10 research outputs found
Continuity of the von Neumann entropy
A general method for proving continuity of the von Neumann entropy on subsets
of positive trace-class operators is considered. This makes it possible to
re-derive the known conditions for continuity of the entropy in more general
forms and to obtain several new conditions. The method is based on a particular
approximation of the von Neumann entropy by an increasing sequence of concave
continuous unitary invariant functions defined using decompositions into finite
rank operators. The existence of this approximation is a corollary of a general
property of the set of quantum states as a convex topological space called the
strong stability property. This is considered in the first part of the paper.Comment: 42 pages, the minor changes have been made, the new applications of
the continuity condition have been added. To appear in Commun. Math. Phy
An Algebraic Jost-Schroer Theorem for Massive Theories
We consider a purely massive local relativistic quantum theory specified by a
family of von Neumann algebras indexed by the space-time regions. We assume
that, affiliated with the algebras associated to wedge regions, there are
operators which create only single particle states from the vacuum (so-called
polarization-free generators) and are well-behaved under the space-time
translations. Strengthening a result of Borchers, Buchholz and Schroer, we show
that then the theory is unitarily equivalent to that of a free field for the
corresponding particle type. We admit particles with any spin and localization
of the charge in space-like cones, thereby covering the case of
string-localized covariant quantum fields.Comment: 21 pages. The second (and crucial) hypothesis of the theorem has been
relaxed and clarified, thanks to the stimulus of an anonymous referee. (The
polarization-free generators associated with wedge regions, which always
exist, are assumed to be temperate.
Scaling algebras and pointlike fields: A nonperturbative approach to renormalization
We present a method of short-distance analysis in quantum field theory that
does not require choosing a renormalization prescription a priori. We set out
from a local net of algebras with associated pointlike quantum fields. The net
has a naturally defined scaling limit in the sense of Buchholz and Verch; we
investigate the effect of this limit on the pointlike fields. Both for the
fields and their operator product expansions, a well-defined limit procedure
can be established. This can always be interpreted in the usual sense of
multiplicative renormalization, where the renormalization factors are
determined by our analysis. We also consider the limits of symmetry actions. In
particular, for suitable limit states, the group of scaling transformations
induces a dilation symmetry in the limit theory.Comment: minor changes and clarifications; as to appear in Commun. Math.
Phys.; 37 page
Gauge-Invariant Quasi-Free States on the Algebra of the Anyon Commutation Relations
Let and let , . For and from , we define a function to be equal to if , and to if . Let , () be operator-valued distributions such that is the adjoint of . We say that , satisfy the anyon commutation relations (ACR) if for and for . In particular, for , the ACR become the canonical commutation relations and for , the ACR become the canonical anticommutation relations. We define the ACR algebra as the algebra generated by operator-valued integrals of , . We construct a class of gauge-invariant quasi-free states on the ACR algebra. Each state from this class is completely determined by a positive self-adjoint operator on the real space which commutes with any operator of multiplication by a bounded function . In the case ), we discuss the corresponding particle density . For , using a renormalization, we rigorously define a vacuum state on the commutative algebra generated by operator-valued integrals of . This state is given by a negative binomial point process. A scaling limit of these states as gives the gamma random measure, depending on parameter
Noninteraction of waves in two-dimensional conformal field theory
In higher dimensional quantum field theory, irreducible representations of
the Poincare group are associated with particles. Their counterpart in
two-dimensional massless models are "waves" introduced by Buchholz. In this
paper we show that waves do not interact in two-dimensional Moebius covariant
theories and in- and out-asymptotic fields coincide. We identify the set of the
collision states of waves with the subspace generated by the chiral components
of the Moebius covariant net from the vacuum. It is also shown that
Bisognano-Wichmann property, dilation covariance and asymptotic completeness
(with respect to waves) imply Moebius symmetry.
Under natural assumptions, we observe that the maps which give asymptotic
fields in Poincare covariant theory are conditional expectations between
appropriate algebras. We show that a two-dimensional massless theory is
asymptotically complete and noninteracting if and only if it is a chiral
Moebius covariant theory.Comment: 28 pages, no figur
The Unitary Gas and its Symmetry Properties
The physics of atomic quantum gases is currently taking advantage of a
powerful tool, the possibility to fully adjust the interaction strength between
atoms using a magnetically controlled Feshbach resonance. For fermions with two
internal states, formally two opposite spin states, this allows to prepare long
lived strongly interacting three-dimensional gases and to study the BEC-BCS
crossover. Of particular interest along the BEC-BCS crossover is the so-called
unitary gas, where the atomic interaction potential between the opposite spin
states has virtually an infinite scattering length and a zero range. This
unitary gas is the main subject of the present chapter: It has fascinating
symmetry properties, from a simple scaling invariance, to a more subtle
dynamical symmetry in an isotropic harmonic trap, which is linked to a
separability of the N-body problem in hyperspherical coordinates. Other
analytical results, valid over the whole BEC-BCS crossover, are presented,
establishing a connection between three recently measured quantities, the tail
of the momentum distribution, the short range part of the pair distribution
function and the mean number of closed channel molecules.Comment: 63 pages, 8 figures. Contribution to the Springer Lecture Notes in
Physics "BEC-BCS Crossover and the Unitary Fermi gas" edited by Wilhelm
Zwerger. Revised version correcting a few typo