There are No Causality Problems for Fermi's Two Atom System

A repeatedly discussed gedanken experiment, proposed by Fermi to check Einstein causality, is reconsidered. It is shown that, contrary to a recent statement made by Hegerfeldt, there appears no causality paradoxon in a proper theoretical description of the experiment.Comment: 6 pages, latex, DESY 94-02

The Quest for Understanding in Relativistic Quantum Physics

We discuss the status and some perspectives of relativistic quantum physics.Comment: Invited contribution to the Special Issue 2000 of the Journal of Mathematical Physics, 38 pages, typos corrected and references added, as to appear in JM

A sharpened nuclearity condition for massless fields

A recently proposed phase space condition which comprises information about the vacuum structure and timelike asymptotic behavior of physical states is verified in massless free field theory. There follow interesting conclusions about the momentum transfer of local operators in this model.Comment: 13 pages, LaTeX. As appeared in Letters in Mathematical Physic

Wightman Functions' Behaviour on the Event Horizon of an Extremal Reissner-Nordstr\"om Black Hole

A weaker Haag, Narnhofer and Stein prescription as well as a weaker Hessling Quantum Equivalence Principle for the behaviour of thermal Wightman functions on an event horizon are analysed in the case of an extremal Reissner-Nordstr\"{o}m black hole in the limit of a large mass. In order to avoid the degeneracy of the metric in the stationary coordinates on the horizon, a method is introduced which employs the invariant length of geodesics which pass the horizon. First the method is checked for a massless scalar field on the event horizon of the Rindler wedge, extending the original procedure of Haag, Narnhofer and Stein onto the {\em whole horizon} and recovering the same results found by Hessling. Afterwards the HNS prescription and Hessling's prescription for a massless scalar field are analysed on the whole horizon of an extremal Reissner-Nordstr\"{o}m black hole in the limit of a large mass. It is proved that the weak form of the HNS prescription is satisfyed for all the finite values of the temperature of the KMS states, i.e., this principle does not determine any Hawking temperature. It is found that the Reissner-Nordstr\"{o}m vacuum, i.e., $T=0$ does satisfy the weak HNS prescription and it is the only state which satisfies weak Hessling's prescription, too. Finally, it is suggested that all the previously obtained results should be valid dropping the requirements of a massless field and of a large mass black hole.Comment: 27 pages, standard LaTex, no figures, final version containing the results following from Hessling's principle as they appeared in the other paper gr-qc/9510016, minor changes in the text and in references, it will appear on Class. Quant. Gra

Infrared cutoffs and the adiabatic limit in noncommutative spacetime

We discuss appropriate infrared cutoffs and their adiabatic limit for field theories on the noncommutative Minkowski space in the Yang-Feldman formalism. In order to do this, we consider a mass term as interaction term. We show that an infrared cutoff can be defined quite analogously to the commutative case and that the adiabatic limit of the two-point function exists and coincides with the expectation, to all orders.Comment: 19 page

Comment on: Modular Theory and Geometry

In this note we comment on part of a recent article by B. Schroer and H.-W. Wiesbrock. Therein they calculate some new modular structure for the U(1)-current-algebra (Weyl-algebra). We point out that their findings are true in a more general setting. The split-property allows an extension to doubly-localized algebras.Comment: 13 pages, corrected versio

Dynamical mapping method in nonrelativistic models of quantum field theory

The solutions of Heisenberg equations and two-particles eigenvalue problems for nonrelativistic models of current-current fermion interaction and $N, \Theta$ model are obtained in the frameworks of dynamical mapping method. The equivalence of different types of dynamical mapping is shown. The connection between renormalization procedure and theory of selfadjoint extensions is elucidated.Comment: 14 page

The Hot Bang state of massless fermions

In 2002, a method has been proposed by Buchholz et al. in the context of Local Quantum Physics, to characterize states that are locally in thermodynamic equilibrium. It could be shown for the model of massless bosons that these states exhibit quite interesting properties. The mean phase-space density satisfies a transport equation, and many of these states break time reversal symmetry. Moreover, an explicit example of such a state, called the Hot Bang state, could be found, which models the future of a temperature singularity. However, although the general results carry over to the fermionic case easily, the proof of existence of an analogue of the Hot Bang state is not quite that straightforward. The proof will be given in this paper. Moreover, we will discuss some of the mathematical subtleties which arise in the fermionic case.Comment: 17 page

Local Thermal Equilibrium in Quantum Field Theory on Flat and Curved Spacetimes

The existence of local thermal equilibrium (LTE) states for quantum field theory in the sense of Buchholz, Ojima and Roos is discussed in a model-independent setting. It is shown that for spaces of finitely many independent thermal observables there always exist states which are in LTE in any compact region of Minkowski spacetime. Furthermore, LTE states in curved spacetime are discussed and it is observed that the original definition of LTE on curved backgrounds given by Buchholz and Schlemmer needs to be modified. Under an assumption related to certain unboundedness properties of the pointlike thermal observables, existence of states which are in LTE at a given point in curved spacetime is established. The assumption is discussed for the sets of thermal observables for the free scalar field considered by Schlemmer and Verch.Comment: 16 pages, some minor changes and clarifications; section 4 has been shortened as some unnecessary constructions have been remove

Positivity violation for the lattice Landau gluon propagator

We present explicit numerical evidence of reflection-positivity violation for the lattice Landau gluon propagator in three-dimensional pure SU(2) gauge theory. We use data obtained at very large lattice volumes (V = 80^3, 140^3) and for three different lattice couplings in the scaling region (beta = 4.2, 5.0, 6.0). In particular, we observe a clear oscillatory pattern in the real-space propagator C(t). We also verify that the (real-space) data show good scaling in the range t \in [0,3] fm and can be fitted using a Gribov-like form. The violation of positivity is in contradiction with a stable-particle interpretation of the associated field theory and may be viewed as a manifestation of confinement.Comment: 5 pages, 6 figures; minor modifications in the text and in the bibliograph