Related papers: Group Theoretical Quantization and the Example of …
The pseudo--rigid body represents an example of a constrained system with a nonunimodular gauge group. This system is treated along the guidelines of an algebraic constraint quantization scheme which focusses on observable quantities,…
A condition of geometric modular action is proposed as a selection principle for physically interesting states on general space-times. This condition is naturally associated with transformation groups of partially ordered sets and provides…
The second alternative conformal limit of the recently proposed general higher derivative dilaton quantum theory in curved spacetime is explored. In this version of the theory the dilaton is transformed, along with the metric, to provide…
We discuss an extended easy quantum group formalism, with the Schur-Weyl theoretic Kronecker symbols being as general as possible, and allowed to take values in $\{-1,0,1\}$, and more generally in $\mathbb T\cup\{0\}$. Our study includes an…
The Group Quantization formalism is a scheme for constructing a functional space that is an irreducible infinite dimensional representation of the Lie algebra belonging to a dynamical symmetry group. We apply this formalism to the…
Satisfiability is a classic problem in computational complexity theory, in which one wishes to determine whether an assignment of values to a collection of Boolean variables exists in which all of a collection of clauses composed of logical…
We review recent results on quantum reactive scattering from a phase space perspective. The approach uses classical and quantum versions of normal form theory and the perspective of dynamical systems theory. Over the past ten years the…
A method of ``blocking'' triangulations that rests on the self-similarity feature of dynamically triangulated random manifolds is proposed. The method is used to define the renormalization group for random geometries. As an illustration,…
Interesting non-linear functions on the phase spaces of classical field theories can never be quantized immediately because the basic fields of the theory become operator valued distributions. Therefore, one is usually forced to find a…
Quantization is studied from a viewpoint of field extension. If the dynamical fields and their action have a periodicity, the space of wave functions should be algebraically extended `a la Galois, so that it may be consistent with the…
Let G be an n-dimensional torus and $\tau$ a Hamiltonian action of G on a compact symplectic manifold, M. If M is pre-quantizable one can associate with $\tau$ a representation of G on a virtual vector space, Q(M), by…
Many interesting C*-algebras can be viewed as quantizations of Poisson manifolds. I propose that a Poisson manifold may be quantized by a twisted polarized convolution C*-algebra of a symplectic groupoid. Toward this end, I define…
The standard formalism of quantum theory is enhanced and definite meaning is given to the concepts of experiment, measurement and event. Within this approach one obtains a uniquely defined piecewise deterministic algorithm generating…
We implement the so-called Weyl-Heisenberg covariant integral quantization in the case of a classical system constrained by a bounded or semi-bounded geometry. The procedure, which is free of the ordering problem of operators, is…
A simple algebraic model for charged particle moving in two dimensional space under influence of singular magnetic field is given. The fundamental assumption for the model is that every charged particle coupled to the magnetic field is…
A generalized Weyl quantization formalism for a particle on the circle investigated in \cite{1} is developed. A Wigner function for the state $\hat{\varrho}$ and the kernel $\mathcal{K}$ for a particle on the circle is defined and its…
Relativistic geometrical action for a quantum particle in the superspace is analyzed from theoretical group point of view. To this end an alternative technique of quantization outlined by the authors in a previous work and that is based in…
Group theory is extremely successful in characterizing the symmetries in quantum systems, which greatly simplifies and unifies our treatments of quantum systems. Here we introduce the concept of the symmetry for a quantum Boltzmann machine…
We present a short review of the group-geometric approach to supergravity theories, from the point of view of recent developments. The central idea is the unification of usual diffeomorphisms, gauge symmetries and supersymmetries into…
A quantization scheme based on the extension of phase space with application of constrained quantization technic is considered. The obtained method is similar to the geometric quantization. For constrained systems the problem of scalar…