Learn More
A functional integral representation is given for a large class of quantum mechanical models with a non{L 2 ground state. As a prototype the particle in a periodic potential is discussed: a unique ground state is shown to exist as a state on the Weyl algebra, and a functional measure (spectral stochastic process) is constructed on trajectories taking values(More)
  • J Löffelholz, Leipzig G Berufsakademie, Morchio, F Strocchi
  • 2002
The problem of existence of ground state representations of the CCR algebra with free evolution are discussed and all the solutions are classified in terms of non regular or indefinite invariant function-als. In both cases one meets unusual mathematical structures which appear as prototypes of phenomena typical of gauge quantum field theory, in particular(More)
The Lie and module (Rinehart) algebraic structure of vector fields of compact support over C ∞ functions on a (connected) manifold M define a unique universal non-commutative Poisson * algebra ΛR(M). For a compact manifold, a (antiher-mitian) variable Z ∈ ΛR(M), central with respect to both the product and the Lie product, relates commutators and Poisson(More)
The classical Maxwell–Dirac and Maxwell–Klein–Gordon theories admit solutions of the field equations where the corresponding electric current vanishes in the causal complement of some bounded region of Minkowski space. This poses the interesting question of whether states with a similarly well localized charge density also exist in quantum electrodynamics.(More)
  • J Löffelholz, Leipzig G Berufsakademie, Morchio, F Strocchi
  • 2004
The conflict between Gauss' law constraint and the existence of the propagator of the gauge fields, at the basis of contradictory proposals in the literature, is shown to lead to only two alternatives, both with peculiar features with respect to standard quantum field theory. In the positive (interacting) case, the Gauss' law holds in operator form, but(More)