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