, an infrared divergence or infrared catastrophe is a situation in which an integral, for example a Feynman diagram, diverges because of contributions of objects with very small energy approaching zero, or, equivalently, because of physical phenomena at very long distances.The infrared ...
  
  , infrared fixed point
  Infrared fixed point
  In physics, an infrared fixed point is a set of coupling constants, or other parameters that evolve from initial values at very high energies , to fixed stable values, usually predictable, at low energies...
  
  
• Ultraviolet divergence
  Ultraviolet divergence
  In physics, an ultraviolet divergence is a situation in which an integral, for example a Feynman diagram, diverges because of contributions of objects with very high energy , or, equivalently, because of physical phenomena at very short distances. An infinite answer to a question that should have a...
  
  
• Fermi's interaction
  Fermi's interaction
  In particle physics, Fermi's interaction also known as Fermi coupling, is an old explanation of the weak force, proposed by Enrico Fermi, in which four fermions directly interact with one another at one vertex...
  
  
• Path-ordering
  Path-ordering
  In theoretical physics, path-ordering is the procedure of ordering a product of many operators according to the value of one chosen parameter:...
  
  
• Landau pole
  Landau pole
  In physics, the Landau pole is the momentum scale at which the coupling constant of a quantum field theory becomes infinite...
  
  
• Higgs mechanism
  Higgs mechanism
  In particle physics, the Higgs mechanism is the process in which gauge bosons in a gauge theory can acquire non-vanishing masses through absorption of Nambu-Goldstone bosons arising in spontaneous symmetry breaking....
  
  
• Wilson line
• Wilson loop
  Wilson loop
  In gauge theory, a Wilson loop is a gauge-invariant observable obtained from the holonomy of the gauge connection around a given loop...
  
  
• Tadpole (physics)
  Tadpole (physics)
  In quantum field theory, a tadpole is a one-loop Feynman diagram with one external leg, giving a contribution to a one-point correlation function . One-loop diagrams with a propagator that connects back to its originating vertex are often also referred as tadpoles...
  
  
• Lattice gauge theory
  Lattice gauge theory
  In physics, lattice gauge theory is the study of gauge theories on a spacetime that has been discretized into a lattice. Gauge theories are important in particle physics, and include the prevailing theories of elementary particles: quantum electrodynamics, quantum chromodynamics and the Standard...
  
  
• BRST charge
• Anomaly (physics)
  Anomaly (physics)
  In quantum physics an anomaly or quantum anomaly is the failure of a symmetry of a theory's classical action to be a symmetry of any regularization of the full quantum theory. In classical physics an anomaly is the failure of a symmetry to be restored in the limit in which the symmetry-breaking...
  
  
• Chiral anomaly
  Chiral anomaly
  A chiral anomaly is the anomalous nonconservation of a chiral current. In some theories of fermions with chiral symmetry, the quantization may lead to the breaking of this chiral symmetry. In that case, the charge associated with the chiral symmetry is not conserved.The non-conservation happens...
  
  
• Braid statistics
  Braid statistics
  In mathematics and theoretical physics, braid statistics is a generalization of the statistics of bosons and fermions based on the concept of braid group. A similar notion exists using a loop braid group.-See also:* Braid symmetry* Parastatistics...
  
  
• Plekton

Computation

Computation

Computation is defined as any type of calculation. Also defined as use of computer technology in Information processing.Computation is a process following a well-defined model understood and expressed in an algorithm, protocol, network topology, etc...

• quantum computing
• qubit
  Qubit
  In quantum computing, a qubit or quantum bit is a unit of quantum information—the quantum analogue of the classical bit—with additional dimensions associated to the quantum properties of a physical atom....
  
  
• pure qubit state
• quantum dot
  Quantum dot
  A quantum dot is a portion of matter whose excitons are confined in all three spatial dimensions. Consequently, such materials have electronic properties intermediate between those of bulk semiconductors and those of discrete molecules. They were discovered at the beginning of the 1980s by Alexei...
  
