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P. M. Lavrov

Publications and source records attributed to P. M. Lavrov.

At least 19 recordsLinked to original sources
arXiv2023

Generalized canonical approach to deformation problem in gauge theories

We develop a general approach to constructing a deformation that describes the mapping of any dynamical system with irreducible first-class constraints in the phase space into another dynamical system with first-class constraints. It is shown that such a deformation problem can be efficiently explored in the framework of the Batalin-Fradkin-Vilkovisky (BFV) formalism. The basic objects of this formalism are the BRST-BFV charge and a generalized Hamiltonian that satisfy the defining equations in the extended phase space in terms of (super)Poisson brackets. General solution to the deformation problem is found in terms of a (super)canonical transformation with a special generating function which is explicitly established. It is proved that this generating function is determined by a single arbitrary function which depends only on coordinates of initial dynamical system. In principle, such a function may be non-local, but the deformed theory may have a local sector. To illustrate the developed approach, we have constructed a non-local deformation of the Abelian gauge theory into a non-local non-Abelian gauge theory whose local sector coincides with the standard Yang-Mills theory.

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arXiv2023

On interactions of massless spin 3 and scalar fields

Using new approach for the deformation procedure in the case of reducible gauge theories (Lavrov in Eur. Phys. J. C 82:429, 2022), it is shown that in the model of massless spin 3 field and a real scalar field local cubic and quartic vertices invariant under original gauge transformations can be explicitly constructed.

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arXiv2023

On interactions of massless integer high spin and scalar fields

We apply an unconstrained formulation of bosonic higher spin fields to study interactions of these fields with a bosonic field using new method for the deformation procedure. It is proved that local vertices of any order containing one higher spin $s$ field and arbitrary number of scalar fields and being invariant under original gauge transformations are described with the help of one local totally symmetric $(s-2)$-rank tensor of scalar fields. This tensor is explicitly constructed for particular cases related to cubic vertices for spin $s$ and vertices of an arbitrary order for spin $s=4$.

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arXiv2023

Quintic vertices of spin 3, vector and scalar fields

As a result of special deformations of free gauge models of massless spin 3, massive vector and real scalar fields, quintic vertices within new approach (Buchbinder and Lavrov in JHEP 06: 097, 2021; Buchbinder and Lavrov in Eur. Phys. J. C 81:856, 2021; Lavrov in Eur. Phys. J. C 82:429, 2022) are constructed. They are described by local functionals which are invariant under original gauge transformations.

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arXiv2022

Cubic vertices of interacting massless spin 4 and real scalar fields in unconstrained formulation

New method (arXiv:2104.11930) is applied to construct cubic interactions of massless spin 4 and real scalar fields. In contrast with the case of massless spin 3 fields (arXiv:2208.05700, 2209.03678, 2210.02842) the procedure requires to use an unconstrained formulation (arXiv:0702.161) for the Fronsdal theory. It is shown that in the unconstrained formulation there exists a four-parameter family of cubic interactions between massless spin 4 and real scalar fields, which contains four derivatives in vertices and is invariant with respect to the original gauge transformation. These vertices contain cubic interactions between auxiliary and scalar fields too. Eliminating all auxiliary fields from the obtained result using the equations of motion for the initial action gives a one-parameter family of cubic vertices for constrained massless spin 4 and real scalar fields, Such cubic vertices are invariant with respect to constrained gauge transformations of the Fronsdal theory.

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arXiv2022

Gauge invariant renormalizability of quantum gravity

The current understanding of renormalization in quantum gravity (QG) is based on the fact that UV divergences of effective actions in the covariant QG models are covariant local expressions. This fundamental statement plays a central role in QG and, therefore, it is important to prove it for the widest possible range of the QG theories. Using the Batalin-Vilkovisky technique and the background field method, we elaborate the proof of gauge invariant renormalizability for a generic model of quantum gravity that is diffeomorphism invariant and does not have additional, potentially anomalous, symmetries.

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arXiv2022

Gauge-invariant models of interacting fields with spins 3,1 and 0

New local gauge-invariant models of interacting fields with spins 3, 1 and 0 are found. The construction of the models is completely based on the new approach to the deformation problem proposed in our papers (Buchbinder and Lavrov in JHEP 06: 097, 2021; Buchbinder and Lavrov in Eur. Phys. J. C 81:856, 2021; Lavrov in Eur. Phys. J. C 82:429, 2022). The approach allows to describe the deformation procedure for theories with gauge freedom in an explicit and closed form in terms of special anticanonical transformations of the Batalin-Vilkovisky formalism. The action of the models appears as a local part of the deformed action which is represented by a functional of the fourth order in fields. This functional is invariant under original gauge transformations.

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arXiv2022

On gauge-invariant deformation of reducible gauge theories

New method for construction of gauge-invariant deformed theory from an initial gauge theory proposed in our previous papers [1], [2] for closed/open gauge algebras is extended to the case of reducible gauge algebras. The deformation procedure is explicitly described with the help of generating functions of anticanonical transformations depending on fields of the initial gauge action only. The deformed gauge-invariant action and the deformed gauge generators are described with the help of the generating functions in a closed and simple form. As an example of reducible gauge systems we consider the free fermionic p-form fields or, in another words, the antisymmetric tensor-spinor fields. It is proved that gauge-invariant deformation of fermionic p-form fields leads always to non-local deformed theory which does not contain a closed local sector. In its turn the model based on two fermionic 2-form fields and a real massive scalar field admits local interactions between these fields in local sector of the deformed action.

