相关论文: Ultracoherence and Canonical Transformations
In many Lagrangian field theories one has a Poisson bracket defined on the space of local functionals. We find necessary and sufficient conditions for a transformation on the space of local functionals to be canonical in three different…
Non-Fock representations of the canonical commutation relations modeled over an infinite-dimensional nuclear space are constructed in an explicit form. The example of the nuclear space of smooth real functions of rapid decrease results in…
We describe the holonomy algebras of all canonical connections of homogeneous structures on real hyperbolic spaces in all dimensions. The structural results obtained then lead to a determination of the types, in the sense of Tricerri and…
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…
Extending earlier work(*), we examine the deformation of the canonical symplectic structure in a cotangent bundle $T^\star(\Q)$ by additional terms implying the Poisson non-commutativity of both configuration and momentum variables. In this…
We survey the existing parts of a classification of finite groups generated by orthogonal transformations in a finite-dimensional Euclidean space whose fixed point subspace has codimension one or two and extend it to a complete…
The analogies between symplectic and orthogonal groups, regarded as symmetries of real bilinear forms, are manifest in their (metaplectic and spin) projective representations. In finite dimensions, those are true representations of doubly…
Symplectic integrators with long-term preservation of integrals of motion are introduced for the guiding-center model of plasma particles in toroidal magnetic fields of general topology. An efficient transformation to canonical coordinates…
Fock representations are constructed for a free scalar field in the closed and quasi-Euclidean isotropic cosmological models. Invariance of their cyclic vector (vacuum) under isometries and the correspondence principle single out a class of…
Unique set of coherent states for the anharmonic oscillator is obtained by requiring i. under the quantum mechanical time evolution a coherent state evolves into another, governed by trajectory in the classical phase space (of a related…
We study the homomorphisms from a fixed finitely generated group to strictly acylindrical colorable hierarchically hyperbolic groups. We prove that any such group is equationally noetherian.
We construct canonical intertwining semi-models with Kobayashi hyperbolic base space for holomorphic self-maps of complex manifolds which are univalent on some absorbing cocompact hyperbolic domain. In particular, in the unit ball we solve…
A complete Fock space representation of the covariant differential calculus on quantum space is constructed. The consistency criteria for the ensuing algebraic structure, mapping to the canonical fermions and bosons and the consequences of…
This paper presents the general theory of canonical transformations of coordinates in quantum mechanics. First, the theory is developed in the formalism of phase space quantum mechanics. It is shown that by transforming a star-product, when…
An element of a group is called bireflectional when it is the product of two involutions of the group (i.e. elements of order 1 or 2). If an element is bireflectional then it is conjugated to its inverse. It is known that all elements of…
In this paper we study the complex symmetry in the several variable Fock space by using the techniques of weighted composition operators and semigroups. We characterize unbounded weighted composition operators that are (real) complex…
We prove a generalization of the quantum de Finetti theorem when the local space is an infinite-dimensional Fock space. In particular, instead of considering the action of the permutation group on $n$ copies of that space, we consider the…
We study cosmological tensor perturbations on a quantized background within the hybrid quantization approach. In particular, we consider a flat, homogeneous and isotropic spacetime and small tensor inhomogeneities on it. We truncate the…
Canonical quantization of abelian BF-type topological field theory coupled to extended sources on generic d-dimensional manifolds and with curved line bundles is studied. Sheaf cohomology is used to construct the appropriate topological…
$Vect(N)$, the algebra of vector fields in $N$ dimensions, is studied. Some aspects of local differential geometry are formulated as $Vect(N)$ representation theory. There is a new class of modules, {\it conformal fields}, whose…