1,214 research outputs found
Functional Representations for Fock Superalgebras
The Fock space of bosons and fermions and its underlying superalgebra are
represented by algebras of functions on a superspace. We define Gaussian
integration on infinite dimensional superspaces, and construct superanalogs of
the classical function spaces with a reproducing kernel -- including the
Bargmann-Fock representation -- and of the Wiener-Segal representation. The
latter representation requires the investigation of Wick ordering on Z2-graded
algebras. As application we derive a Mehler formula for the Ornstein-Uhlenbeck
semigroup on the Fock space.Comment: 33 pages, Late
Exactly soluble models of decoherence
Superselection rules induced by the interaction with the environment are a
basis to understand the emergence of classical observables within quantum
theory. The aim of this article is to investigate the decoherence effects,
which lead to superselection sectors, with the help of exactly soluble
Hamiltonian models. Starting from the examples of Araki and of Zurek more
general models with scattering are presented for which the projection operators
onto the induced superselection sectors do no longer commute with the
Hamiltonian. The example of an environment given by a free quantum field
indicates that infrared divergence plays an essential role for the emergence of
induced superselection sectors. For all models the induced superselection
sectors are uniquely determined by the Hamiltonian, whereas the time scale of
the decoherence depends crucially on the initial state of the total system.Comment: 12 pages, Late
States of quantum systems and their liftings
Let H(1), H(2) be complex Hilbert spaces, H be their Hilbert tensor product
and let tr2 be the operator of taking the partial trace of trace class
operators in H with respect to the space H(2). The operation tr2 maps states in
H (i.e. positive trace class operators in H with trace equal to one) into
states in H(1). In this paper we give the full description of mappings that are
linear right inverse to tr2. More precisely, we prove that any affine mapping
F(W) of the convex set of states in H(1) into the states in H that is right
inverse to tr2 is given by the tensor product of W with some state D in H(2).
In addition we investigate a representation of the quantum mechanical state
space by probability measures on the set of pure states and a representation --
used in the theory of stochastic Schroedinger equations -- by probability
measures on the Hilbert space. We prove that there are no affine mappings from
the state space of quantum mechanics into these spaces of probability measures.Comment: 14 page
Superselection rules induced by infrared divergence
Superselection rules induced by the interaction with a mass zero Boson field
are investigated for a class of exactly soluble Hamiltonian models. The
calculations apply as well to discrete as to continuous superselection rules.
The initial state (reference state) of the Boson field is either a normal state
or a KMS state. The superselection sectors emerge if and only if the Boson
field is infrared divergent, i. e. the bare photon number diverges and the
ground state of the Boson field disappears in the continuum. The time scale of
the decoherence depends on the strength of the infrared contributions of the
interaction and on properties of the initial state of the Boson system. These
results are first derived for a Hamiltonian with conservation laws. But in the
most general case the Hamiltonian includes an additional scattering potential,
and the only conserved quantity is the energy of the total system. The
superselection sectors remain stable against the perturbation by the scattering
processes.Comment: One reference added; minor corrections in App. B
Ecological and socio-economic effects of industrial oil palm plantations in Southwest Cameroon
Mathematical Aspects of Decoherence
Abstract: The aim of this lecture is to investigate the mathematical frame for environment induced superselection rules. Some exactly soluble models are dicussed in detail and norm estimates on decoherence effects are derived
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