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arXiv2021

On classical and quantum deformations of gauge theories

We elaborate the generalizations of the approach to gauge-invariant deformations of the gauge theories developed in our previous work [1]. In the given paper we construct the exact transformations defying the gauge-invariant deformed theory on the base of initial gauge theory with irreducible open gauge algebra. Like in [1], for the theories with open gauge algebras these transformations are the shifts of the initial gauge fields $A \rightarrow A+h(A)$, with the help of the arbitrary and in general non-local functions $h(A)$. The results are applied to study the quantum aspects of the deformed theories. We derive the exact relation between the quantum effective actions for the above classical theories, where one is obtained from another with the help of the deformation.

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arXiv2021

On a gauge-invariant deformation of a classical gauge-invariant theory

We consider a general gauge theory with independent generators and study the problem of gauge-invariant deformation of initial gauge-invariant classical action. The problem is formulated in terms of BV-formalism and is reduced to describing the general solution to the classical master equation. We show that such general solution is determined by two arbitrary generating functions of the initial fields. As a result, we construct in explicit form the deformed action and the deformed gauge generators in terms of above functions. We argue that the deformed theory must in general be non-local. The developed deformation procedure is applied to Abelian vector field theory and we show that it allows to derive non-Abelain Yang-Mills theory. This procedure is also applied to free massless integer higher spin field theory and leads to local cubic interaction vertex for such fields.

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arXiv2021

Covariant quantization of Yang-Mills theory in the first order formalism

In the present paper the Yang-Mills theory in the first order formalism is studied. On classical level the first order formulation is equivalent to the standard second order description of the Yang-Mills theory. It is proven that both formulations remain equivalent on quantum level as well.

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arXiv2018

BRST-BV quantization of gauge theories with global symmetries

We consider the general gauge theory with a closed irreducible gauge algebra possessing the non-anomalous global (super)symmetry in the case when the gauge fixing procedure violates the global invariance of classical action. The theory is quantized in the framework of BRST-BV approach in the form of functional integral over all fields of the configuration space. It is shown that the global symmetry transformations are deformed in the process of quantization and the full quantum action is invariant under such deformed global transformations in the configuration space. The deformed global transformations are calculated in an explicit form in the one-loop approximation.

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arXiv2017

Superfield generating equation of field-antifield formalism

A simple quantum superfield generating equation of the field-antifield formalism is proposed. The Schroedinger equation with the Hamiltonian having $Δ$-exact form is derived. An $Sp(2)$ symmetric extension to the main construction, with specific features caused by the principal fact that all basic equations become $Sp(2)$ vector-valued ones, is presented. A principal role of quantum antibrackets in formulation of the Heisenberg equations of motion is shown.

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arXiv2014

Jacobi - type identities in algebras and superalgebras

We introduce two remarkable identities written in terms of single commutators and anticommutators for any three elements of arbitrary associative algebra. One is a consequence of other (fundamental identity). From the fundamental identity, we derive a set of four identities (one of which is the Jacobi identity) represented in terms of double commutators and anticommutators. We establish that two of the four identities are independent and show that if the fundamental identity holds for an algebra, then the multiplication operation in that algebra is associative. We find a generalization of the obtained results to the super case and give a generalization of the fundamental identity in the case of arbitrary elements. For nondegenerate even symplectic (super)manifolds, we discuss analogues of the fundamental identity.

math-ph↗
arXiv2014

Supersymmetric invariant theories

We study field models for which a quantum action (i.e. the action appearing in the generating functional of Green functions) is invariant under supersymmetric transformations. We derive the Ward identity which is direct consequence of this invariance. We consider a change of variables in functional integral connected with supersymmetric transformations when its parameter is replaced by a nilpotent functional of fields. Exact form of the corresponding Jacobian is found. We find restrictions on generators of supersymmetric transformations when a consistent quantum description of given field theories exists.

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arXiv2012

Soft breaking of BRST symmetry and gauge dependence

We continue investigation of soft breaking of BRST symmetry in the Batalin-Vilkovisky (BV) formalism beyond regularizations like dimensional ones used in our previous paper [JHEP 1110 (2011) 043, arXiv:1108.4820 [hep-th]]. We generalize a definition of soft breaking of BRST symmetry valid for general gauge theories and arbitrary gauge fixing. The gauge dependence of generating functionals of Green's functions is investigated. It is proved that such introduction of a soft breaking of BRST symmetry into gauge theories leads to inconsistency of the conventional BV formalism.

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arXiv2011

On manifolds admitting the consistent Lagrangian formulation for higher spin fields

We study a possibility of Lagrangian formulation for free higher spin bosonic totally symmetric tensor field on the background manifold characterizing by the arbitrary metric, vector and third rank tensor fields in framework of BRST approach. Assuming existence of massless and flat limits in the Lagrangian and using the most general form of the operators of constraints we show that the algebra generated by these operators will be closed only for constant curvature space with no nontrivial coupling to the third rank tensor and the strength of the vector fields. This result finally proves that the consistent Lagrangian formulation at the conditions under consideration is possible only in constant curvature Riemann space.

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