  
• Kane quantum computer
  Kane quantum computer
  The Kane quantum computer is a proposal for a scalable quantum computer proposed by Bruce Kane in 1998, then at the University of New South Wales. Often thought of as a hybrid between quantum dot and NMR quantum computers, the Kane computer is based on an array of individual phosphorus donor atoms...
  
  
• quantum cryptography
  Quantum cryptography
  Quantum key distribution uses quantum mechanics to guarantee secure communication. It enables two parties to produce a shared random secret key known only to them, which can then be used to encrypt and decrypt messages...
  
  
• quantum decoherence
  Quantum decoherence
  In quantum mechanics, quantum decoherence is the loss of coherence or ordering of the phase angles between the components of a system in a quantum superposition. A consequence of this dephasing leads to classical or probabilistically additive behavior...
  
  
• quantum circuit
  Quantum circuit
  In quantum information theory, a quantum circuit is a model for quantum computation in which a computation is a sequence of quantum gates, which are reversible transformations on a quantum mechanical analog of an n-bit register...
  
  
• universal quantum computer
• timeline of quantum computing
  Timeline of quantum computing
  -1970s:* 1970 – Stephen Wiesner invents conjugate coding.* 1973 – Alexander Holevo publishes a paper showing that n qubits cannot carry more than n classical bits of information . Charles H. Bennett shows that computation can be done reversibly.* 1975 – R. P...
  
  

Supersymmetry

Supersymmetry

In particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...

• Lie superalgebra
  Lie superalgebra
  In mathematics, a Lie superalgebra is a generalisation of a Lie algebra to include a Z2-grading. Lie superalgebras are important in theoretical physics where they are used to describe the mathematics of supersymmetry...
  
  
• supergroup (physics)
  Supergroup (physics)
  The concept of supergroup is a generalization of that of group. In other words, every group is a supergroup but not every supergroup is a group. A supergroup is like a Lie group in that there is a well defined notion of smooth function defined on them....
  
  
• supercharge
  Supercharge
  In theoretical physics, a supercharge is a generator of supersymmetry transformations.Supercharge, denoted by the symbol Q, is an operator which transforms bosons into fermions, and vice versa...
  
  
• supermultiplet
  Supermultiplet
  In theoretical physics, a supermultiplet is formally a group representation of a supersymmetry algebra. It consists of a collection of particles, called superpartners, corresponding to operators in a quantum field theory which in superspace are represented by superfields.Superfields were...
  
  
• supergravity
  Supergravity
  In theoretical physics, supergravity is a field theory that combines the principles of supersymmetry and general relativity. Together, these imply that, in supergravity, the supersymmetry is a local symmetry...
  
  

Quantum gravity

Quantum gravity

Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...

• theory of everything
  Theory of everything
  A theory of everything is a putative theory of theoretical physics that fully explains and links together all known physical phenomena, and predicts the outcome of any experiment that could be carried out in principle....
  
  
• loop quantum gravity
  Loop quantum gravity
  Loop quantum gravity , also known as loop gravity and quantum geometry, is a proposed quantum theory of spacetime which attempts to reconcile the theories of quantum mechanics and general relativity...
  
  
• spin network
  Spin network
  In physics, a spin network is a type of diagram which can be used to represent states and interactions between particles and fields in quantum mechanics. From a mathematical perspective, the diagrams are a concise way to represent multilinear functions and functions between representations of...
  
  
• black hole thermodynamics
  Black hole thermodynamics
  In physics, black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black hole event horizons...
  
  

Non-commutative geometry

• Quantum group
  Quantum group
  In mathematics and theoretical physics, the term quantum group denotes various kinds of noncommutative algebra with additional structure. In general, a quantum group is some kind of Hopf algebra...
  
  
• Hopf algebra
  Hopf algebra
  In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously an algebra and a coalgebra, with these structures' compatibility making it a bialgebra, and that moreover is equipped with an antiautomorphism satisfying a certain property.Hopf algebras occur naturally...
  
  
• Noncommutative quantum field theory
  Noncommutative quantum field theory
  In mathematical physics, noncommutative quantum field theory is an application of noncommutative mathematics to the spacetime of quantum field theory that is an outgrowth of noncommutative geometry and index theory in which the coordinate functions are noncommutative...