Gauge global

Legates, D. R. and Willmott, C. J. (1990b). Mean seasonal and spatial variability in gauge-corrected, global precipitation, Int. ]. Climatol. 10, 111-127. 

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

Therefore the Lehnert equation (253) correctly conserves action under a local U(l) gauge transformation in the vacuum. Such a transformation leads to a vacuum charge current density as the result of gauge theory itself, because U(l) gauge theory has a scalar internal space that supports A and A. These must be complex in order to define the globally conserved charge ... 

Global gauge transformation on these vectors produces a shift in the electromagnetic phase... 

The Lagrangian (868) is invariant under a global gauge transformation ... 

This type of transformation is not dependent on spacetime and is purely internal [46] in Noether s theorem. Under a global gauge transformation, Noether s theorem gives the conserved current... 

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. 

This can be written according to Lie derivative, and if A is a generator for a global gauge transformation, then this double commutator vanishes. We are then left with... 

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. 

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