Related papers: Geometry of Batalin-Vilkovisky quantization
In this paper we investigate the possibility of constructing a complete quantization procedure consisting of geometric and deformation quantization. The latter assigns a noncommutative algebra to a symplectic manifold, by deforming the…
An extension of the notion of classical equivalence of equivalence in the Batalin--(Fradkin)--Vilkovisky (BV) and (BFV) framework for local Lagrangian field theory on manifolds possibly with boundary is discussed. Equivalence is phrased in…
Extended Schwinger's quantization procedure is used for constructing quantum mechanics on a manifold with a group structure. The considered manifold $M$ is a homogeneous Riemannian space with the given action of isometry transformation…
We consider Khudaverdian's geometric version of a Batalin-Vilkovisky (BV) operator \Delta_E in the case of a degenerate anti-Poisson manifold. The characteristic feature of such an operator (aside from being a Grassmann-odd, nilpotent,…
In this paper a comprehensive review is given on the current status of achievements in the geometric aspects of the Painlev\'e equations, with a particular emphasis on the discrete Painlev\'e equations. The theory is controlled by the…
We offer a new approach to large $N$ limits using the Batalin-Vilkovisky formalism, both commutative and noncommutative, and we exhibit how the Loday-Quillen-Tsygan Theorem admits BV quantizations in that setting. Matrix integrals offer a…
The aim of these notes is to introduce the quantum master equation $\{S,S\}-2i\hbar\Delta S=0$, and to show its relations to the theory of Lie algebras representations and to perturbative expansions of Gaussian integrals. The relations of…
In our previous works, we introduced, for each (super)manifold, a commutative algebra of densities. It is endowed with a natural invariant scalar product. In this paper, we study geometry of differential operators of second order on this…
A path-integral quantization method is proposed for dynamical systems whose classical equations of motion do \textit{not} necessarily follow from the action principle. The key new notion behind this quantization scheme is the Lagrange…
The physical meaning of the particularly simple non-degenerate supermetric, introduced in the previous part by the authors, is elucidated and the possible connection with processes of topological origin in high energy physics is analyzed…
We provide a new general scheme for the geometric quantisation of $\operatorname{Sp}(1)$-symmetric hyper-K\"ahler manifolds, considering Hilbert spaces of holomorphic sections with respect to the complex structures in the hyper-K\"ahler…
We provide a rigorous perturbative quantization of the B-twisted topological sigma model via a first order quantum field theory on derived mapping space in the formal neighborhood of constant maps. We prove that the first Chern class of the…
Superintegrable systems are classical and quantum Hamiltonian systems which enjoy much symmetry and structure that permit their solubility via analytic and even, algebraic means. They include such well-known and important models as the…
In the previous papers we present a construction of the set ${\cal U}_{SBS}$ in the direct product ${\cal B}_S \times \mathbb{P} \Gamma (M, L)$ of the moduli space of Bohr - Sommerfeld lagrangian submanifolds of fixed topological type and…
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…
On the basis of a thorough discussion of the Batalin-Vilkovisky formalism for classical field theory presented in our previous publication, we construct in this paper the Batalin-Vilkovisky complex in perturbatively renormalized quantum…
We analyze geometry of the second order differential operators, having in mind applications to Batalin--Vilkovisky formalism in quantum field theory. As we show, an exhaustive picture can be obtained by considering pencils of differential…
We quantize the chiral Schwinger Model by using the Batalin-Tyutin formalism. We show that one can systematically construct the first class constraints and the desired involutive Hamiltonian, which naturally generates all secondary…
When the gauge group of a theory has infinite volume, defining the inner product on physical states becomes subtle. This is the case for gravity, even in exactly solvable models such as minisuperspace or low-dimensional theories: the…
We revisit the Lagrange and Delaunay systems of equations for the orbital elements, and point out a previously neglected aspect of these equations: in both cases the orbit resides on a certain 9-dimensional submanifold of the 12-dimensional…