In the presence of the electromagnetic potential, [A.sub.[mu]] = ([A.sub.0], [??]), gauge invariant
coupling to the charged spinor is accomplished by the minimal substitution [[partial derivative].sub.[mu]] [right arrow] [[partial derivative].sub.[mu]] + i[alpha][A.sub.[mu]], which transforms free Dirac equation into
It has been argued that the photon angular momentum cannot be separated into a spin part and an orbital part in a gauge invariant
way and the paradox was a subject for several papers and in standard textbooks for the past few decades .
Abstract: I will show a general gauge invariant
formalism for defining cosmological averages that are relevant for observations based on light-like signals.
In the minimal supersymmetric standard model (MSSM), unlike in the SM, the conservation of lepton number (L) and of baryon number (B) is not automatic: the superpotential can contain renormalizable and gauge invariant
L- and B-violating terms.
We require that H be 'gauge invariant
' (see below).
As we will detail below, this issue can be fixed if the mediator is assumed to couple at tree level only to the DM and to the Higgs through the gauge invariant
portal terms S[[absolute value of H].sup.2], [S.sup.2][[absolute value of H].sup.2], etc.
We will extend the lagrangian with auxiliary fields so that this is not necessary but only that the gauge invariant
functions of the collective reality of these fields evolve causally.
After the celebrated paper by Wu and Yang , most physicists accepted a 'third way' between non-local fields and local potentials: global, gauge invariant
properties of the potentials are fundamental (Hong-Mo and Tsun ).
The latter superfield approach [9-12] has been christened as the augmented version of superfield approach to BRST formalism, where, consistent with the HC, additional restrictions (i.e., gauge invariant
conditions) are also invoked.
Thirteen of them are in the fermion sector, and the Higgs interactions with the fermions are not gauge invariant
so their strengths are arbitrary.