Global gauge symmetry

Onsager s reciprocal relations state that, provided a proper choice is made for the flows and forces, the matrix of phenomenological coefficients is symmetrical. These relations are proved to be an implication of the property of microscopic reversibility , which is the symmetry of all mechanical equations of motion of individual particles with respect to time t. The Onsager reciprocal relations are the results of the global gauge symmetries of the Lagrangian, which is related to the entropy of the system considered. This means that the results in general are valid for an arbitrary process. 

The most telling example is the way in which the, often sterile, laws based on the symmetry of special relativity acquire physical significance within the broken symmetry of general relativity. It removes the major anomaly of time-reversible laws of microphysics underpinning reversible macro effects, and shows how local, rather than global gauge-symmetry breaking may cause the creation of massive particles. 

QCD with 2 massless flavors has gauge symmetry SUC(3) and global symmetry... 

One such symmetry, which is associated with charge conservation, is gauge invariance of the first kind or global gauge invariance. The field transformation is a phase transformation... 

In the case of global gauge invariance the phase 9 is not measurable and can be chosen arbitrarily, but once chosen it must be the same for all times everywhere in space. Could it happen that one can fix the phase locally and diflferently at diflferent places It turns out that in electrodynamics one can do this. It possesses a local gauge symmetry (or gauge... 

The formalism generalizes immediately to higher global non-Abelian gauge symmetries. Let Tj j = be the generators... 

Non-Abelian electrodynamics has been presented in considerable detail in a nonrelativistic setting. However, all gauge fields exist in spacetime and thus exhibits Poincare transformation. In flat spacetime these transformations are global symmetries that act to transform the electric and magnetic components of a gauge field into each other. The same is the case for non-Abelian electrodynamics. Further, the electromagnetic vector potential is written according to absorption and emission operators that act on element of a Fock space of states. It is then reasonable to require that the theory be treated in a manifestly Lorentz covariant manner. 

It has already been shown that for constant a this invariance (symmetry) implies conservation of the charge of a free particle. In general relativity, which is based on a curved manifold rather than flat space with a globally fixed coordinate system, each point has its own coordinate system and hence its own gauge factor. This means that the gauge factor a is no longer a constant, but a function of space-time, i.e. 

Apart from the above symmetry considerations the SB functional-integral formalism reveals additional global and local gauge invariances [25, 30-32]. 

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