Related papers: Prequantization, geometric quantization, corrected…
Circuit quantization is an extraordinarily successful theory that describes the behavior of quantum circuits with high precision. The most widely used approach of circuit quantization relies on introducing a classical Lagrangian whose…
The methods of Information geometry have been glowing up to develop various subjects of theoretical physics, including quantum information systems. The present article has two purposes. The first one is to develop general theory of…
The algebraic method of singular reduction is applied for non regular group action on manifolds which provides singular symplectic spaces. The problem of deformation quantization of the singular surfaces is the focus. For some examples of…
In this article we discuss the geometric quantization on a certain type of infinite dimensional super-disc. Such systems are quite natural when we analyze coupled bosons and fermions. The large-N limit of a system like that corresponds to a…
Invited contribution to the Encyclopedia of Mathematical Physics (2nd edition), providing an overview over some main ideas and results in quantum cosmology. Key points: Canonical quantisation of homogeneous, isotropic cosmology; discussion…
Counterfactuals in quantum theory are briefly reviewed and it is argued that they are very different from counterfactuals considered in the general philosophical literature. The issue of time symmetry of quantum counterfactuals is…
We gather material from many sources about the quantum potential and its geometric nature. The presentation is primarily expository but some new observations relating Q, V, and psi are indicated.
This is a very biased and incomplete survey of some basic notions, old and new results, as well as open problems concerning Weinstein symplectic manifolds.
In this paper we study overcomplete systems of coherent states associated to compact integral symplectic manifolds by geometric quantization. Our main goals are to give a systematic treatment of the construction of such systems and to…
I present a method of performing geometric quantization using cohomology groups extended via coefficient groups of different types. This is possible according to the Universal Coefficient Theorem (UTC). I also show that by using this method…
Connecting ideas of geometric formulation of quantum mechanics with new results in symplectic geometry a new approach to geometrical quantization procedure is proposed. As a first result we verify that the correspondence between "classical"…
Study of symmetry, topology and geometric phase can reveal many new and interesting results on the topological states of matter. Here we present a completely new and interesting result of symmetry, topology and quantization of geometric…
``Pseudo-cohomology'', as a refinement of Lie group cohomology, is soundly studied aiming at classifying of the symplectic manifolds associated with Lie groups. In this study, the framework of symplectic cohomology provides fundamental new…
Gromov-Witten invariants of a symplectic manifold are a count of holomorphic curves. We describe a formula expressing the GW invariants of a symplectic sum $X# Y$ in terms of the relative GW invariants of $X$ and $Y$. This formula has…
Kostant gave a model for the real geometric quantization associated to polarizations via the cohomology associated to the sheaf of flat sections of a pre-quantum line bundle. This model is well-adapted for real polarizations given by…
This brief set of notes presents a modest introduction to the basic features entering the construction of supersymmetric quantum field theories in four-dimensional Minkowski spacetime, building a bridge from similar lectures presented at a…
In this note we briefly review some recent results of the authors on the topological and geometrical properties of 3-cosymplectic manifolds.
We consider a geometrization, i.e., we identify geometrical structures, for the space of density states of a quantum system. We also provide few comments on a possible application of this geometrization for composite systems.
We study the problem of deformation quantization for (algebraic) symplectic manifolds over a base field of positive characteristic. We prove a reasonably complete classification theorem for one class of such quantizations; in the course of…
We use the method of homological quantum reduction to construct a deformation quantization on singular symplectic quotients in the situation, where the coefficients of the moment map define a complete intersection. Several examples are…