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The transformations between possible gauges, called gauge transformations, form a Lie group—referred to as the symmetry group or the gauge group of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises a corresponding field (usually a vector field) called the gauge ...
Gauge symmetries in the Standard Model, used to describe three of the fundamental interactions, are based on the SU(3) × SU(2) × U(1) group. (Roughly speaking, the symmetries of the SU(3) group describe the strong force, the SU(2) group describes the weak interaction and the U(1) group describes the electromagnetic force.)
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]
This article describes the mathematics of the Standard Model of particle physics, a gauge quantum field theory containing the internal symmetries of the unitary product group SU(3) × SU(2) × U(1). The theory is commonly viewed as describing the fundamental set of particles – the leptons, quarks, gauge bosons and the Higgs boson.
In theoretical physics, the notion of gauge symmetries depending on parameter functions is a cornerstone of contemporary field theory. A gauge symmetry of a Lagrangian L {\displaystyle L} is defined as a differential operator on some vector bundle E {\displaystyle E} taking its values in the linear space of (variational or exact) symmetries of ...
Noether's theorem is used in theoretical physics and the calculus of variations. It reveals the fundamental relation between the symmetries of a physical system and the conservation laws. It also made modern theoretical physicists much more focused on symmetries of physical systems.
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.
One important consequence of the distinction between true symmetries and gauge symmetries, is that the massless Nambu–Goldstone resulting from spontaneous breaking of a gauge symmetry are absorbed in the description of the gauge vector field, providing massive vector field modes, like the plasma mode in a superconductor, or the Higgs mode ...