Related papers: On necessary and sufficient conditions of the BV q…
A generic degenerate Lagrangian system of even and odd fields is examined in algebraic terms of the Grassmann-graded variational bicomplex. Its Euler-Lagrange operator obeys Noether identities which need not be independent, but satisfy…
A generic degenerate Lagrangian system of even and odd variables on an arbitrary smooth manifold is examined in terms of the Grassmann-graded variational bicomplex. Its Euler-Lagrange operator obeys Noether identities which need not be…
Quantization of a Lagrangian field system essentially depends on its degeneracy and implies its BRST extension defined by sets of non-trivial Noether and higher-stage Noether identities. However, one meets a problem how to select trivial…
General Lagrangian theory of even and odd fields on an arbitrary smooth manifold is considered. Its non-trivial reducible gauge symmetries and their algebra are defined in this very general setting by means of the inverse second Noether…
Given a generic Lagrangian system, its Euler-Lagrange operator obeys Noether identities which need not be independent, but satisfy first-stage Noether identities, and so on. This construction is generalized to arbitrary differential…
The Ward identities are the relations which the complete Green functions of quantum fields satisfy if an original classical Lagrangian system is degenerate. A generic degenerate Lagrangian system of even and odd fields is considered. It is…
The first and second Noether theorems are formulated in a general case of reducible degenerate Grassmann-graded Lagrangian theory of even and odd variables on graded bundles. Such Lagrangian theory is characterized by a hierarchy of…
We review the basics of the Lagrangian approach to field theory and recast Noether's Second Theorem formulated in her language of dependencies using a slight modernization of terminology and notation. We then present the Cattaneo-Felder…
The most convenient tool to study the renormalization of a Lagrangian field theory invariant under non linear local or global symmetries is the proper solution to the master equation of the extended antifield formalism. It is shown that,…
We present Noether's second theorem for graded Lagrangian systems of even and odd variables on an arbitrary body manifold X in a general case of BRST symmetries depending on derivatives of dynamic variables and ghosts of any finite order.…
Graded Lagrangian formalism in terms of a Grassmann-graded variational bicomplex on graded manifolds is developed in a very general setting. This formalism provides the comprehensive description of reducible degenerate Lagrangian systems,…
The Lagrangian field-antifield formalism of Batalin and Vilkovisky (BV) is used to investigate the application of the collective coordinate method to soliton quantisation. It is shown how Noether identities and local symmetries of the…
A variant of the usual Lagrangian scheme is developed which describes both the equations of motion and the variational equations of a system. The required (prolonged) Lagrangian is defined in an extended configuration space comprising both…
We elaborate on a new representation of Lagrangians of 4D nonlinear electrodynamics including the Born-Infeld theory as a particular case. In this new formulation, in parallel with the standard Maxwell field strength $F_{\alpha\beta},…
We discuss the geometry of the Lagrangian quantization scheme based on (generalized) Schwinger-Dyson BRST symmetries. When a certain set of ghost fields are integrated out of the path integral, we recover the Batalin-Vilkovisky formalism,…
The quantization of the complex linear superfield requires an infinite tower of ghosts. Using the Batalin-Vilkovisky technique, Grisaru, Van Proeyen, and Zanon have been able to define a correct procedure to construct a gauge-fixed action.…
According to the nonuniqueness principle, the homogeneous scalar field Lagrangian can be expressed in various forms both standard and nonstandard ones. Therefore, the standard and all possible nonstandard Lagrangians can be linearly…
Starting from the requirement that a Lagrangian field theory be invariant under both Schwinger-Dyson BRST and Schwinger-Dyson anti-BRST symmetry, we derive the BRST--anti-BRST analogue of the Batalin-Vilkovisky formalism. This is done…
We illustrate the cosmological Friedmann-Robertson-Walker (FRW) models realized as gauge theory in the extended configuration space with its Becchi-Rouet-Stora-Tyutin (BRST) invariance upto total derivative. To investigate the model in…
Classical field theory is adequately formulated as Lagrangian theory on fibre bundles and graded manifolds. One however observes that non-trivial higher stage Noether identities and gauge symmetries of a generic reducible degenerate…