Related papers: Coherent States for the Manin Plane via Toeplitz Q…
In this paper, we construct nonlinear coherent states for the generalized isotonic oscillator and study their non-classical properties in-detail. By transforming the deformed ladder operators suitably, which generate the quadratic algebra,…
The convenience of coherent state representation is discussed from the viewpoint of what is in a broad sense called the measurement problem in quantum mechanics. Standard quantum theory in coherent state representation is intrinsically…
Coherent states are usually defined as eigenstates of an unbounded operator, the so-called annihilation operator. We propose here possible constructions of {\em quasi-coherent states}, which turn out to be {\em quasi} eigenstate of a…
The thesis is devoted to the phase space representation of relativistic quantum mechanics. For a class of observables with matrix-valued Weyl symbols proportional to the identity matrix, the Weyl-Wigner-Moyal formalism is proposed. The…
The multiphoton coherent states, a generalization to coherent sates, are derived for electrons in bilayer graphene placed in a constant homogeneous magnetic field which is orthogonal to the bilayer surface. For that purpose a generalized…
We review some aspects of the relation between ordinary coherent states and q-deformed generalized coherent states with some of the simplest cases of quantum Lie algebras. In particular, new properties of (q-)coherent states are utilized to…
Quantum dynamics of coherent states is studied within quantum field theory using two complementary methods: by organizing the evolution as a Taylor series in elapsed time and by perturbative expansion in coupling within the…
State representations summarize our knowledge about a system. When unobservable quantities are introduced the state representation is typically no longer unique. However, this non-uniqueness does not affect subsequent inferences based on…
The definition of Toeplitz operators in the Bergman space $A^2(D)$ of square integrable analytic functions in the unit disk in the complex plane is extended in such way that it covers many cases where the traditional definition does not…
The main characteristics of the quantum oscillator coherent states including the two-particle Calogero interaction are investigated. We show that these Calogero coherent states are the eigenstates of the second-order differential…
A generalization of the canonical coherent states of a quantum harmonic oscillator has been performed by requiring the conditions of normalizability, continuity in the label and resolution of the identity operator with a positive weight…
We describe the eigenvalues and eigenvectors of real-analytic, non-self-adjoint Berezin--Toeplitz operators, up to exponentially small error, on complex one-dimensional compact manifolds, under the hypothesis of regularity of the energy…
A careful reexamination of the quantization of systems with first- and second-class constraints from the point of view of coherent-state phase-space path integration reveals several significant distinctions from more conventional…
Within the generalized definition of coherent states as group orbits we study the orbit spaces and the orbit manifolds in the projective spaces constructed from linear representations. Invariant functions are suggested for arbitrary groups.…
The Heisenberg algebra is first deformed with the set of parameters ${q, l, \lambda}$ to generate a new family of generalized coherent states. In this framework, the matrix elements of relevant operators are exactly computed. A proof on…
A geometric characterization of transition amplitudes between coherent states, or equivalently, of the hermitian scalar product of holomorphic cross sections in the associated D - M tilda - module, in terms of the embedding of the cohe-…
We construct the coherent states and Schr\"odinger cat states associated with new types of ladder operators for a particular case of a rationally extended harmonic oscillator involving type III Hermite exceptional orthogonal polynomials. In…
The domain of application of quantization methods is traditionally restricted to smooth classical observables. We show that the coherent states or "anti-Wick" quantization enables us to construct fairly reasonable quantum versions of…
We characterize operator-theoretic properties (boundedness, compactness, and Schatten class membership) of Toeplitz operators with positive measure symbols on Bergman spaces of holomorphic hermitian line bundles over K\"ahler…
We present a rigorous and functorial quantization scheme for affine field theories, i.e., field theories where local spaces of solutions are affine spaces. The target framework for the quantization is the general boundary formulation,…