Particle Weights and their Disintegration I

The notion of Wigner particles is attached to irreducible unitary representations of the Poincare group, characterized by parameters m and s of mass and spin, respectively. However, the Lorentz symmetry is broken in theories with long-range interactions, rendering this approach inapplicable (infraparticle problem). A unified treatment of both particles and infraparticles via the concept of particle weights can be given within the framework of Local Quantum Physics. They arise as temporal limits of physical states in the vacuum sector and describe the asymptotic particle content. In this paper their definition and characteristic properties are worked out in detail. The existence of the temporal limits is established by use of suitably defined seminorms which are also essential in proving the characteristic features of particle weights.Comment: 33 pages, amslatex, mathptm, minor corrections including numbering schem

A note on real Killing spinors in Weyl geometry

This text is dedicated to the real Killing equation on 3-dimensional Weyl manifolds. Any manifold admitting a real Killing spinor of weight 0 satisfies the conditions of a Gauduchon-Tod geometry. Conversely, any simply connected Gauduchon-Tod geometry has a 2-dimensional space of solutions of the real Killing equation on the spinor bundle of weight 0.Comment: Latex2.09, 5 page

On Infravacua and Superselection Theory

In the DHR theory of superselection sectors, one usually considers states which are local excitations of some vacuum state. Here, we extend this analysis to local excitations of a class of "infravacuum" states appearing in models with massless particles. We show that the corresponding superselection structure, the statistics of superselection sectors and the energy-momentum spectrum are the same as with respect to the vacuum state. (The latter result is obtained with a novel method of expressing the shape of the spectrum in terms of properties of local charge transfer cocycles.) These findings provide evidence to the effect that infravacua are a natural starting point for the analysis of the superselection structure in theories with long-range forces.Comment: LaTeX, 18 pages, spelling errors correcte

The resolvent algebra of non-relativistic Bose fields: observables, dynamics and states

The structure of the gauge invariant (particle number preserving) C*-algebra generated by the resolvents of a non-relativistic Bose field is analyzed. It is shown to form a dense subalgebra of the bounded inverse limit of a system of approximately finite dimensional C*-algebras. Based on this observation, it is proven that the closure of the gauge invariant algebra is stable under the dynamics induced by Hamiltonians involving pair potentials. These facts allow to proceed to a description of interacting Bosons in terms of C*-dynamical systems. It is outlined how the present approach leads to simplifications in the construction of infinite bosonic states and sheds new light on topics in many body theory.Comment: 36 pages, no figures; v2 - v6: references added, typos and mistakes corrected; v7: version published in CM

On hot bangs and the arrow of time in relativistic quantum field theory

A recently proposed method for the characterization and analysis of local equilibrium states in relativistic quantum field theory is applied to a simple model. Within this model states are identified which are locally (but not globally) in thermal equilibrium and it is shown that their local thermal properties evolve according to macroscopic equations. The largest space-time regions in which local equilibrium states can exist are timelike cones. Thus, although the model does not describe dissipative effects, such states fix in a natural manner a time direction. Moreover, generically they determine a distinguished space-time point where a singularity in the temperature (a hot bang) must have occurred if local equilibrium prevailed thereafter. The results illustrate how the breaking of the time reflection symmetry at macroscopic scales manifests itself in a microscopic setting.Comment: 21 pages; v2: minor linguistic changes and some typos correcte