Spectral and scattering theory of massive Pauli-Fierz Hamiltonians is studied. Asymptotic completeness of these Hamiltonians is shown. The proof consists of three parts. The first is a construction of asymptotic fields and a proof of their Fock property. The second part is a geometric analysis of observables. Its main result is what we call geometric asymptotic completeness. Finally, the last part is a proof of asymptotic completeness itself. 1 Introduction Our paper is devoted to a class of Hamiltonians used in physics to describe a quantum system ("matter" or "an atom") interacting with a bosonic field ("radiation"). K and K are respectively the Hilbert space and the Hamiltonian describing the matter. The bosonic field is described by a Fock space \Gamma(h) with the one-particle space eg. h = L 2 (IR d ; dk), where IR d is the momentum space, and a free Hamiltonian of the form d\Gamma(!(k)) = Z !(k)a (k)a(k)dk: The function !(k) is called the dispersion relation. The inte...

Abstract. The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading

Abstract. A perturbative formulation of algebraic field theory is presented, both for the classical and for the quantum case, and it is shown that the relation between them may be understood in terms of deformation quantization. 1

As it is clear from the title, I shall deal with some question connected with the theory of Quantum Groups. If I remember right, Moshe did not like Quantum Groups after this notion was cristallized by Drinfeld [1] in pure algebraic manner. However his own attraction to the deformations (as well as the pressure of authors in LMP) made him to change his mind. So when I presented the subject described below at St. Petersburg meeting on May 1998, he did not express any bad feelings. So I decided to publish it in this memorial volume. There are several sources of my proposal. I shall give just two, one ”mathematical” and another ”physical”, as it is appropriate for a paper on Mathematical Physics. 1. In the definition of Quantum Group one uses the deformation of the Chevalley generators K, f, e, whereas for the construction of the universal R-matrix one needs nonpolinomial elements like H = ln K. Explicite formulas will be reminded below. This unfortunate obstacle can be circumvented in

Reichenbach's principle of a probabilistic common cause of probabilistic correlations is formulated in terms of relativistic quantum field theory and the problem is raised whether correlations in relativistic quantum field theory between events represented by projections in local observable algebras A(V1) and A(V2) pertaining to spacelike separated spacetime regions V1 and V2 can be explained by finding a probabilistic common cause of the correlation in Reichenbach's sense. While this problem remains open, it is shown that if all superluminal correlations predicted by the vacuum state between events in A(V1) and A(V2) have a genuinely probabilistic common cause, then the local algebras A(V1) and A(V2) must be statistically independent in the sense of C*-independence.

hep-th/0008044 revised version

Abstract not found

If {A(V)} is a net of local von Neumann algebras satisfying standard axioms of algebraic relativistic quantum field theory and V 1 and V 2 are spacelike separated spacetime regions, then the system (A(V 1), A(V 2), f) is said to satisfy the Weak Reichenbach’s Common Cause Principle iff for every pair of projections A ¥ A(V 1), B ¥ A(V 2) correlated in the normal state f there exists a projection C belonging to a von Neumann algebra associated with a spacetime region V contained in the union of the backward light cones of V 1 and V 2 and disjoint from both V 1 and V 2, a projection having the properties of a Reichenbachian common cause of the correlation between A and B. It is shown that if the net has the local primitive causality property then every local system (A(V 1), A(V 2), f) with a locally normal and locally faithful state f and suitable bounded V 1 and V 2 satisfies the

We propose an extension of some structural aspects that have successfully been applied in the development of the theory of quantum fields propagating on a general spacetime manifold so as to include superfield models on a supermanifold.

Abstract. As a starting point for this manuscript, we remark how the cosmological horizon of a certain class of Friedmann-Robertson-Walker backgrounds shares some non trivial geometric properties with null infinity in an asymptotically flat spacetime. Such a feature is generalized to a larger class of expanding spacetimes M admitting a geodesically complete cosmological horizon ℑ − common to all co-moving observers. This property is later exploited in order to recast, in a cosmological background, some recent results for a linear scalar quantum field theory in spacetimes asymptotically flat at null infinity. Under suitable hypotheses on M – valid for deSitter spacetime and some other FRW spacetimes obtained by perturbing deSitter space – the algebra of observables for a Klein-Gordon field is mapped into a subalgebra of the algebra of observables W(ℑ − ) constructed on the cosmological horizon. There is exactly one pure quasifree state λ on W(ℑ − ) which fulfils a suitable energypositivity condition with respect to a generator related with the cosmological time displacements. Furthermore λ induces a preferred physically meaningful quantum state λM for the quantum theory in the bulk. If M admits a timelike Killing generator preserving ℑ − , then the associated self-adjoint generator in the GNS representation of λM has positive spectrum (i.e. energy). Moreover λM turns out to be invariant under every symmetry of the bulk metric which preserves the cosmological horizon. In the case of an expanding deSitter spacetime, λM coincides with the Euclidean (Bunch-Davies) vacuum state, hence being Hadamard in this case. Remarks on the validity