Related papers: Quantization of the canonically conjugate pair ang…
Co-oriented contact manifolds quite generally describe classical dynamical systems. Quantization is achieved by suitably associating a Schr\"odinger equation to every path in the contact manifold. We quantize the standard contact seven…
Various classical counterparts for the two-level pairing model in a many-fermion system are presented in the Schwinger boson representation. It is shown that one of the key ingredients giving the classical descriptions for quantal system is…
We use the mathematical structure of group algebras and $H^{+}$-algebras for describing certain problems concerning the quantum dynamics of systems of angular momenta, including also the spin systems. The underlying groups are ${\rm SU}(2)$…
Canonical quantization of spherically symmetric space-times is carried out, using real-valued densitized triads and extrinsic curvature components, with specific factor ordering choices ensuring in an anomaly free quantum constraint…
We calculate the relative amplitude of orbital angular momentum (OAM) entangled photon pairs from the spontaneous parametric down conversion. The results show that the amplitude depends on both the two Laguerre indices l, p. We also discuss…
The spectrum of excited states observed in the finite volume of lattice QCD is governed by the discrete symmetries of the cubic group. This finite group permits the mixing of orbital angular momentum quanta in the finite volume. As…
Particle localization within quantum field theory is revisited. Canonical quantization of a free scalar field theory is performed in a manifestly Lorentz covariant way with respect to an arbitrary 3-surface $\Sigma$, which is the…
We establish an exact relation between the S-symplectomorphism and the S-matrix by means of the phase space formulation of quantum mechanics. The adjoint action of the S-matrix defines a fuzzy diffeomorphism on phase space whose classical…
Generalized Fourier transformation between the position and the momentum representation of a quantum state is constructed in a coordinate independent way. The only ingredient of this construction is the symplectic (canonical) geometry of…
High-dimensional quantum systems offer many advantages over low-dimensional quantum systems. Meanwhile, unitary transformations on quantum states are important parts in various quantum information tasks, whereas they become technically…
The real plane with its set of orientations or angles in $[0,\pi)$ is the simplest non trivial example of a (projective) Hilbert space and provides nice illustrations of quantum formalism. We present some of them, namely covariant integral…
Generalized Weyl quantization formalism for the cylindrical phase space $S^1 \times \mathbb{R}^1$ is developed. It is shown that the quantum observables relevant to the phase of linear harmonic oscillator or electromagnetic field can be…
Quantum phase transitions in a system of N bosons with angular momentum L=0,2 (s,d) and a single fermion with angular momentum j are investigated both classically and quantum mechanically. It is shown that the presence of the odd fermion…
Quantum mechanical phase factors can be related to dynamical effects or to the geometrical properties of a trajectory in a given space - either parameter space or Hilbert space. Here, we experimentally investigate a quantum mechanical phase…
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…
Fluctuation terms and higher moments of a quantum state imply corrections to the classical equations of motion that may have implications in early-universe cosmology, for instance in the state-dependent form of effective potentials. In…
Conventional approach to quantum mechanics in phase space, (q,p), is to take the operator based quantum mechanics of Schrodinger, or and equivalent, and assign a c-number function in phase space to it. We propose to begin with a higher…
In this first of a series of four articles, it is shown how a hamiltonian quantum dynamics can be formulated based on a generalization of classical probability theory using the notion of quasi-invariant measures on the classical phase space…
We propose and investigate the quasi-phase matched (QPM) nonlinear optical frequency conversion of optical vortices in periodically poled Lithium Niobate (PPLN). Laguerre-Gaussian (LG) modes are used to represent the orbital angular…
It is shown that the Bohm equations for the phase $S$ and squared modulus $\rho$ of the quantum mechanical wave function can be derived from the classical ensemble equations admiting an aditional momentum $p_s$ of the form proportional to…