Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userWard Identity and Basis Tensor Gauge Theory at One Loop
64
0
0.0
(
0
)
Authors
Daniel J. H. Chung
Ask ChatGPT about the research
No Arabic 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.
rate research
Read More
We reformulate gauge theories in analogy with the vierbein formalism of general relativity. More specifically, we reformulate gauge theories such that their gauge dynamical degrees of freedom are local fields that transform linearly under the dual representation of the charged matter field. These local fields, which naively have the interpretation of non-local operators similar to Wilson lines, satisfy constraint equations. A set of basis tensor fields are used to solve these constraint equations, and their field theory is constructed. A new local symmetry in terms of the basis tensor fields is used to make this field theory local and maintain a Hamiltonian that is bounded from below. The field theory of the basis tensor fields is what we call the basis tensor gauge theory.
Basis tensor gauge theory is a vierbein analog reformulation of ordinary gauge theories in which the difference of local field degrees of freedom has the interpretation of an object similar to a Wilson line. Here we present a non-Abelian basis tensor gauge theory formalism. Unlike in the Abelian case, the map between the ordinary gauge field and the basis tensor gauge field is nonlinear. To test the formalism, we compute the beta function and the two-point function at the one-loop level in non-Abelian basis tensor gauge theory and show that it reproduces the well-known results from the usual formulation of non-Abelian gauge theory.
Basis tensor gauge theory (BTGT) is a vierbein analog reformulation of ordinary gauge theories in which the vierbein field describes the Wilson line. After a brief review of the BTGT, we clarify the Lorentz group representation properties associated with the variables used for its quantization. In particular, we show that starting from an SO(1,3) representation satisfying the Lorentz-invariant U(1,3) matrix constraints, BTGT introduces a Lorentz frame choice to pick the Abelian group manifold generated by the Cartan subalgebra of u(1,3) for the convenience of quantization even though the theory is frame independent. This freedom to choose a frame can be viewed as an additional symmetry of BTGT that was not emphasized before. We then show how an $S_4$ permutation symmetry and a parity symmetry of frame fields natural in BTGT can be used to construct renormalizable gauge theories that introduce frame dependent fields but remain frame independent perturbatively without any explicit reference to the usual gauge field.
We verify Standard Model Effective Field Theory Ward identities to one loop order when background field gauge is used to quantize the theory. The results we present lay the foundation of next to leading order automatic generation of results in the SMEFT, in both the perturbative and non-perturbative expansion using the geoSMEFT formalism, and background field gauge.
Basic properties of gauge theories in the framework of Faddeev-Popov (FP) method, Batalin-Vilkovisky (BV) formalism, functional renormalization group approach are considered. The FP- and BV- quantizations are characterized by the BRST symmetry while the BRST symmetry is broken in the FRG approach. It is shown that the FP-method, the BV-formalism and the FRG approach can be provided with the Slavnov-Taylor identity, the Ward identity and the modified Slavnov-Taylor identity respectively. It is proved that using the background field method, the background gauge invariance of effective action within the FP and FRG quantization procedures can be achieved in non-linear gauges. The gauge dependence problem within the FP-, BV- and FRG quantizations is studied. Arguments allowing to state impossibility of gauge independence of physical results obtained within the FRG approach are given.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
