相关论文: Quantization via Star Products
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,…
The global symmetry data of a $D$-dimensional absolute quantum field theory can sometimes be packaged in terms of a $(D+1)$-dimensional bulk system obtained by extending along an interval, with a relative QFT$_D$ at one end and suitable…
Tomograms introduced for the description of quantum states in terms of probability distributions are shown to be related to a standard star-product quantization with appropriate kernels. Examples of symplectic tomograms and spin tomograms…
A review of the symplectic tomographic approaches within the framework of star-product quantization is presented. The classical statistical mechanics within the framework of the tomographic representation is considered. The kernels of…
In a system of coupled harmonic oscillators, the interaction can be represented by a real, symmetric and positive definite interaction matrix. The quantization of a Hamiltonian describing such a system has been done in the canonical case.…
The Hilbert space of a free massless particle moving on a group manifold is studied in details using canonical quantisation. While the simplest model is invariant under a global symmetry, $G \times G$, there is a very natural way to…
We perform the canonical quantization of a relativistic spinless particle moving in a curved and static spacetime. We show that the classical theory already describes at the same time both particle and antiparticle. The analyses involves…
We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…
This note aims to subsume several apparently unrelated models under a common framework. Several examples of well-known quantum field theories are listed which are connected via stochastic quantization. We highlight the fact that the…
The Projection Postulate from Standard Quantum Mechanics relies fundamentally on measurements. But measurements implicitly suggest the existence of anthropocentric notions like measuring devices, which should rather emerge from the theory.…
The interest in quantum-optical states confined in finite-dimensional Hilbert spaces has recently been stimulated by the progress in quantum computing, quantum-optical state preparation, and measurement techniques, in particular, by the…
We show that $\frak{su}(2)$ Lie algebras of coordinate operators related to quantum spaces with $\frak{su}(2)$ noncommutativity can be conveniently represented by $SO(3)$-covariant poly-differential involutive representations. We show that…
Quantum spaces with $\frak{su}(2)$ noncommutativity can be modelled by using a family of $SO(3)$-equivariant differential $^*$-representations. The quantization maps are determined from the combination of the Wigner theorem for $SU(2)$ with…
The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general study of the mathematical properties of the models used in Physics to represent systems, we prove that the states of a system can…
The tomographic representation of quantum fields within the deformation quantization formalism is constructed. By employing the Wigner functional we obtain the symplectic tomogram associated with quantum fields. In addition, the tomographic…
We study properties of a family of algebraic star products defined on coadjoint orbits of semisimple Lie groups. We connect this description with the point of view of differentiable deformations and geometric quantization.
A convenient way to calculate $N$-particle quantum partition functions is by confining the particles in a weak harmonic potential instead of using a finite box or periodic boundary conditions. There is, however, a slightly different…
We describe a midi-superspace quantization scheme for generic single horizon black holes in which only the spatial diffeomorphisms are fixed. The remaining Hamiltonian constraint yields an infinite set of decoupled eigenvalue equations: one…
When we have noncommutativity among coordinates (or conjugate momenta), we consider Wigner's formulation of quantum mechanics, including a new derivation of path integral formula. We also propose the Moyal star product based on the Dirac…
Motivated by certain concepts introduced by the Refined Algebraic Quantization formalism for constrained systems which has been successfully applied within the context of Loop Quantum Gravity, in this paper we propose a phase space…