Related papers: Berezin quantization and representation theory
We obtain a criterion on the commutativity of polynomials in the enveloping algebra of a Lie algebra in terms of an involution condition with respect to the Berezin bracket. As an application, it is shown that the commutativity requirement…
The approach of Berezin to the quantization of so(n,2) via generalized coherent states is considered in detail. A family of n commuting observables is found in which the basis for an associated Fock-type representation space is expressed.…
By parametrizing the action integral for the standard Schrodinger equation we present a derivation of the recently proposed method for quantizing a parametrized theory. The reformulation suggests a natural extension from conventional to…
We introduce a variant of the birational symbols group of Kontsevich, Pestun, and the second author, and use this to define birational invariants of algebraic orbifolds.
We explain the powerful role that operator-valued measures can play in quantizing any set equipped with a measure, for instance a group (resp. group coset) with its invariant (resp. quasi-invariant) measure. Coherent state quantization is a…
We give a quantum field theory interpretation of Kontsevich's deformation quantization formula for Poisson manifolds. We show that it is given by the perturbative expansion of the path integral of a simple topological bosonic open string…
We apply the algebraic quantization programme proposed by Ashtekar to the analysis of the Belinski\v{\i}-Zakharov classical spacetimes, obtained from the Kasner metrics by means of a generalized soliton transformation. When the solitonic…
Supersymmetry between bosons and fermions is modeled within PT- symmetric quantum mechanics. A non-Hermitian alternative to the Witten's supersymmetric quantum mechanics is obtained.
The BRST quantization of particle motion on the hypersurface $V_{(N-1)}$ embedded in Euclidean space $R_N$ is carried out both in Hamiltonian and Lagrangian formalism. Using Batalin-Fradkin-Fradkina-Tyutin (BFFT) formalism, the second class…
For~weights $\rho$ which are either radial on the unit ball or depend only on the vertical coordinate on the upper half-space, we describe the asymptotic behaviour of the corresponding weighted harmonic Bergman kernels with respect to…
Equivariant quantization is a new theory that highlights the role of symmetries in the relationship between classical and quantum dynamical systems. These symmetries are also one of the reasons for the recent interest in quantization of…
In quantum computation and information science, the geometrical representations based on the Bloch sphere representation for transformations of two state systems have been traditionally used. While this representation is very useful for the…
The transparent way for the invariant (Hamiltonian) description of equivariant localization of the integrals over phase space is proposed. It uses the odd symplectic structure, constructed over tangent bundle of the phase space and permits…
We propose a superfield formalism of Lagrangian BRST-antiBRST quantization of arbitrary gauge theories in general coordinates with the base manifold of fields and antifields desribed in terms of both bosonic and fermionic variables.
We discuss a link between "hard" symplectic topology and an unsharpness principle for generalized quantum observables (positive operator valued measures). The link is provided by the Berezin-Toeplitz quantization.
We construct an equivariant microlocal lift for locally symmetric spaces. In other words, we demonstrate how to lift, in a ``semi-canonical'' fashion, limits of eigenfunction measures on locally symmetric spaces to Cartan-invariant measures…
We propose a new star pruduct which interpolates the Berezin and Moyal quantization. A multiple of this product is shown to reduce to a path-integral quantization in the continuous time limit. In flat space the action becomes the one of…
A class of pseudo-hermitian quantum system with an explicit form of the positive-definite metric in the Hilbert space is presented. The general method involves a realization of the basic canonical commutation relations defining the quantum…
Extended quantum mechanics using non-Hermitian, pseudo-Hermitian Hamiltonians is briefly reviewed. Supersymmetric regularizations, solvable simulations and large-N expansion techniques are recollected as suitable means for the study of…
After sketching recent advances and subtleties in classical relativistically covariant field theories, we give in this short Note some indications as to how the deformation quantization approach can be used to solve or at least give a…