scholarly journals When does the Weyl-von Neumann Theorem hold?

2017 ◽  
Vol 49 (4) ◽  
pp. 742-744
Author(s):  
Hiroshi Ando ◽  
Yasumichi Matsuzawa
Keyword(s):  
Von Neumann ◽  
Neumann Theorem ◽  
Von Neumann Theorem

scholarly journals Superunitary Representations of Heisenberg Supergroups

2018 ◽  
Vol 2020 (19) ◽  
pp. 5926-6006 ◽  
Author(s):  
Axel de Goursac ◽  
Jean-Philippe Michel
Keyword(s):  
Representation Theory ◽  
Heisenberg Group ◽  
Fourier Transformation ◽  
Coadjoint Orbits ◽  
New Approach ◽  
Von Neumann ◽  
Neumann Theorem ◽  
Lie Supergroups ◽  
Definition Of ◽  
Von Neumann Theorem

Abstract Numerous Lie supergroups do not admit superunitary representations (SURs) except the trivial one, for example, Heisenberg and orthosymplectic supergroups in mixed signature. To avoid this situation, we introduce in this paper a broader definition of SUR, relying on a new definition of Hilbert superspace. The latter is inspired by the notion of Krein space and was developed initially for noncommutative supergeometry. For Heisenberg supergroups, this new approach yields a smooth generalization, whatever the signature, of the unitary representation theory of the classical Heisenberg group. First, we obtain Schrödinger-like representations by quantizing generic coadjoint orbits. They satisfy the new definition of irreducible SURs and serve as ground to the main result of this paper: a generalized Stone–von Neumann theorem. Then, we obtain the superunitary dual and build a group Fourier transformation, satisfying Parseval theorem. We eventually show that metaplectic representations, which extend Schrödinger-like representations to metaplectic supergroups, also fit into this definition of SURs.

scholarly journals FUNDAMENTAL SYMMETRIES OF THE EXTENDED SPACETIME

2008 ◽  
Vol 23 (08) ◽  
pp. 1266-1269
Author(s):  
ORCHIDEA MARIA LECIAN ◽  
GIOVANNI MONTANI
Keyword(s):  
Uncertainty Relations ◽  
Fundamental Symmetries ◽  
Von Neumann ◽  
Neumann Theorem ◽  
Von Neumann Theorem

On the basis of Fourier duality and Stone-von Neumann theorem, we will examine polymer-quantization techniques and modified uncertainty relations as possible 1-extraD compactification schemes for a phenomenological truncation of the extraD tower.

The Weyl–von Neumann theorem in von Neumann factors

2017 ◽  
Vol 23 (1) ◽  
Author(s):  
Krzysztof Kamiński
Keyword(s):  
Von Neumann ◽  
Neumann Theorem ◽  
Von Neumann Theorem

AbstractIn a von Neumann factor

scholarly journals Coherent state transforms and the Mackey-Stone-Von Neumann theorem

2014 ◽  
Vol 55 (10) ◽  
pp. 102101 ◽  
Author(s):  
William D. Kirwin ◽  
José M. Mourão ◽  
João P. Nunes
Keyword(s):  
Coherent State ◽  
Von Neumann ◽  
Neumann Theorem ◽  
Von Neumann Theorem

Representations of Quantum Heisenberg Algebras

1994 ◽  
Vol 46 (5) ◽  
pp. 920-929 ◽  
Author(s):  
Marc A. Fabbri ◽  
Frank Okoh
Keyword(s):  
Heisenberg Algebra ◽  
Roots Of Unity ◽  
Direct Sums ◽  
Von Neumann ◽  
One Dimensional ◽  
Infinite Dimensional ◽  
Root Of Unity ◽  
Heisenberg Algebras ◽  
Neumann Theorem ◽  
Von Neumann Theorem

AbstractA Lie algebra is called a Heisenberg algebra if its centre coincides with its derived algebra and is one-dimensional. When is infinite-dimensional, Kac, Kazhdan, Lepowsky, and Wilson have proved that -modules that satisfy certain conditions are direct sums of a canonical irreducible submodule. This is an algebraic analogue of the Stone-von Neumann theorem. In this paper, we extract quantum Heisenberg algebras, q(), from the quantum affine algebras whose vertex representations were constructed by Frenkel and Jing. We introduce the canonical irreducible q()-module Mq and a class Cq of q()-modules that are shown to have the Stone-von Neumann property. The only restriction we place on the complex number q is that it is not a square root of 1. If q1 and q2 are not roots of unity, or are both primitive m-th roots of unity, we construct an explicit isomorphism between q1() and q2(). If q1 is a primitive m-th root of unity, m odd, q2 a primitive 2m-th or a primitive 4m-th root of unity, we also construct an explicit isomorphism between q1() and q2().

ERGODICITY FOR THE PHASE-FIELD EQUATIONS PERTURBED BY GAUSSIAN NOISE

2011 ◽  
Vol 14 (01) ◽  
pp. 35-55 ◽  
Author(s):  
VIOREL BARBU ◽  
GIUSEPPE DA PRATO
Keyword(s):  
Invariant Measure ◽  
Phase Field ◽  
Gaussian Noise ◽  
Phase Field Model ◽  
Field Equations ◽  
Von Neumann ◽  
Neumann Theorem ◽  
Phase Field Equations ◽  
Unique Invariant Measure ◽  
Von Neumann Theorem

We prove that the transition semigroup associated with the phase-field equations perturbed by a Gaussian noise has an invariant measure and it is irreducible and strong Feller. This implies by Doob's theorem that it possesses a unique invariant measure which is ergodic and strongly mixing. This implies the ergodicity of the flow associated with the phase-field model of phase transition in the sense of Birkhoff–von Neumann theorem. Such a result seems to be new in this context.

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