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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 ...
The line is the equivalent of a gauge function; it need not be straight. Almost any line is a valid gauge fixing, i.e., there is a large gauge freedom. In summary, to tell whether the rod is twisted, the gauge must be known. Physical quantities, such as the energy of the torsion, do not depend on the gauge, i.e., they are gauge invariant.
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]
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. In gauge I, we still have the residual gauge e Λ where ¯ ˙ = and in gauge II, we have the residual gauge e Λ satisfying d α Λ = 0. Under ...
Any such term must be both gauge and reference-frame invariant, otherwise the laws of physics would depend on an arbitrary choice or the frame of an observer. Therefore, the global Poincaré symmetry , consisting of translational symmetry , rotational symmetry and the inertial reference frame invariance central to the theory of special ...
Calculating the expectation value in a gauge invariant way always gives zero, in agreement with Elitzur's theorem. The Higgs mechanism can however be reformulated entirely in a gauge invariant way in what is known as the Fröhlich–Morchio–Strocchi mechanism which does not involve spontaneous symmetry breaking of any symmetry. [11]
In contrast to the Berry connection, which is physical only after integrating around a closed path, the Berry curvature is a gauge-invariant local manifestation of the geometric properties of the wavefunctions in the parameter space, and has proven to be an essential physical ingredient for understanding a variety of electronic properties. [4] [5]
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 ...