相关论文: A matrix-valued Berezin-Toeplitz quantization
We show that a semibounded Toeplitz quadratic form is closable in the space $\ell^2({\Bbb Z}_{+})$ if and only if its matrix elemens are Fourier coefficients of an absolutely continuous measure. We also describe the domain of the…
Toeplitz quantization is defined in a general setting in which the symbols are the elements of a possibly non-commutative algebra with a conjugation and a possibly degenerate inner product. We show that the quantum group $SU_q(2)$ is such…
Recently, it has been observed that a certain class of classical theories with constraints can be quantized by a mathematical procedure known as Rieffel induction. After a short exposition of this idea, we apply the new quantization theory…
The prime number decomposition of a finite dimensional Hilbert space reflects itself in the representations that the space accommodates. The representations appear in conjugate pairs for factorization to two relative prime factors which can…
In this article we define Berezin-type and Odzijewicz-type quantizations on compact smooth manifolds. The method is we embed the smooth manifold of real dimension $n$ into ${\mathbb C}P^n$ and induce the quantizations from there. The…
We consider the eigenvalues of a fixed, non-normal matrix subject to a small additive perturbation. In particular, we consider the case when the fixed matrix is a banded Toeplitz matrix, where the bandwidth is allowed to grow slowly with…
In the framework of geometric quantization we extend the Bohr-Sommerfeld rules to a full quantization theory which resembles Heisenberg's matrix theory. This extension is possible because Bohr-Sommerfeld rules not only provide an orthogonal…
A finite-dimensional Hilbert space is usually described in terms of an orthonormal basis, but in certain approaches or applications a description in terms of a finite overcomplete system of vectors, called a finite tight frame, may offer…
We consider a new class of determinantal point processes in the complex plane coming from the ground state of free fermions associated with Berezin--Toeplitz operators. These processes generalize the Ginibre ensemble from random matrix…
An operator-valued quantum phase space formula is constructed. The phase space formula of Quantum Mechanics provides a natural link between first and second quantization, thus contributing to the understanding of quantization problem. By…
We prove sharp remainder bounds for the Berezin-Toeplitz quantization and present applications to semiclassical quantum measurements.
Lorentz violation frequently induces modified dispersion relations that can yield space-like states that impede the standard quantization procedures. In certain cases, an extended hamiltonian formalism can be used to define…
We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between…
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.…
In this article we show that a Berezin-type quantization can be achieved on a compact even dimensional manifold $M^{2d}$ by removing a skeleton $M_0$ of lower dimension such that what remains is diffeomorphic to $R^{2d}$ (cell…
We explore the quantization of classical models with position-dependent mass (PDM) terms constrained to a bounded interval in the canonical position. This is achieved through the Weyl-Heisenberg covariant integral quantization by properly…
The large N limit of a one-dimensional infinite chain of random matrices is investigated. It is found that in addition to the expected Kosterlitz--Thouless phase transition this model exhibits an infinite series of phase transitions at…
In this paper, we study Toeplitz operators on generalized flag manifolds of compact Lie groups using a representation-theoretic point of view. We prove several basic properties of these Toeplitz operators, including an abstract formula for…
In this paper, we construct a family of Berezin-Toeplitz type quantizations of a compact symplectic manifold. For this, we choose a Riemannian metric on the manifold such that the associated Bochner Laplacian has the same local model at…
Phase Space is the framework best suited for quantizing superintegrable systems--systems with more conserved quantities than degrees of freedom. In this quantization method, the symmetry algebras of the hamiltonian invariants are preserved…