相关论文: The classical master equation

In this article, we extend our preceding studies on higher algebraic structures of (co)homology theories defined by a left bialgebroid (U,A). For a braided commutative Yetter-Drinfel'd algebra N, explicit expressions for the canonical…

The so-called covariant Poincare lemma on the induced cohomology of the spacetime exterior derivative in the cohomology of the gauge part of the BRST differential is extended to cover the case of arbitrary, non reductive Lie algebras. As a…

We show that the Quantum Master Equation and the Wilsonian renormalization group (RG) flow equation can be combined such that for the continuum effective action, quantum BRST invariance is not broken by the presence of an effective…

I point out an unexpected relation between the BV (Batalin-Vilkovisky) and the BFV (Batalin-Fradkin-Vilkovisky) formulations of the same pure gauge (topological) theory. The nonminimal sector in the BV formulation of the topological theory…

This paper is a review of the works devoted to understanding and reinterpretation of the theory of quantum integrable models solvable by Bethe ansatz in terms of the theory of purely classical soliton equations. Remarkably, studying…

We prove that extension groups in strict polynomial functor categories compute the rational cohomology of classical algebraic groups. This result was previously known only for general linear groups. We give several applications to the study…

In this article, we use the language of $\mathbb{P}_0$-factorization algebras to articulate a classical bulk-boundary correspondence between 1) the observables of a Poisson Batalin-Vilkovisky (BV) theory on a manifold $N$ and 2) the…

We introduce affine Stanley symmetric functions for the special orthogonal groups, a class of symmetric functions that model the cohomology of the affine Grassmannian, continuing the work of Lam and Lam, Schilling, and Shimozono on the…

Let G be a Lie group with Lie algebra $ \Cal G: = T_\epsilon G$ and $T^*G = \Cal G^* \rtimes G$ its cotangent bundle considered as a Lie group, where G acts on $\Cal G^*$ via the coadjoint action. We show that there is a 1-1 correspondance…

We construct and study some vertex theoretic invariants associated to Poisson varieties, specialising in the conformal weight $0$ case to the familiar package of Poisson homology and cohomology. In order to do this conceptually we sketch a…

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…

The basic cohomology of a Riemannian foliation on a complete manifold with all leaves closed is the cohomology of the leaf space. In this paper we introduce various methods to compute the basic cohomology in the presence of both closed and…

We construct a two-dimensional topological sigma model whose target space is endowed with a Poisson algebra for differential forms. The model consists of an equal number of bosonic and fermionic fields of worldsheet form degrees zero and…

An equivariant stable birational invariant of an action of a finite group on a smooth projective variety is the first cohomology group of the Picard module. Bogomolov-Prokhorov and Shinder computed this for actions of cyclic groups on…

We investigate the tension between symplecticity and gauge covariance in classical Hamiltonian mechanics. The pursuit of manifest covariance over manifest symplecticity results in a unique geometric formulation. Firstly, covariant yet…

Poisson algebra is usually defined to be a commutative algebra together with a Lie bracket, and these operations are required to satisfy the Leibniz rule. We describe Poisson structures in terms of a single bilinear operation. This enables…

We give a simple geometrical picture of the basic structures of the covariant $Sp(2)$ symmetric quantization formalism -- triplectic quantization -- recently suggested by Batalin, Marnelius and Semikhatov. In particular, we show that the…

This submission is a PhD dissertation. It constitutes the summary of the author's work concerning the relations between cohomology rings of algebraic varieties and rings of functions on zero schemes and fixed point schemes. It includes the…

These notes present an introduction to an analytic version of deformation quantization. The central point is to study algebras of physical observables and their irreducible representations. In classical mechanics one deals with real Poisson…

One may introduce at least three different Lie algebras in any Lagrangian field theory : (i) the Lie algebra of local BRST cohomology classes equipped with the odd Batalin-Vilkovisky antibracket, which has attracted considerable interest…