Local gauge invariance symmetry

The principle of local invariance in a curved Riemannian manifold leads to the appearance of compensating fields. Like the electromagnetic field, which is the compensating field of local phase transformation, the gravitational field may be interpreted as the compensating field of local Lorentz transformations. In modern physics all interactions are understood in terms of theories which combine local gauge invariance with spontaneous symmetry breaking. 

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

It was demonstrated by Higgs [50] that the appearance of massless bosons can be avoided by combining the spontaneous breakdown of symmetry under a compact Lie group with local gauge symmetry. The potential V() which is invariant under the local transformation of the charged field... 

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... 

Chemical behaviour depends on chemical potential and electromagnetic interaction. Both of these factors depend on the local curvature of space-time, commonly identified with the vacuum. Any chemical or phase transformation is caused by an interaction that changes the symmetry of the gauge field. It is convenient to describe such events in terms of a Lagrangian density which is invariant under gauge transformation and reveals the details of the interaction as a function of the symmetry. The chemically important examples of crystal nucleation and the generation of entropy by time flow will be discussed next. The important conclusion is that in all cases, the gauge field arises from a symmetry of space-time and the nature of chemical matter and interaction reduces to a function of space-time structure. 

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