The s-matrix in background field quantization

McKeon, Gerry; Phillips, S.B.; Samant, S.S.; Sherry, T. N.

doi:10.1016/0550-3213(86)90132-x

Cited by 5 publications

(4 citation statements)

References 9 publications

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“…The DeWitt-Kallosh theorem asserts that the loop counterterms on the mass-shell calculated by means of the background field method are independent of the gaugefixing term. This statement has been verified in many papers [33] - [36]. It turns out that the proof of this theorem is valid only for renormalizable theories (such as Yang-Mills theory, QED, QCD).…”

Section: Introductionmentioning

confidence: 76%

Gauge and parametrization dependencies of the one-loop counterterms in Einstein gravity

Kalmykov

1995

Class. Quantum Grav.

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Section: Introductionmentioning

confidence: 76%

Gauge and parametrization dependencies of the one-loop counterterms in Einstein gravity

Kalmykov

1995

Class. Quantum Grav.

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“…In Refs [5,31,32] it is shown that the S-matrix is independent of the vertices generated by dependence of gauge fixing on the background field, both with covariant gauge fixing of Eq. (1.2) and with other non-covariant gauges [31,32].…”

Section: Discussionmentioning

confidence: 99%

First order formulation of the Yang–Mills theory in a background field

2019

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The background gauge renormalization of the first order formulation of the Yang-Mills theory is studied by using the BRST identities. Together with the background symmetry, these identities allow for an iterative proof of renormalizability to all orders in perturbation theory. However, due to the fact that certain improper diagrams which violate the BRST symmetry should be removed, the renormalizability must be deduced indirectly. The recursive method involves rescalings and mixings of the fields, which lead to a renormalized effective action for the background field theory.

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“…This shows that the background field B i is not just inserted by hand; it is the field associated with the current j i when making a Legendre transform of the generating functional for connected Green's functions W [j i ] [66,67].…”

Section: Appendix A: the Background Fieldmentioning

confidence: 99%

“…with non-covariant choices considered in Ref. [73]. For the EH action in both first and second order form, if the background metric is ḡµν and the quantum metric φ µν , then the gauge transformation of φ µν that follows from Eq.…”

Section: Appendix A: the Background Fieldmentioning

confidence: 99%

Use of Lagrange multiplier fields to eliminate multiloop corrections

et al. 2019

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The problem of eliminating divergences arising in quantum gravity is generally addressed by modifying the classical Einstein-Hilbert action. These modifications might involve the introduction of local supersymmetry, the addition of terms that are higher-order in the curvature to the action, or invoking compactification of superstring theory from ten to four dimensions. An alternative to these approaches is to introduce a Lagrange multiplier field that restricts the path integral to field configurations that satisfy the classical equations of motion; this has the effect of doubling the usual one-loop contributions and of eliminating all effects beyond one loop. We show how this reduction of loop contributions occurs and find the gauge invariances present when such a Lagrange multiplier is introduced into the Yang-Mills and Einstein-Hilbert actions. Moreover, we quantize using the path integral, discuss the renormalization, and then show how Becchi-Rouet-Stora-Tyutin (BRST) invariance can be used to both demonstrate that unitarity is retained and to find BRST relations between Greens functions. In the Appendices we show how background field quantization can be implemented, consider the use of a Lagrange multiplier field to restrict higher-order contributions in supersymmetric theories, and derive the BRST equations satisfied by the generating functional.

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The s-matrix in background field quantization

Cited by 5 publications

References 9 publications

Gauge and parametrization dependencies of the one-loop counterterms in Einstein gravity

Gauge and parametrization dependencies of the one-loop counterterms in Einstein gravity

First order formulation of the Yang–Mills theory in a background field

Use of Lagrange multiplier fields to eliminate multiloop corrections

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