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2. Coleman–Weinberg potential - Wikipedia

   en.wikipedia.org/wiki/Coleman–Weinberg_potential

   However, as was shown by Sidney Coleman and Erick Weinberg, even if the renormalized mass is zero, spontaneous symmetry breaking still happens due to the radiative corrections (this introduces a mass scale into a classically conformal theory - the model has a conformal anomaly). The same can happen in other gauge theories.

3. Gauge symmetry (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Gauge_symmetry_(mathematics)

   A gauge symmetry of a Lagrangian is defined as a differential operator on some vector bundle taking its values in the linear space of (variational or exact) symmetries of . Therefore, a gauge symmetry of L {\displaystyle L} depends on sections of E {\displaystyle E} and their partial derivatives. [ 1 ]

4. Introduction to gauge theory - Wikipedia

   en.wikipedia.org/wiki/Introduction_to_gauge_theory

   A gauge theory is a type of theory in physics.The word gauge means a measurement, a thickness, an in-between distance (as in railroad tracks), or a resulting number of units per certain parameter (a number of loops in an inch of fabric or a number of lead balls in a pound of ammunition). [1]

5. Gauge group (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Gauge_group_(mathematics)

   A gauge group is a group of gauge symmetries of the Yang–Mills gauge theory of principal connections on a principal bundle. Given a principal bundle P → X {\displaystyle P\to X} with a structure Lie group G {\displaystyle G} , a gauge group is defined to be a group of its vertical automorphisms.

6. Gauge theory - Wikipedia

   en.wikipedia.org/wiki/Gauge_theory

   Quantum electrodynamics is an abelian gauge theory with the symmetry group U(1) and has one gauge field, the electromagnetic four-potential, with the photon being the gauge boson. The Standard Model is a non-abelian gauge theory with the symmetry group U(1) × SU(2) × SU(3) and has a total of twelve gauge bosons: the photon , three weak bosons ...

7. Supersymmetric gauge theory - Wikipedia

   en.wikipedia.org/wiki/Supersymmetric_gauge_theory

   A gauge theory is a field theory with gauge symmetry. Roughly, there are two types of symmetries, global and local. A global symmetry is a symmetry applied uniformly (in some sense) to each point of a manifold. A local symmetry is a symmetry which is position dependent.

8. Gauge theory (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Gauge_theory_(mathematics)

   Gauge theory in mathematics should not be confused with the closely related concept of a gauge theory in physics, which is a field theory which admits gauge symmetry. In mathematics theory means a mathematical theory , encapsulating the general study of a collection of concepts or phenomena, whereas in the physical sense a gauge theory is a ...

9. Gauge covariant derivative - Wikipedia

   en.wikipedia.org/wiki/Gauge_covariant_derivative

   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 ...