Abstract
Basis tensor gauge theory (BTGT) is a reformulation of ordinary gauge theory that is an analog of the vierbein formulation of gravity and is related to the Wilson line formulation. To match ordinary gauge theories coupled to matter, the BTGT formalism requires a continuous symmetry that we call the BTGT symmetry in addition to the ordinary gauge symmetry. After classically interpreting the BTGT symmetry, we construct using the BTGT formalism the Ward identities associated with the BTGT symmetry and the ordinary gauge symmetry. As a way of testing the quantum stability and the consistency of the Ward identities with a known regularization method, we explicitly renormalize the scalar QED at one-loop using dimensional regularization using the BTGT formalism.
Highlights
Gauge theories used to write the Standard Model of particle physics [8,9,10,11,12,13,14,15,16,17] are usually written in terms of fields that transform inhomogeneously under the gauge group; i.e., these are connections on principal bundles
We have investigated the Ward identities in the basis tensor gauge theory (BTGT) formalism associated with the BTGT symmetry and the Uð1Þ symmetry
The Uð1Þ current conservation and the conservation of a particular sum of the BTGT symmetry currents imply the same equation as the residual gauge symmetry current conservation as can be seen in Eq (31)
Summary
Gauge theories (see, e.g., Refs. [1,2,3,4,5,6,7,8]) used to write the Standard Model of particle physics [8,9,10,11,12,13,14,15,16,17] are usually written in terms of fields that transform inhomogeneously under the gauge group; i.e., these are connections on principal bundles (see, e.g., Refs. [18,19]). Since the lowest-rank Lorentz tensor for such a field was shown to be 2, the field Gαβ (which replaces the usual Aμ gauge field) carries two Lorentz indices, transforms as a multiplicative Uð1Þ phase representation, and satisfies a nonlinear constraint equation. This constraint equation was solved in Ref. There, we point out a minor typo in Eq (36) of Ref. [20]
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