Related papers: Introduction to the BV-BFV formalism
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…
We consider the Batalin-Vilkovisky formulation of both 1-form and 2-form gauge theories, in the context of generalized BRST transformations with finite field dependent parameter. In the usual Faddeev-Popov formulation of gauge theories such…
These are expanded notes of author's talk at the ECM 2008 attempting to give an elementary introduction into the main ideas of the theory of wheeled props for beginners, and also a survey of its most recent major applications (ranging from…
The goal of this article is to develop BV (Batalin-Vilkovisky) formalism in the $p$-adic Dwork theory. Based on this formalism, we explicitly construct a $p$-adic dGBV algebra (differential Gerstenhaber-Batalin-Vilkovisky algebra) for a…
In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…
The Batalin-Vilkovisky master equations, both classical and quantum, are precisely the integrability equations for deformations of algebras and differential algebras respectively. This is not a coincidence; the Batalin-Vilkovisky approach…
The methods developed by authors are applied to some reductions of BBGKY hierarchy, namely, various examples of Vlasov-like systems which are important both for fusion modeling and for particular physical problems related to plasma/beam…
The present paper shows that general relativity in the Arnowitt-Deser-Misner formalism admits a BV-BFV formulation. More precisely, for any $d + 1 \not= 2$ (pseudo-) Riemannian manifold M with space-like or time-like boundary components,…
We introduce the concept of duality between quantum field theories in the Batalin-Vilkovisky formalism, which is interpreted either as a BV morphism, the result of dual BV pushforwards or a combination of both. When a BV morphism affects…
I present a selection of conceptual and mathematical problems in the foundations of modern physics as they derive from the title question. Contribution to a panel session, "Springer Forum: Quantum Structures -- Physical, Mathematical and…
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…
In Batalin-Vilkovisky formalism a classical mechanical system is specified by means of a solution to the {\sl classical master equation}. Geometrically such a solution can be considered as a $QP$-manifold, i.e. a super\m equipped with an…
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 purpose of this contribution is to give an introduction to quantum geometry and loop quantum gravity for a wide audience of both physicists and mathematicians. From a physical point of view the emphasis will be on conceptual issues…
A qualitative but formalized representation of microstates is first established quite independently of the quantum mechanical mathematical formalism, exclusively under epistemological-operational-methodological constraints. Then, using this…
Using the BV-formalism of mathematical physics an explicit construction for the minimal model of a quantum L-infinity-algebra is given as a formal super integral. The approach taken herein to these formal integrals is axiomatic; they can be…
We present the Batalin-Fradkin-Vilkovisky quantization of the quadratic gravity theory, which is the most general theory with terms up to quadratic order in curvature. This approach of quantization is based on the Hamiltonian formulation.…
This is an expanded version of the notes by the second author of the lectures on Hitchin systems and their quantization given by the first author at the Beijing Summer Workshop in Mathematics and Mathematical Physics ``Integrable Systems…
This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in…
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…