The s-matrix in background field quantization

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

Nuclear Physics B

Volume 267, Issues 3–4, 21 April 1986, Pages 566-574

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Abstract

An argument showing that the S-matrix obtained in the background field approach to gauge theories is identical to the S-matrix obtained in the conventional approach is presented for an arbitrary gauge. This considerably extends the work of Abbott, Grisaru and Schaefer. In particular, non-covariant gauges that involve Nielsen-Kallosh ghost fields are shown to be suitable for computing the S-matrix.

References (11)

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(1986)

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Cited by (7)

First order formulation of the Yang–Mills theory in a background field
2019, Annals of Physics
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.
Operator regularization and quantum gravity
1989, Nuclear Physics, Section B
Operator regularization has been shown to be a symmetry preserving means of computing Green functions in gauge symmetric and supersymmetric theories which avoids the explicit occurrence of divergences. In this paper we examine how this technique can be applied to computing quantities in non-renormalizable theories in general and quantum gravity in particular. Specifically, we consider various processes to one- and two-loop order in φ₄^N theory for N > 4 for which the theory is non-renormalizable. We then apply operator regularization to determine the one-loop graviton correction to the spinor propagator. The effective action for quantum scalars in a background gravitational field is evaluated in operator regularization using both the weak-field method and the normal coordinate expansion. This latter case yields a new derivation of the Schwinger-de Witt expansion which avoids the use of recursion relations. Finally we consider quantum gravity coupled to scalar fields in n dimensions, evaluating those parts of the effective action that (in other methods) diverge as n → 4. We recover the same divergence structure as is found using dimensional regularization if n ≠ 4, but if n = 4 at the outset no divergence arises at any stage of the calculation. The non-renormalizability of such theories manifests itself in the scale-dependence at one-loop order of terms that do not appear in the original lagrangian. In all cases our regularization procedure does not break any invariances present in the theory and avoids the occurence of explicit divergences.
Background field quantization in non-covariant gauges: renormalization and WTST identities
1986, Nuclear Physics, Section B
Background field quantization of pure YM theories in non-covariant gauges is treated with particular emphasis on renormalization. Gauge fixing terms of the form $(1 2α)n · Q^{a} ƒ^{ab} n · Q^{b}$ are considered where $ƒ^{ab}$ can assume the forms $ƒ_{(i)}^{ab} = −δ^{ab}$ (the axial gauge), $ƒ_{(ii)}^{ab} = (n · D(A))^{2ab} /n^{4}$ and $ƒ_{(iii)}^{ab} = D^{2} (A)^{ab} /n^{2}$ (the planar gauge). For the cases where $ƒ^{ab}$ depends explicitly on the background field A_μ^a the ghost sector is enlarged by the addition of appropriate Nielsen-Kallosh ghost fields. The BRS identities for these gauge choices are derived and solved. The quantum-corrected versions of both the bare background field gauge transformations and the bare quantum field gauge transformations are obtained from the BRS analysis. It is also shown that, to one loop, all the counter terms are determined by the background field independent part of the theory and this result is used, in cases (ii) and (iii), to derive all the counter terms and to show that Kallosh's theorem is verified. The result is also used to demonstrate the pathological nature of case (i) for α ≠ 0, in particular the result that Kallosh's theorem is not applicable. The result that the generating functional of Green functions is independent of the background field A_μ^a in the absence of all external sources is generalized to the case of non-covariant gauges. The equality established by Abbott between the 1PI generating functionals $Γ [A, 0] and Γ_{c} [Q; A]_{Q= A}, where Γ_{c}$ is a conventional generating functional in an A-dependent gauge, is analysed. We show that the WTST identities satisfied by Γ_c reduce, when $Q$ is set equal to A, to the naive Ward-identity satisfied by $Γ [A, 0]$ .
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2019, Physical Review D
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¹: Permanent address: Department of Mathematical Physics, National University of Ireland, University College, Galway, Ireland.

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Nuclear Physics B

The s-matrix in background field quantization

Abstract

Nucl. Phys.

Nucl. Phys.

Nucl. Phys.

Nucl. Phys.

Nucl. Phys.

Nucl. Phys.

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

Operator regularization and quantum gravity

Background field quantization in non-covariant gauges: renormalization and WTST identities

Use of Lagrange multiplier fields to eliminate multiloop corrections

Use of Lagrange multiplier fields to eliminate multiloop corrections

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