Related papers: Group quantization of parametrized systems II. Pas…
By decomposing the regular representation of a particular (Heisenberg-like) Lie supergroup into irreducible subspaces, we show that not all of them can be obtained by applying geometric quantization to coadjoint orbits with an even…
When the gauge group of a theory has infinite volume, defining the inner product on physical states becomes subtle. This is the case for gravity, even in exactly solvable models such as minisuperspace or low-dimensional theories: the…
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…
In this work, Schr\"odinger and Dirac equations will be examined in geometries that confine the particles to hypersurfaces. For this purpose, two methods will be considered. The first method is the thin layer method which relies on explicit…
Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space. This is well known and it usually proceeds by partitioning…
We propose in this paper an alternative method for the quantisation of systems with first-class constraints. This method is a combination of the coherent-state-path-integral quantisation developed by Klauder, with the ideas of reduced state…
It is shown that quantization of the dynamical systems with second class constraints actually can be reduced to quantization of the systems with first class constraints. The motion of the non-relativistic particle along the plane curve and…
The problem of quantizing a particle on a 2-sphere has been treated by numerous approaches, including Isham's global method based on unitary representations of a symplectic symmetry group that acts transitively on the phase space. Here we…
The paper is devoted to integral quantization, a procedure based on operator-valued measure and resolution of the identity. We insist on covariance properties in the important case where group representation theory is involved. We also…
Usually in quantum mechanics the Heisenberg algebra is generated by operators of position and momentum. The algebra is then represented on an Hilbert space of square integrable functions. Alternatively one generates the Heisenberg algebra…
We study the question of how to decompose Hilbert space into a preferred tensor-product factorization without any pre-existing structure other than a Hamiltonian operator, in particular the case of a bipartite decomposition into "system"…
The general boundary formulation of quantum field theory is applied to a massive scalar field in two dimensional Rindler space. The field is quantized according to both the Schr\"odinger-Feynman quantization prescription and the holomorphic…
I study the canonical formulation and quantization of some simple parametrized systems, including the non-relativistic parametrized particle and the relativistic parametrized particle. Using Dirac's formalism I construct for each case the…
The existing relation between the tomographic description of quantum states and the convolution algebra of certain discrete groupoids represented on Hilbert spaces will be discussed. The realizations of groupoid algebras based on qudit,…
An elementary introduction is provided to the phase space quantization method of Moyal and Wigner. We generalize the method so that it applies to 2-dimensional surfaces, where it has an interesting connection with quantum holography. In the…
Quantization with coherent states allows to " quantize " any space X of parameters. In the case where X is a phase space, this leads to the usual quantum mechanics. But the procedure is much more general, and does not require a symplectic,…
Symmetries of finite Heisenberg groups represent an important tool for the study of deeper structure of finite-dimensional quantum mechanics. This short contribution presents extension of previous investigations to composite quantum systems…
We discuss the dynamical quantum systems which turn out to be bi-unitary with respect to the same alternative Hermitian structures in a infinite-dimensional complex Hilbert space. We give a necessary and sufficient condition so that the…
The temporal evolution of a quantum system can be characterized by quantum process tomography, a complex task that consumes a number of physical resources scaling exponentially with the number of subsystems. An alternative approach to the…
In this paper we give examples of applications of general methods of quantization by symmetrization of classical integrable systems, which have been illustrated in two previous works by the same authors. We consider two classes of systems…