Asymptotic Abelianness and Braided Tensor C*-Categories

By introducing the concepts of asymptopia and bi-asymptopia, we show how braided tensor C*-categories arise in a natural way. This generalizes constructions in algebraic quantum field theory by replacing local commutativity by suitable forms of asymptotic Abelianness.Comment: 20 pages, no figures. Final version, as to appear in "Rigorous Quantum Field Theory", Progress in Mathematics, Volume 25

On Macroscopic Energy Gap for qq-Quantum Mechanical Systems

The q-deformed harmonic oscillator within the framework of the recently introduced Schwenk-Wess $q$-Heisenberg algebra is considered. It is shown, that for "physical" values $q\sim1$, the gap between the energy levels decreases with growing energy. Comparing with the other (real) $q$-deformations of the harmonic oscillator, where the gap instead increases, indicates that the formation of the macroscopic energy gap in the Schwenk-Wess $q$-Quantum Mechanics may be avoided.Comment: 6 pages, TeX, PRA-HEP-92/1

A new picture on (3+1)D topological mass mechanism

We present a class of mappings between the fields of the Cremmer-Sherk and pure BF models in 4D. These mappings are established by two distinct procedures. First a mapping of their actions is produced iteratively resulting in an expansion of the fields of one model in terms of progressively higher derivatives of the other model fields. Secondly an exact mapping is introduced by mapping their quantum correlation functions. The equivalence of both procedures is shown by resorting to the invariance under field scale transformations of the topological action. Related equivalences in 5D and 3D are discussed. A cohomological argument is presented to provide consistency of the iterative mapping.Comment: 13 page

Quantum theory: the role of microsystems and macrosystems

We stress the notion of statistical experiment, which is mandatory for quantum mechanics, and recall Ludwig's foundation of quantum mechanics, which provides the most general framework to deal with statistical experiments giving evidence for particles. In this approach particles appear as interaction carriers between preparation and registration apparatuses. We further briefly point out the more modern and versatile formalism of quantum theory, stressing the relevance of probabilistic concepts in its formulation. At last we discuss the role of macrosystems, focusing on quantum field theory for their description and introducing for them objective state parameters.Comment: 12 pages. For special issue of J.Phys.A, "The Quantum Universe", on the occasion of 70th birthday of Professor Giancarlo Ghirard

Anyons and the Bose-Fermi duality in the finite-temperature Thirring model

Solutions to the Thirring model are constructed in the framework of algebraic QFT. It is shown that for all positive temperatures there are fermionic solutions only if the coupling constant is $\lambda=\sqrt{2(2n+1)\pi}, n\in {\bf N}$. These fermions are inequivalent and only for $n=1$ they are canonical fields. In the general case solutions are anyons. Different anyons (which are uncountably many) live in orthogonal spaces and obey dynamical equations (of the type of Heisenberg's "Urgleichung") characterized by the corresponding values of the statistic parameter. Thus statistic parameter turns out to be related to the coupling constant $\lambda$ and the whole Hilbert space becomes non-separable with a different "Urgleichung" satisfied in each of its sectors. This feature certainly cannot be seen by any power expansion in $\lambda$. Moreover, since the latter is tied to the statistic parameter, it is clear that such an expansion is doomed to failure and will never reveal the true structure of the theory. The correlation functions in the temperature state for the canonical dressed fermions are shown by us to coincide with the ones for bare fields, that is in agreement with the uniqueness of the $\tau$-KMS state over the CAR algebra ($\tau$ being the shift automorphism). Also the $\alpha$-anyon two-point function is evaluated and for scalar field it reproduces the result that is known from the literature.Comment: 25 pages, LaTe

Limitations on the superposition principle: superselection rules in non-relativistic quantum mechanics

The superposition principle is a very basic ingredient of quantum theory. What may come as a surprise to many students, and even to many practitioners of the quantum craft, is tha superposition has limitations imposed by certain requirements of the theory. The discussion of such limitations arising from the so-called superselection rules is the main purpose of this paper. Some of their principal consequences are also discussed. The univalence, mass and particle number superselection rules of non-relativistic quantum mechanics are also derived using rather simple methods.Comment: 22 pages, no figure

CMB Imprints of a Pre-Inflationary Climbing Phase

We discuss the implications for cosmic microwave background (CMB) observables, of a class of pre-inflationary dynamics suggested by string models where SUSY is broken due to the presence of D-branes and orientifolds preserving incompatible portions of it. In these models the would-be inflaton is forced to emerge from the initial singularity climbing up a mild exponential potential, until it bounces against a steep exponential potential of "brane SUSY breaking" scenarios, and as a result the ensuing descent gives rise to an inflationary epoch that begins when the system is still well off its eventual attractor. If a pre-inflationary climbing phase of this type had occurred within 6-7 e-folds of the horizon exit for the largest observable wavelengths, displacement off the attractor and initial-state effects would conspire to suppress power in the primordial scalar spectrum, enhancing it in the tensor spectrum and typically superposing oscillations on both. We investigate these imprints on CMB observables over a range of parameters, examine their statistical significance, and provide a semi-analytic rationale for our results. It is tempting to ascribe at least part of the large-angle anomalies in the CMB to pre-inflationary dynamics of this type.Comment: 38 pages, LaTeX, 11 eps figures, references added, matches version to appear in JCA

Geometrization of Quantum Mechanics

We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified geometrical description for the different pictures of Quantum Mechanics. This construction provides an alternative to the usual GNS construction for pure states.Comment: 16 pages. To appear in Theor. Math. Phys. Some typos corrected. Definition 2 in page 5 rewritte