Related papers: Effective Batalin-Vilkovisky quantization and geom…
In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schr\"odinger framework from this perspective and provide a description of the Weyl-Wigner construction. Finally,…
This article reviews the program on connecting Batalin-Vilkovisky (BV) quantization with index theories of algebraic type. We explain how the classical algebraic index theorem can be proved in terms of BV quantization of topological quantum…
We adopt the Y-formalism to study beta-gamma systems on hypersurfaces. We compute the operator product expansions of gauge-invariant currents and we discuss some applications of the Y-formalism to model on Calabi-Yau spaces.
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…
Krasnov (arXiv: hep-th/0005106) identified the renormalized volume of a Schottky 3-manifold with the action of the Liouville theory on the conformal infiinity. We try to compute the renormalized volume in terms of more transparent geometric…
We consider the two-dimensional model of W3-gravity within Lagrangian quantization methods for general gauge theories. We use the Batalin-Vilkovisky formalism to study the arbitrariness in the realization of the gauge algebra. We obtain a…
Using an infinitesimal approach, this work addresses the renormalization problem to deal with the ultraviolet divergences arising in quantum field theory. Under the assumption that the action has already been renormalized to yield an…
We develop an algebraic quantisation approach, based on quantisation ideals, and apply it to integrable non-Abelian differential--difference equations. We show that the Toda hierarchy admits a bi-quantum structure whose classical…
We give a complete geometrical description of the effective Hamiltonians common in nuclear shell model calculations. By recasting the theory in a manifestly geometric form, we reinterpret and clarify several points. Some of these results…
In this paper we will present an ongoing project which aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We will argue that this approach provides a geometric semantics for such…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
We quantize the topological $\sigma$-model. The quantum master equation of the Batalin-Vilkovisky formalism $\Delta_\rho \Psi = 0$ appears as a condition which eliminates the exact states from the BRST invariant states $\Psi$ defined by $Q…
We present the basic ideas of geometric engineering of the supersymmetric quantum field theories viewed as a low energy limit of type II strings and F-theory on singular Calabi Yau manifolds. We first give the main lines of toric geometry…
This thesis studies matrix field theories, which are a special type of matrix models. First, the different types of applications are pointed out, from (noncommutative) quantum field theory over 2-dimensional quantum gravity up to algebraic…
Renormalization group equations play a central role in effective field theories, both maintaining perturbative control and allowing one to determine the correct low-energy phenomenology. In this work, we complete the one-loop…
Three dimensional topological field theories associated with the three dimensional version of Abelian and non-Abelian Seiberg-Witten monopoles are presented. These three dimensional monopole equations are obtained by a dimensional reduction…
Batalin-Vilkovisky algebras are a new type of algebraic structure on graded vector spaces, which first arose in the work of Batalin and Vilkovisky on gauge fixing in quantum field theory. In this article, we show that there is a natural…
It is a review of some results in Odd symplectic geometry related to the Batalin-Vilkovisky Formalism
Lobachewsky geometry simulates a medium with special constitutive relations. The situation is specified in quasi-cartesian coordinates (x,y,z). Exact solutions of the Maxwell equations in complex 3-vector form, extended to curved space…
We consider abstract operator equations $Fu=y$, where $F$ is a compact linear operator between Hilbert spaces $U$ and $V$, which are function spaces on \emph{closed, finite dimensional Riemannian manifolds}, respectively. This setting is of…