Modular Groups of Quantum Fields in Thermal States

For a quantum field in a thermal equilibrium state we discuss the group generated by time translations and the modular action associated with an algebra invariant under half-sided translations. The modular flows associated with the algebras of the forward light cone and a space-like wedge admit a simple geometric description in two dimensional models that factorize in light-cone coordinates. At large distances from the domain boundary compared to the inverse temperature the flow pattern is essentially the same as time translations, whereas the zero temperature results are approximately reproduced close to the edge of the wedge and the apex of the cone. Associated with each domain there is also a one parameter group with a positive generator, for which the thermal state is a ground state. Formally, this may be regarded as a certain converse of the Unruh-effect.Comment: 28 pages, 4 figure

The Reeh-Schlieder property for thermal field theories

We show that the Reeh-Schlieder property w.r.t. the KMS-vector is a direct consequence of locality, additivity and the relativistic KMS-condition. The latter characterises the thermal equilibrium states of a relativistic quantum field theory. The statement remains vaild even if the given equilibrium state breaks spatial translation invariance.Comment: plain tex, 10 page

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.

How far does the analogy between causal horizon-induced thermalization with the standard heat bath situation go?

After a short presentation of KMS states and modular theory as the unifying description of thermalizing systems we propose the absence of transverse vacuum fluctuations in the holographic projections as the mechanism for an area behavior (the transverse area) of localization entropy as opposed to the volume dependence of ordinary heat bath entropy. Thermalization through causal localization is not a property of QM, but results from the omnipresent vacuum polarization in QFT and does not require a Gibbs type ensemble avaraging (coupling to a heat bath).Comment: 10 pages, based on talk given at the 2002 Londrina Winter Schoo

Wedge Local Deformations of Charged Fields leading to Anyonic Commutation Relations

The method of deforming free fields by using multiplication operators on Fock space, introduced by G. Lechner in [11], is generalized to a charged free field on two- and three-dimensional Minkowski space. In this case the deformation function can be chosen in such a way that the deformed fields satisfy generalized commutation relations, i.e. they behave like Anyons instead of Bosons. The fields are "polarization free" in the sense that they create only one-particle states from the vacuum and they are localized in wedges (or "paths of wedges"), which makes it possible to circumvent a No-Go theorem by J. Mund [12], stating that there are no free Anyons localized in spacelike cones. The two-particle scattering matrix, however, can be defined and is different from unity

Endomorphism Semigroups and Lightlike Translations

Certain criteria are demonstrated for a spatial derivation of a von Neumann algebra to generate a one-parameter semigroup of endomorphisms of that algebra. These are then used to establish a converse to recent results of Borchers and of Wiesbrock on certain one-parameter semigroups of endomorphisms of von Neumann algebras (specifically, Type III_1 factors) that appear as lightlike translations in the theory of algebras of local observables.Comment: 9 pages, Late

Charged sectors, spin and statistics in quantum field theory on curved spacetimes

The first part of this paper extends the Doplicher-Haag-Roberts theory of superselection sectors to quantum field theory on arbitrary globally hyperbolic spacetimes. The statistics of a superselection sector may be defined as in flat spacetime and each charge has a conjugate charge when the spacetime possesses non-compact Cauchy surfaces. In this case, the field net and the gauge group can be constructed as in Minkowski spacetime. The second part of this paper derives spin-statistics theorems on spacetimes with appropriate symmetries. Two situations are considered: First, if the spacetime has a bifurcate Killing horizon, as is the case in the presence of black holes, then restricting the observables to the Killing horizon together with "modular covariance" for the Killing flow yields a conformally covariant quantum field theory on the circle and a conformal spin-statistics theorem for charged sectors localizable on the Killing horizon. Secondly, if the spacetime has a rotation and PT symmetry like the Schwarzschild-Kruskal black holes, "geometric modular action" of the rotational symmetry leads to a spin-statistics theorem for charged covariant sectors where the spin is defined via the SU(2)-covering of the spatial rotation group SO(3).Comment: latex2e, 73 page

Carrier-mediated antiferromagnetic interlayer exchange coupling in diluted magnetic semiconductor multilayers Ga1−x_{1-x}Mnx_xAs/GaAs:Be

We use neutron reflectometry to investigate the interlayer exchange coupling between Ga$_{0.97}$Mn$_{0.03}$As ferromagnetic semiconductor layers separated by non-magnetic Be-doped GaAs spacers. Polarized neutron reflectivity measured below the Curie temperature of Ga$_{0.97}$Mn$_{0.03}$As reveals a characteristic splitting at the wave vector corresponding to twice the multilayer period, indicating that the coupling between the ferromagnetic layers are antiferromagnetic (AFM). When the applied field is increased to above the saturation field, this AFM coupling is suppressed. This behavior is not observed when the spacers are undoped, suggesting that the observed AFM coupling is mediated by charge carriers introduced via Be doping. The behavior of magnetization of the multilayers measured by DC magnetometry is consistent with the neutron reflectometry results.Comment: 4 pages, 4 figure

Local Nature of Coset Models

The local algebras of the maximal Coset model C_max associated with a chiral conformal subtheory A\subset B are shown to coincide with the local relative commutants of A in B, provided A contains a stress energy tensor. Making the same assumption, the adjoint action of the unique inner-implementing representation U^A associated with A\subset B on the local observables in B is found to define net-endomorphisms of B. This property is exploited for constructing from B a conformally covariant holographic image in 1+1 dimensions which proves useful as a geometric picture for the joint inclusion A\vee C_max \subset B. Immediate applications to the analysis of current subalgebras are given and the relation to normal canonical tensor product subfactors is clarified. A natural converse of Borchers' theorem on half-sided translations is made accessible.Comment: 33 pages, no figures; typos, minor improvement