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Quantum electrodynamics is an abelian gauge theory with the symmetry group U(1) ... A gauge transformation is just a transformation between two such sections.
Further gauge transformations that retain the Coulomb gauge condition might be made with gauge functions that satisfy ∇ 2 ψ = 0, but as the only solution to this equation that vanishes at infinity (where all fields are required to vanish) is ψ(r, t) = 0, no gauge arbitrariness remains. Because of this, the Coulomb gauge is said to be a ...
If a gauge transformation θ is applied to the electron waves, for example, then one must also apply a corresponding transformation to the potentials that describe the electromagnetic waves. [18] Gauge symmetry is required in order to make quantum electrodynamics a renormalizable theory, i.e., one in which the calculated predictions of all ...
The Lorenz gauge condition is used to eliminate the redundant spin-0 component in Maxwell's equations when these are used to describe a massless spin-1 quantum field. It is also used for massive spin-1 fields where the concept of gauge transformations does not apply at all.
Consider a generic (possibly non-Abelian) gauge transformation acting on a component field = =.The main examples in field theory have a compact gauge group and we write the symmetry operator as () = where () is an element of the Lie algebra associated with the Lie group of symmetry transformations, and can be expressed in terms of the hermitian generators of the Lie algebra (i.e. up to a ...
The gauge-fixed potentials still have a gauge freedom under all gauge transformations that leave the gauge fixing equations invariant. Inspection of the potential equations suggests two natural choices. In the Coulomb gauge, we impose ∇ ⋅ A = 0, which is mostly used in the case of magneto statics when we can neglect the c −2 ∂ 2 A/∂t ...
A gauge transformation of a vector bundle or principal bundle is an automorphism of this object. For a principal bundle, a gauge transformation consists of a diffeomorphism φ : P → P {\displaystyle \varphi :P\to P} commuting with the projection operator π {\displaystyle \pi } and the right action ρ {\displaystyle \rho } .
In order to bridge between the two different gauges, we need a gauge transformation. Call it e −V (by convention). If we were using one gauge for all fields, X X would be gauge invariant. However, we need to convert gauge I to gauge II, transforming X to (e −V) q X. So, the gauge invariant quantity is X e −qV X.