Loop integral
Encyclopedia
In quantum field theory
and statistical mechanics
, loop integrals are the integrals which appear when evaluating the Feynman diagram
s with one or more loops by integrating over the internal momenta.
There are two standard techniques for evaluating loop integrals:
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...
and statistical mechanics
Statistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
, loop integrals are the integrals which appear when evaluating the 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...
s with one or more loops by integrating over the internal momenta.
There are two standard techniques for evaluating loop integrals:
- Feynman parametrizationFeynman parametrizationFeynman parametrization is a technique for evaluating loop integrals which arise from Feynman diagrams with one or more loops. However, it is sometimes useful in integration in areas of pure mathematics as well.Richard Feynman observed that:...
- Schwinger parametrization