This form contains terms which cannot be elliminated by a holomorphic

gauge transformation.

It will be essential to find a mathematical criterion that distinguishes this condition rather than simply asserting some

gauge transformation exists on the lagrangian and seeking the ones that preserve this.

Indian Railways intend to add 4000 kms of new lines besides over 7500 kms of increasing and 5500 kms of

gauge transformation.

1) into a symmetric form (which is only meaningful for spinless classical charges), the following

gauge transformation has to be applied for tensor entities:

As this phase shift is essentially due to the vector potential, the

gauge transformation of this potential also only affects the phase of the wave function of the particle.

This result highlights the importance of carefully selecting the

gauge transformation used to simplify calculations.

39) is invariant under the local

gauge transformation of the spinor [psi] (Bjorken, 1964 [5]).

An alternative modification of U(I) gauge invariance explored in ([21], where we demand that the Lagrangian density be invariant under a time-local (rather than space-local) U(1)

gauge transformation [psi] [right arrow] [psi]' = U[psi] with U being time-dependent (rather than space-dependent), generated a scalar spin0 field (rather than a 3-vector spin1 field) which we identify as the gravitational field (instead of the magnetic field).

By following the usual approach of deriving a chiral symmetry from a

gauge transformation of a gauge field we have the following chiral symmetry which is derived by applying an analytic

gauge transformation with an analytic function [omega] for the transformation:

The things that are permuted by

gauge transformations are not, for example, spacetime points, but elements of the fibre over each spacetime point; these elements do not represent 'individuals' according to any extant (or any plausible) metaphysical interpretation.

So the gauge group is now being given an active interpretation, but with the proviso that events linked by

gauge transformations are observationally indistinguishable.

Now we introduce the new

gauge transformations of [?