Related papers: Deformation quantization and the tomographic repre…
We present a theory of quantized radiation fields described in terms of q-deformed harmonic oscillators. The creation and annihilation operators satisfy deformed commutation relations and the Fock space of states is constructed in this…
In these lecture notes I give an introduction to deformation quantization. The quantization problem is discussed in some detail thereby motivating the notion of star products. Starting from a deformed observable algebra, i.e. the star…
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…
Starting from the famous Pauli problem on the possibility to associate quantum states with probabilities, the formulation of quantum mechanics in which quantum states are described by fair probability distributions (tomograms, i.e.…
The deformation star product of smooth functions on the momentum phase space of covariant (polysymplectic) Hamiltonian field theory is introduced.
Different approaches are compared to formulation of quantum mechanics of a particle on the curved spaces. At first, the canonical, quasi-classical and path integration formalisms are considered for quantization of geodesic motion on the…
Deformation quantization is a powerful tool for quantizing theories with bosonic and fermionic degrees of freedom. The star products involved generate the mathematical structures which have recently been used in attempts to analyze the…
We present a construction of the Wigner function for a bosonic quantum field theory that has well-defined ultraviolet (UV) and infrared (IR) properties. Our construction uses the local mode formalism in algebraic quantum field theory that…
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…
What does it mean to quantize a symplectic map $\chi$? In deformation quantization, it means to construct an automorphism of the $*$ algebra associated to $\chi$. In quantum chaos it means to construct unitary operators $U_{\chi}$ such that…
We discuss the deformation quantization approach for the teaching of quantum mechanics. This approach has certain conceptual advantages which make its consideration worthwhile. In particular, it sheds new light on the relation between…
Starting from a new principle inspired by quantum tomography rather than from Born's rule, this paper gives a self-contained deductive approach to quantum mechanics and quantum measurement. A suggestive notion for what constitutes a quantum…
Following the idea of a field quantization of gravity as realized in group field theory, we construct a minisuperspace model where the wavefunction of canonical quantum cosmology (either Wheeler-DeWitt or loop quantum cosmology) is promoted…
We consider the time-independent Wigner functions of phase-space quantum mechanics (a.k.a. deformation quantization) for a Morse potential. First, we find them by solving the $\ast$-eigenvalue equations, using a method that can be applied…
Systems built out of N-body interactions, beyond 2-body interactions, are formulated on the plane, and investigated classically and quantum mechanically (in phase space). Their Wigner Functions--the density matrices in phase-space…
A deformation technique, known as the warped convolution, takes quantum fields in Minkowski spacetime to quantum fields in noncommutative Minkowski space-time. Since a quantum field is an operator valued regular distribution and the warped…
We establish a general principle for the tomographic approach to quantum state reconstruction, till now based on a simple rotation transformation in the phase space, which allows us to consider other types of transformations. Then, we will…
In the usual formulation of quantum mechanics, groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex Hilbert space, in accordance with Wigner's Theorem. In the phase-space…
On the base of symplectic quantum tomogram we define a probability distribution on the plane. The dual map transfers all observables which are polynomials of the position and momentum operators to the set of polynomials of two variables. In…
The tomographic approach to quantum mechanics is revisited as a direct tool to investigate violation of Bell-like inequalities. Since quantum tomograms are well defined probability distributions, the tomographic approach is emphasized to be…