Related papers: Integral quantizations with two basic examples
We present a novel, universal description of quantum entanglement using group theory and generalized characteristic functions. It leads to new reformulations of the separability problem, and the positivity of partial transpose (PPT)…
I present a method of performing geometric quantization using cohomology groups extended via coefficient groups of different types. This is possible according to the Universal Coefficient Theorem (UTC). I also show that by using this method…
A normal form transformation is carried out on the operators of a complete set of commuting observables in a multidimensional, integrable quantum system, mapping them by unitary conjugation into functions of the harmonic oscillators in the…
We carry out a generalization of quantum group co-representations in order to encode in this structure those cases where non-commutativity between endomorphism matrix entries and quantum space coordinates happens.
We give a path integral construction of the quantum mechanical partition function for gauged finite groups. Our construction gives the quantization of a system of $d$, $N\times N$ matrices invariant under the adjoint action of the symmetric…
Let $M$ be a smooth manifold equipped with a conformal structure, $E[w]$ the space of densities with the the conformal weight $w$ and $D_{w,w+\de}$ the space of differential operators from $E[w]$ to $E[w+\delta]$. Conformal quantization $Q$…
We axiomatize path integral quantization of symplectic manifolds. We prove that this path integral formulation of quantization is equivalent to an abstract operator formulation, ie. abstract coherent state (or Berezin) quantization. We use…
The characterization of the quantum ensemble is a fundamental issue in quantum information theory and foundations. The ensemble is also useful for various quantum information processing. To characterize the quantum ensemble, in this…
Schwinger's algebra of selective measurements has a natural interpretation in terms of groupoids. This approach is pushed forward in this paper to show that the theory of coherent states has a natural setting in the framework of groupoids.…
We quantize punctured plane, $X=\mathbb{R}^2-\{0\}$, employing Isham's group theoretic quantization procedure. After sketching out a brief review of group theoretic quantization procedure, we apply the quantization scheme to the phase…
Quantisation on spaces with properties of curvature, multiple connectedness and non orientablility is obtained. The geodesic length spectrum for the Laplacian operator is extended to solve the Schroedinger operator. Homotopy fundamental…
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…
The method of group quantization described in the preceeding paper I is extended so that it becomes applicable to some parametrized systems that do not admit a global transversal surface. A simple completely solvable toy system is studied…
For a connected simply connected nilpotent Lie group $\G$ with Lie algebra $\g$ and unitary dual $\wG$ one has (a) a global quantization of operator-valued symbols defined on $\G\times\wG$, involving the representation theory of the group,…
Many mathematical models of physical phenomena that have been proposed in recent years require more general spaces than manifolds. When taking into account the symmetry group of the model, we get a reduced model on the (singular) orbit…
Motivated by the recent rapid development of complexity theory applied to quantum mechanical processes we present the complete derivation of Nielsen's complexity of unitaries belonging to the representations of oscillator group. Our…
The measurement processes that are traditionally described within the realm of non-relativistic quantum mechanics are transcribed into the covariant framework of Cartan's space, the four-valued representation space of the restricted…
A series of successive quantizations is considered, starting with the quantization of a non relativistic or relativistic point particle: 1) quantization of a particle's position, 2) quantization of wave function, 3) quantization of wave…
The density operator for a quantum system in thermal equilibrium with its environment depends on Planck's constant, as well as the temperature. At high temperatures, the Weyl representation, that is, the thermal Wigner function, becomes…
In this paper is considered relativistic quantum field theory expressed by elementary units of quantum information as they are considered as fundamental entity of nature by Carl Friedrich von Weizsaecker. Through quantization of a Weyl…