arXiv subjects
Publications and source records attributed to Peter M. Lavrov.
We propose an action for the extended sigma - models in the most general setting of the kinetic term allowed in the nontrivially deformed field - antifield formalism. We show that the classical motion equations do naturally take their desired canonical form.
We develop a new version of the superfield Hamiltonian quantization. The main new feature is that the BRST-BFV charge and the gauge fixing Fermion are introduced on equal footing within the sigma model approach, which provides for the actual use of the quantum/derived antibrackets. We study in detail the generating equations for the quantum antibrackets and their primed counterparts. We discuss the finite quantum anticanonical transformations generated by the quantum antibracket.
By proceeding with the idea that the presence of physical (BRST invariant) extra factors in the path integral is equivalent to taking into account explicitly the arbitrariness in resolving the quantum master equation, we consider the field-antifield quantization procedure both with the Abelian and the non-Abelian gauge fixing.
Within a superfield approach, we formulate a simple quantum generating equation of the field - antifield formalism. Then, we derive the Schroedinger equation with the Hamiltonian whose $Δ$ - exact part serves as a generator to the quantum master-transformations. We show that these generators do satisfy a nice composition law in terms of the quantum antibrackets. We also present an $Sp(2)$ symmetric extension as to the main construction, with specific features caused with the principal fact that all basic equations become $Sp(2)$ vector valued ones.
For topological sigma models, we propose that their local Lagragian density is allowed to depend non-linearly on the de Rham's "velocities" $D Z^{A}$. Then, by differentiating the Lagrangian density with respect to the latter de Rham's "velocities", we define a "dynamical" anti-symplectic potential, in terms of which a "dynamical" anti-symplectic metric is defined, as well. We define the local and the functional antibracket via the dynamical anti-symplectic metric. Finally, we show that the generalized action of the sigma model satisfies the functional master equation, as required.
A general quantum-mechanical setting is proposed for the field-antifield formalism as a unique hyper-gauge theory in the field-antifield space. We formulate a Schrödinger-type equation to describe the quantum evolution in a "current time" purely formal in its nature. The corresponding Hamiltonian is defined in the form of a supercommutator of the delta-operator with a hyper-gauge Fermion. The initial wave function is restricted to be annihilated with the delta-operator. The Schrödinger's equation is resolved in a closed form of the path integral, whose action contains the symmetric Weyl's symbol of the Hamiltonian. We take the path integral explicitly in the case of being a hyper-gauge Fermion an arbitrary function rather than an operator.
We show that there exists a representation of a matrix valued gauge field via intrinsic "BRST" operator assigned to matrix valued generators of a gauge algebra. In this way, we reproduce the standard formulation of the ordinary Yang - Mills theory. In the case of a generating quasigroup/groupoid, we give a natural counterpart to the Yang - Mills action. The latter counterpart does also apply as to the most general case of an involution for matrix-valued gauge generators.
Quantum localization of classical mechanics within the BRST-BFV and BV (or field-antifield) quantization methods are studied. It is shown that a special choice of gauge fixing functions (or BRST-BFV charge) together with the unitary limit leads to Hamiltonian localization in the path integral of the BRST-BFV formalism. In turn, we find that a special choice of gauge fixing functions being proportional to extremals of an initial non-degenerate classical action together with a very special solution of the classical master equation result in Lagrangian localization in the partition function of the BV formalism.
In the approach to the geometric quantization, based on the conversion of second-class constraints, we resolve the respective non-linear zero curvature conditions for the extended symplectic potential. From the zero curvature conditions, we deduce new, linear, equations for the extended symplectic potential. Then we show that being the linear equations satisfied, their solution does certainly satisfy the non-linear zero curvature condition, as well. Finally, we give the functional resolution to the new linear equations, and then deduce the respective path integral representation. We do our consideration as to the general case of a phase superspace where both Boson and Fermion coordinates are present on equal footing.
In the most general case of the Delta exact operator valued generators constructed of an arbitrary Fermion operator, we present a closed solution for the transformed master action in terms of the original master action in the closed form of the corresponding path integral. We show in detail how that path integral reduces to the known result in the case of being the Delta exact generators constructed of an arbitrary Fermion function.
We study systematically finite BRST-BFV transformations in the generalized Hamiltonian formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate arbitrary finite change of gauge-fixing functions in the path integral.
Finite BRST-BV transformations are studied systematically within the W-X formulation of the standard and the Sp(2)-extended field-antifield formalism. The finite BRST-BV transformations are introduced by formulating a new version of the Lie equations. The corresponding finite change of the gauge-fixing master action X and the corresponding Ward identity are derived.
It is noted that the Legendre transformations in the standard formulation of quantum field theory have the form of functional Clairaut-type equations. It is shown that in presence of composite fields the Clairaut-type form holds after loop corrections are taken into account. A new solution to the functional Clairaut-type equation appearing in field theories with composite fields is found.
We formulate a perturbation expansion for the effective action in a new approach to the functional renormalization group method based on the concept of composite fields for regulator functions being their most essential ingredients. We demonstrate explicitly the principal difference between the properties of effective actions in these two approaches existing already on the one-loop level in a simple gauge model.
The gauge dependence problem existing in the original Gribov-Zwanziger theory is discussed.
We study finite field dependent BRST-BFV transformations for dynamical systems with first- and second-class constraints within the generalized Hamiltonian formalism. We find explicitly their Jacobians and the form of a solution to the compensation equation necessary for generating an arbitrary finite change of gauge-fixing functionals in the path integral.
We study the role of arbitrary (finite) anticanonical transformations in the field-antifield formalism, and the gauge-fixing procedure based on the use of these transformations. The properties of the generating functionals of the Green functions subjected to finite anticanonical transformations are considered.
We review the study of influence of the so-called soft BRST symmetry breaking within the Batalin-Vilkovisky (BV) formalism introduced in our papers [JHEP 1110 (2011) 043, arXiv:1108.4820 [hep-th], MPLA 27 (2012) 1250067, arXiv:1201.4720 [hep-th]] on gauge dependence of the effective action and vacuum expectation values of gauge invariant operators. We derive the Ward identities for generating functionals of Green's functions for a given theory with soft BRST symmetry breaking term being added to the quantum action and investigate theirs gauge dependence. It is strongly argued that gauge theories with a soft breaking of BRST symmetry are inconsistent within the BV formalism because of the gauge-dependence of $S$-matrix. The application to the Gribov-Zwanziger action (enlarging SU(N) Yang-Mills gauge theory by means of not gauge-invariant horizon function) for the one-parameter family of $R_ξ$ gauges with use of the new form of the Hermitian augmented Faddeev-Popov operator (being by Faddeev-Popov operator for transverse components of Yang--Mills fields) is considered.