9 research outputs found
Asymptotic Abelianness and Braided Tensor C*-Categories
By introducing the concepts of asymptopia and bi-asymptopia, we show how
braided tensor C*-categories arise in a natural way. This generalizes
constructions in algebraic quantum field theory by replacing local
commutativity by suitable forms of asymptotic Abelianness.Comment: 20 pages, no figures. Final version, as to appear in "Rigorous
Quantum Field Theory", Progress in Mathematics, Volume 25
The extension problem for partial Boolean structures in Quantum Mechanics
Alternative partial Boolean structures, implicit in the discussion of
classical representability of sets of quantum mechanical predictions, are
characterized, with definite general conclusions on the equivalence of the
approaches going back to Bell and Kochen-Specker. An algebraic approach is
presented, allowing for a discussion of partial classical extension, amounting
to reduction of the number of contexts, classical representability arising as a
special case. As a result, known techniques are generalized and some of the
associated computational difficulties overcome. The implications on the
discussion of Boole-Bell inequalities are indicated.Comment: A number of misprints have been corrected and some terminology
changed in order to avoid possible ambiguitie
Quantum mechanics on manifolds and topological effects
A unique classification of the topological effects associated to quantum
mechanics on manifolds is obtained on the basis of the invariance under
diffeomorphisms and the realization of the Lie-Rinehart relations between the
generators of the diffeomorphism group and the algebra of infinitely
differentiable functions on the manifold. This leads to a unique
("Lie-Rinehart") C* algebra as observable algebra; its regular representations
are shown to be locally Schroedinger and in one to one correspondence with the
unitary representations of the fundamental group of the manifold. Therefore, in
the absence of spin degrees of freedom and external fields, the first homotopy
group of the manifold appears as the only source of topological effects.Comment: A few comments have been added to the Introduction, together with
related references; a few words have been changed in the Abstract and a Note
added to the Titl
Bell inequalities as constraints on unmeasurable correlations
The interpretation of the violation of Bell-Clauser-Horne inequalities is
revisited, in relation with the notion of extension of QM predictions to
unmeasurable correlations. Such extensions are compatible with QM predictions
in many cases, in particular for observables with compatibility relations
described by tree graphs. This implies classical representability of any set of
correlations , , , and the equivalence of the
Bell-Clauser-Horne inequalities to a non void intersection between the ranges
of values for the unmeasurable correlation associated to different
choices for B. The same analysis applies to the Hardy model and to the "perfect
correlations" discussed by Greenberger, Horne, Shimony and Zeilinger. In all
the cases, the dependence of an unmeasurable correlation on a set of variables
allowing for a classical representation is the only basis for arguments about
violations of locality and causality.Comment: Some modifications have been done in order to improve clarity of
presentation and comparison with other approache
Quantum delocalization of the electric charge
The classical Maxwell-Dirac and Maxwell-Klein-Gordon theories admit solutions
of the field equations where the corresponding electric current vanishes in the
causal complement of some bounded region of Minkowski space. This poses the
interesting question of whether states with a similarly well localized charge
density also exist in quantum electrodynamics. For a large family of charged
states, the dominant quantum corrections at spacelike infinity to the
expectation values of local observables are computed. It turns out that certain
moments of the charge density decrease no faster than the Coulomb field in
spacelike directions. In contrast to the classical theory, it is therefore
impossible to define the electric charge support of these states in a
meaningful way.Comment: 17 page