We subject the methodology used to derive the effective dynamics of topological defects to a critical reappraisal, using the two-dimensional kink as an illustrative example. Special care is taken on how the zero-modes should be handled in order to avoid overcounting of degrees of freedom. This is an issue that has been overlooked in many recent contributions on the derivation of domain wall effective actions. We show that, unless such redundancy is completely removed by means of a sort of gauge fixing, the expression obtained for the effective action will not be consistent. We readdress some earlier calculations over the existence of curvature corrections in the light of the previous discussion and briefly comment on the application of this method to higher dimensional topological defects.

An algebraic program of computation and characterization of higher-loop BRST anomalies is presented. We propose a procedure for disentangling a genuine local higher-loop anomaly from the quantum dressings of lower-loop anomalies. For such higher-loop anomalies we derive a local consistency condition, which is the generalisation of the Wess-Zumino condition for the one-loop anomaly, The development is presented in the framework of the field-antifield formalism, making use of a non-local regularization method. The theoretical construction is exemplified by explicitly computing the two-loop anomaly of chiral W-3 gravity. We also give, for the first time, an explicit check of the local two-loop consistency condition that is associated with this anomaly.

Anomalies and BRST invariance are governed, in the context of Lagrangian Batalin-Vilkovisky quantisation, by the master equation, whose classical limit is (S, S) = 0. Using Zimmerman's normal products and the BPHZ renormalisation method, we obtain a corresponding local quantum operator equation, which is valid to all orders in perturbation theory. The formulation implies a calculational method for anomalies that is useful also outside this context and that remains completely within regularised perturbation theory. It makes no difference in principle whether the anomaly appears at one loop or at higher loops. The method is illustrated by computing the one- and two-loop anomalies in chiral W3 gravity.

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The non-local regularization method, recently proposed by Evans et al., and Kleppe and Woodward, is extended to general gauge theories by reformulating it along the ideas of the antibracket-antifield formalism. From the interplay of both frameworks a fully regularized version of the field-antifield (FA) formalism arises, being able to deal with higher order loop corrections and to describe higher order loop contributions to the BRST anomaly. The quantum master equation, considered in the FA framework as the quantity parametrizing BRST anomalies, is argued to be incomplete at two and higher order loops and conjectured to reproduce only the one-loop corrections to the ($) over bar h(p) anomaly generated by the addition of O(($) over bar h(k)), k < p, counterterms.Chiral W-3 gravity is used to exemplify the non-locally regularized FA formalism. First, the regularized one-loop quantum master equation is used to compute the complete one-loop anomaly. Its two-loop order, however, is shown to reproduce only the modification to the two-loop anomaly produced by the addition of a suitable one-loop counterterm, thereby providing an explicit verification of the previous statement for p = 2. The well-known universal two-loop anomaly, instead, is alternatively obtained from the BRST variation of the non-locally regulated effective action. Incompleteness of the quantum master equation is thus concluded to be a consequence of a naive derivation of the FA BRST Ward identity.

The antibracket formalism for gauge theories, at both the classical and quantum level, is reviewed. Gauge transformations and the associated gauge structure are analyzed in detail. The basic concepts involved in the antibracket formalism are elucidated. Gauge-fixing, quantum effects, and anomalies within the field-antifield formalism are developed. The concepts, issues and constructions are illustrated using eight gauge-theory models.

Quantization of anomalous gauge theories with closed, irreducible gauge algebra within the extended Field-Antifield formalism is further pursued. Using a Pauli-Villars (PV) regularization of the generating functional at one loop level, an alternative form for the anomaly is found which involves only the regulator. The analysis of this expression allows to conclude that recently found ghost number one cocycles with nontrivial antifield dependence can not appear in PV regularization. Afterwards, the extended Field-Antifield formalism is further completed by incorporating quantum effects of the extra variables, i.e., by explicitly taking into account the regularization of the extra sector. In this context, invariant PV regulators are constructed from non-invariant ones, leading to an alternative interpretation of the Wess-Zumino action as the local counterterm relating invariant and non-invariant regularizations. Finally, application of the above ideas to the bosonic string reproduces the well-known Liouville action and the shift $(26-D)\rightarrow(25-D)$ at one loop.

An extension of the Field-Antifield formalism to treat anomalous gauge theories with a closed, irreducible classical gauge algebra is proposed. Introducing extra degrees of freedom, we construct the gauge transformations for these new fields, the Wess-Zumino term and the corresponding measure.

A generalization of the Faddeev-Popov procedure to deal with either anomalous and non-anomalous gauge theories with closed, irreducible gauge algebra is presented. An expression for the Wess-Zumino action is obtained.

The Batalin–Vilkovisky formalism is studied in the framework of perturbation theory by analyzing the antibracket Becchi–Rouet–Stora–Tyutin (BRST) cohomology of the proper solution S0. It is concluded that the recursive equations for the complete proper solution S can be solved at any order of perturbation theory. If certain conditions on the classical action and on the gauge generators are imposed the solution can be taken local.

We prove that the field-antifield formalism in the framework of perturbation theory gives an effective action which coincides with the one obtained by Frolov and Slavnov from unitarity requirements. The analysis of the free BRST charge in the particular case of first-stage reducible theories is worked out in detail. We conclude that in general the theory will not be unitary due to the possible presence of gauge invariant degrees of freedom with negative norm.

The quantization of a higher-order derivative Lagrangian for a relativistic spinning particle is performed. The Dirac equation is recovered.

We consider the open and closed gauge algebras for the spinning particle resulting from two different sets of gauge generators. Using the Batalin-Vilkovisky lagrangian formalism, the BRST and anti-BRST generators are constructed for both cases.

Using the field-antifield formalism and the Dirac constraint analysis we present, in a gauge independent way, the lagrangian and hamiltonian BRST structures of the spinning string.

Introducing the BRST symmetry in the space of fields and antifields a BRST charge at the lagrangian level is constructed in a gauge invariant way. For the case of irreducible first rank theories, we establish, at the classical level, the equivalence of the field-antifield formalism with the standard BRST formalism.

We establish, at the classical level, the equivalence between the standard BRST hamiltonian formalism and the lagranian BRST approach with fields and antifields for irreducible first rank theories.