1,720,982 research outputs found
On the quadratic Fock functor
Full text linkWe prove that the quadratic second quantization of an operator p on is an orthogonal projection on the quadratic Fock space if and only if p =MI, where MI is a multiplication operator by a characteristic function I.ou
Quasi-invariant states
Full text linkIn this paper, we develop the theory of quasi-invariant (respectively, strongly quasi-invariant) states under the action of a group G of normal & lowast;-automorphisms of a & lowast;-algebra (or von Neumann algebra) A. We prove that these states are naturally associated to left-G-1-cocycles. If G is compact, the structure of strongly G-quasi-invariant states is determined. For any G-strongly quasi-invariant state phi, we construct a unitary representation associated to the triple (A,G,phi). We prove, under some conditions, that any quantum Markov chain with commuting, invertible and Hermitian conditional density amplitudes on a countable tensor product of type I factors is strongly quasi-invariant with respect to the natural action of the group S-infinity of local permutations and we give the explicit form of the associated cocycle. This provides a family of nontrivial examples of strongly quasi-invariant states for locally compact groups obtained as inductive limit of an increasing sequence of compact groups
2-Point Markov Evolutions
Full text linkWe study the Markov evolutions associated to the expected Markov processes
Conditional expectations associated with strongly quasi-invariant states and an application to spin systems
Full text linkWe discuss the conditional expectations and martingales in relevance with G-strongly quasi-invariant states on a C*-algebra A , where G is a separable locally compact group of ∗-automorphisms of A . In the von Neumann algebra A of the GNS representation, we define a unitary representation of the group and a group G ̂ of ∗-automorphisms of A , which is homomorphic to G. For the case of compact G, we find a G ̂ -invariant state on A and define a conditional expectation with range the G ̂ -fixed subalgebra. When G is the union of increasing compact groups, we construct a sequence of conditional expectations and thereby construct (backward) martingales, which have limits by the martingale convergence theorem. As an example we consider S∞ the group of local permutations which acts on a C*-algebra of infinite tensor product of finite dimensional C*-algebras. We also find an application in classical spin systems
Group of automorphisms for strongly quasi-invariant states
Full text linkFor a & lowast;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}-automorphism group G on a von Neumann algebra, we study the G-quasi-invariant states and their properties. The G-quasi-invariance or G-strongly quasi-invariance is weaker than the G-invariance and has wide applications. We develop several properties for G-strongly quasi-invariant states. Many of them are the extensions of the already developed theories for G-invariant states. Among others, we consider the relationship between the group G and modular automorphism group, invariant subalgebras, ergodicity, modular theory, and abelian subalgebras. We provide with some examples to support the results
Quadratic exponential vectors
Full text linkWe give a necessary and sufficient condition for the existence of a quadratic exponential vector with test function in .
We prove the linear independence and totality, in the quadratic Fock space,
of these vectors.
Using a technique different from the one used in \cite {ADS}, we also extend, to a more general class of test functions, the explicit form of the scalar product between two such vectors
Self-adjointness and boundedness in quadratic quantization
No full textWe construct a counter example showing, for the quadratic quantization, the identity (Gamma(T))* = Gamma(T*) is not necessarily true. We characterize all operators on the one-particle algebra whose quadratic quantization are self-adjoint operators on the quadratic Fock space. Finally, we discuss the boundedness of the quadratic quantization. (c) 2014 AIP Publishing LLC
- …
