Scalar electrodynamics
Encyclopedia
In theoretical physics
, scalar electrodynamics is a theory of a U(1) gauge field coupled to a charged spin 0 scalar field
that takes the place of the Dirac fermion
s in "ordinary" quantum electrodynamics
. The scalar field is charged, and with an appropriate potential, it has the capacity to break the gauge symmetry via the Abelian
Higgs mechanism
.
The model consists of a complex scalar field
minimally coupled to a gauge field 
. The dynamics is given by the Lagrangian density
where
is the electromagnetic field strength,
is the covariant derivative of the field 
, 
is the electric charge and 
is the potential for the complex scalar field. This model is invariant under gauge transformations parametrized by 
If the potential is such that its minimum occurs at non-zero value of
, this model exhibits the Higgs mechanism
. This can be seen by studying fluctuations about the lowest energy configuration, one sees that gauge field behaves as a massive field with its mass proportional to the
times the minimum value of 
. As shown in 1973 by Nielsen and Olesen, this model, in 
dimensions, admits time-independent finite energy configurations corresponding to vortices carrying magnetic flux. The magnetic flux carried by these vortices are quantized (in units of 
) and appears as a topological charge associated with the topological current
These vortices are similar to the vortices appearing in type-II superconductors. This analogy was used by Nielsen and Olesen in obtaining their solutions.
Theoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
, scalar electrodynamics is a theory of a U(1) gauge field coupled to a charged spin 0 scalar field
Scalar field
In mathematics and physics, a scalar field associates a scalar value to every point in a space. The scalar may either be a mathematical number, or a physical quantity. Scalar fields are required to be coordinate-independent, meaning that any two observers using the same units will agree on the...
that takes the place of the Dirac fermion
Dirac fermion
In particle physics, a Dirac fermion is a fermion which is not its own anti-particle. It is named for Paul Dirac. All fermions in the standard model, except possibly neutrinos, are Dirac fermions...
s in "ordinary" quantum electrodynamics
Quantum electrodynamics
Quantum electrodynamics is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved...
. The scalar field is charged, and with an appropriate potential, it has the capacity to break the gauge symmetry via the Abelian
Abelian
In mathematics, Abelian refers to any of number of different mathematical concepts named after Niels Henrik Abel:- Group theory :*Abelian group, a group in which the binary operation is commutative...
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....
.
The model consists of a complex scalar field
minimally coupled to a gauge field . The dynamics is given by the Lagrangian densitywhere
is the electromagnetic field strength, is the covariant derivative of the field , is the electric charge and is the potential for the complex scalar field. This model is invariant under gauge transformations parametrized by If the potential is such that its minimum occurs at non-zero value of
, this model exhibits the Higgs mechanismHiggs 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....
. This can be seen by studying fluctuations about the lowest energy configuration, one sees that gauge field behaves as a massive field with its mass proportional to the
times the minimum value of . As shown in 1973 by Nielsen and Olesen, this model, in dimensions, admits time-independent finite energy configurations corresponding to vortices carrying magnetic flux. The magnetic flux carried by these vortices are quantized (in units of ) and appears as a topological charge associated with the topological currentThese vortices are similar to the vortices appearing in type-II superconductors. This analogy was used by Nielsen and Olesen in obtaining their solutions.