BRST quantization of the chiral Schwinger model in the extended field-antifield space

Abstract

It is shown that the quantization of the chiral Schwinger model in the Batalin-Vilkovisky framework can be carried out in an extended space of fields and antifields, where the master equation has a local solution. The Wess-Zumino term is generated in this way, avoiding the use of nonlocal expressions. The nilpotency of the new BRST charge is proven explicitly.PACS number(s): 11.15.Bt, 1 l.lO.Ef, 11.30.RdThe Batalin-Vilkovisky (BV) Lagrangian BRST quantization [I] is a powerful method of quantization df field theories. It is very useful for the treatment of a wide range of theories, including those gauge theories whose constraints do not close an algebra. However, when anomalous gauge theories are concerned, the pathological problems of this kind of theories emerge troubling the construction of a gauge-independent generating functional. As was shown recently by Troost, van Nieuwenhuizen, and Van Proeyen, the presence of anomalies corresponds to the nonexistence of local solutions to the master equation [2]. This fact is the BRST reflection of those original perturbative calculations of Feynman diagrams that gave rise to the so-called anomalous Ward identities and that, from the current algebra point of view, appear as a failure of the chiral generators in closing an algebra in perturbation theory [3,4]. The chiral Schwinger model (CSM) is a twodimensional theory that is very useful for understanding several features of anomalous models. Jackiw and Rajaraman [ 5 ] showed that a unitary and consistent effective theory can be constructed for this model, in spite of losing the gauge invariance. On the other hand, following the idea of Faddeev and Shatashvili [6] of introducing additional degrees of freedom through the WessZumino term, in Ref.[7] the Faddeev-Popov procedure was applied to obtain a gauge-independent vacuum functional. In Ref.[8] we showed that a gauge-independent generating functional for the CSM can be built up using the BV procedure. In this case a nonlocal solution for the master equation was considered. Afterwards, the introduction of an auxiliary field (the so called WessZumino field) makes it possible to write out a local generating functional. The same procedure is worthless in the non-Abelian case, where one is not able to build a nonlocal solution for the master equation. The naive application of the BV procedure to this model would not work, in the sense that the eauation that defines the method, the so-called master equation, has no solution.In the same spirit of the Faddeev-Shatashvili works, recently we proposed in Ref.[9] the introduction of extra '~lectronic address (bitnet): IFT03001 B UFRJ degrees of freedom in the BV formalism. We showed that an enlargement of the field-antifield space of the chiral two-dimensional QCD (QCD,) model makes possible the construction of local solutions for the master equation. There, by the introduction of a field-antifield pair associated with the gauge symmetry group we got a gauge-independent generating functional for chiral QCD2, obtaining the Wess-Zum...

Antibracket, antifields and gauge-theory quantization

“…[61,63]. Methods of quantizing anomalous gauge theories using the antibracket formalism were developed in [61,62,131,133,134,77,63].…”

“…Although this model has not been discussed in previous sections, it is straightforward to apply the field-antifield formalism [61,63]. The proper solution for the gauge sector corresponds to the solution for the Yang-Mills example given in Sect.…”

“…A treatment of anomalous chiral QCD in two dimensions within the field-antifield formalism was obtained in refs. [61,63]. Methods of quantizing anomalous gauge theories using the antibracket formalism were developed in [61,62,131,133,134,77,63].…”