203 research outputs found
Passive States for Essential Observers
The aim of this note is to present a unified approach to the results given in
\cite{bb99} and \cite{bs04} which also covers examples of models not presented
in these two papers (e.g. -dimensional Minkowski space-time for ).
Assuming that a state is passive for an observer travelling along certain
(essential) worldlines, we show that this state is invariant under the isometry
group, is a KMS-state for the observer at a temperature uniquely determined by
the structure constants of the Lie algebra involved and fulfills (a variant of)
the Reeh-Schlieder property. Also the modular objects associated to such a
state and the observable algebra of an observer are computed and a version of
weak locality is examined.Comment: 27 page
A separability criterion for density operators
We give a necessary and sufficient condition for a mixed quantum mechanical
state to be separable. The criterion is formulated as a boundedness condition
in terms of the greatest cross norm on the tensor product of trace class
operators.Comment: REVTeX, 5 page
A Topos Foundation for Theories of Physics: II. Daseinisation and the Liberation of Quantum Theory
This paper is the second in a series whose goal is to develop a fundamentally
new way of constructing theories of physics. The motivation comes from a desire
to address certain deep issues that arise when contemplating quantum theories
of space and time. Our basic contention is that constructing a theory of
physics is equivalent to finding a representation in a topos of a certain
formal language that is attached to the system. Classical physics arises when
the topos is the category of sets. Other types of theory employ a different
topos. In this paper, we study in depth the topos representation of the
propositional language, PL(S), for the case of quantum theory. In doing so, we
make a direct link with, and clarify, the earlier work on applying topos theory
to quantum physics. The key step is a process we term `daseinisation' by which
a projection operator is mapped to a sub-object of the spectral presheaf--the
topos quantum analogue of a classical state space. In the second part of the
paper we change gear with the introduction of the more sophisticated local
language L(S). From this point forward, throughout the rest of the series of
papers, our attention will be devoted almost entirely to this language. In the
present paper, we use L(S) to study `truth objects' in the topos. These are
objects in the topos that play the role of states: a necessary development as
the spectral presheaf has no global elements, and hence there are no
microstates in the sense of classical physics. Truth objects therefore play a
crucial role in our formalism.Comment: 34 pages, no figure
On supremum of bounded quantum observable
In this paper, we present a new necessary and sufficient condition for which
the supremum exists with respect to the logic order. Moreover, we give out a
new and much simpler representation of the supremum with respect to the order,
our results have nice physical meanings
String-- and Brane--Localized Causal Fields in a Strongly Nonlocal Model
We study a weakly local, but nonlocal model in spacetime dimension
and prove that it is maximally nonlocal in a certain specific quantitative
sense. Nevertheless, depending on the number of dimensions , it has
string--localized or brane--localized operators which commute at spatial
distances. In two spacetime dimensions, the model even comprises a covariant
and local subnet of operators localized in bounded subsets of Minkowski space
which has a nontrivial scattering matrix. The model thus exemplifies the
algebraic construction of local observables from algebras associated with
nonlocal fields.Comment: paper re-written with a change of emphasis and new result
Leibniz Seminorms and Best Approximation from C*-subalgebras
We show that if B is a C*-subalgebra of a C*-algebra A such that B contains a
bounded approximate identity for A, and if L is the pull-back to A of the
quotient norm on A/B, then L is strongly Leibniz. In connection with this
situation we study certain aspects of best approximation of elements of a
unital C*-algebra by elements of a unital C*-subalgebra.Comment: 24 pages. Intended for the proceedings of the conference "Operator
Algebras and Related Topics". v2: added a corollary to the main theorem, plus
several minor improvements v3: much simplified proof of a key lemma,
corollary to main theorem added v4: Many minor improvements. Section numbers
increased by
The Uniqueness Problem of Sequence Product on Operator Effect Algebra
A quantum effect is an operator on a complex Hilbert space that satisfies
. We denote the set of all quantum effects by . In
this paper we prove, Theorem 4.3, on the theory of sequential product on which shows, in fact, that there are sequential products on which are not of the generalized L\"{u}ders form. This result answers a
Gudder's open problem negatively
Thermal Quantum Fields without Cut-offs in 1+1 Space-time Dimensions
We construct interacting quantum fields in 1+1 dimensional Minkowski space,
representing neutral scalar bosons at positive temperature. Our work is based
on prior work by Klein and Landau and Hoegh-KrohnComment: 48 page
On the mixing property for a class of states of relativistic quantum fields
Let be a factor state on the quasi-local algebra of
observables generated by a relativistic quantum field, which in addition
satisfies certain regularity conditions (satisfied by ground states and the
recently constructed thermal states of the theory). We prove that
there exist space and time translation invariant states, some of which are
arbitrarily close to in the weak* topology, for which the time
evolution is weakly asymptotically abelian
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