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The effective action and quantum gauge transformations
| Content Provider | Semantic Scholar |
|---|---|
| Author | Alexandrov, Sergei |
| Copyright Year | 1999 |
| Abstract | The concept of symmetry was and remains a very powerful tool for construction of the quantum field theory. One of its main virtues is that the symmetry restricts a form of the action, which lies in the ground of the theory. Consequences of the classical symmetry play a crucial role for renormalizability of the quantum theory. And in the investigation of this problem the effective action takes a very important place [1]. Besides it is the only quantum object in which the symmetry should be reflected by the same way as in the classical action also restricting the number of available structures. So it is natural to find this quantum realization of the symmetry, i.e. the symmetry transformations of the effective action, in an explicit form. One of first steps in this direction was done by DeWitt in his construction of the classically gauge invariant effective action for the Yang–Mills theory [2]. This work gave rise to the number of papers devoted to this problem [3]. But all of them do not go beyond linear gauge transformations and background gauges of the certain kind. This is a very strong limitation on the physical theory. As we know the Hamiltonian forms of gravity, supersymmetry theories and many others require nonlinear transformations. So an investigation of general gauge theories from the point of view of the quantum gauge symmetry is needed. The following break-through is connected with the concept of the effective average action or Vilkovisky–DeWitt’s action [4]– [6]. Its gauge invariance and gauge independence are very attractive properties. However its actual construction in arbitrary gauge and for arbitrary gauge theory is an enormously hard task because the connection on the frame bundle on the space–of–histories is needed. Besides the effective average action is connected to the ordinary generating functional for the one–particle–irreducible Green functions in a nontrivial way. So we simply bypass the subject and consider the effective action constructed in the usual way as Legendre transformation. The common approach to the symmetry properties of the effective action for general gauge theories is investigation of the Ward identities (see for example [7], [8]). They are the reflection of the global BRST symmetry which replaces the gauge symmetry in path integral quantization [9]. This symmetry plays a leading role in quantization of general gauge theories being the basis for Hamiltonian BFV [10] and Lagrangian BV [11] quantization schemes. Within these approaches global symmetry transformations of the effective action, which are called quantum BRST transformations, can easily be found [12–15]. Here we are interested in their local counterparts which are realized on the physical fields only. Explicit formulas for them, to our knowledge, are absent in the literature and our aim is to fill in this gap. Besides we discuss the symmetry transformations in presence of background fields and apply the obtained results to the rank one theory. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://cds.cern.ch/record/360483/files/9807159.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | BRST algorithm Byers-Yang theorem Fill Out Form Irreducibility Legendre transformation Newton–Cotes formulas Nonlinear system Paper Path integral formulation Quantization (signal processing) Quantum field theory Quantum mechanics Sense of identity (observable entity) T-symmetry Ward (environment) YANG biopsychosocial AOD use disorder theory bypass cell transformation |
| Content Type | Text |
| Resource Type | Article |
