I discuss the concept of quasi-state decompositions for ground states and equilibrium states of quantum spin systems. Some recent results on the ground states of a class of one-dimensional quantum spin models are summarized and new work in progress is presented. I also outline some challenging open problems and conjectures. INTRODUCTION The aim of this contribution is threefold. First I would l...

We point out that R ≡ Br(b → dγ)/Br(b → sγ) is a sensitive probe of possible violation of CKM unitarity. We compute R in a minimal extension of the Standard Model containing an additional isosinglet charge (−1/3) quark, which leads to a deviation from CKM unitarity. CERN-TH. 7294/94 June 1994 ♥) [email protected] ♣) [email protected] ♦) [email protected] *) On leave of absenc...

We study the action of a relatively hyperbolic group on its boundary, by methods of symbolic dynamics. Under a condition on the parabolic subgroups, we show that this dynamical system is finitely presented. We give examples where this condition is satisfied, including geometrically finite kleinian groups. Associated to any word-hyperbolic group Γ, there is a dynamical system arising from the ac...

A supersymmetric theory in two-dimensions has enough data to define a noncommutative space thus making it possible to use all tools of noncommutative geometry. In particular, we apply this to the N = 1 supersymmetric non-linear sigma model and derive an expression for the generalized loop space Dirac operator, in presence of a general background, using canonical quantization. The spectral actio...

We use the results of integrable field theory to determine the universal amplitude ratios in the two-dimensional Ising model. In particular, the exact values of the ratios involving amplitudes computed at nonzero magnetic field are provided. Work supported by the European Union under contract FMRX-CT96-0012 Universality is one of the most fascinating concepts of statistical mechanics [1]. Brief...

We compute the photon asymmetry for near threshold parity violating (PV) pion photoproduction through sub-leading order. We find a potentially significant contribution from new PV low-energy constants not considered previously. We observe that a measurement of this asymmetry may help clarify the theoretical intepretation of backward angle PV electron-proton scattering, provided that the PV πNN ...

We calculate in chiral perturbation theory the parity-violating two-pion exchange nucleon-nucleon potentials at leading one-loop order. At a distance of r = m−1 π ≃ 1.4 fm they amount to about ±16% of the parity-violating 1π-exchange potential. We evaluate also the parity-violating effects arising from 2π-exchange with excitation of virtual ∆(1232)-isobars. These come out to be relatively small...

I review and discuss some recent developments in non-perturbative approaches to quantum gravity, with an emphasis on discrete formulations, and those coming from a classical connection description. 1 Invited talk at the 12th Italian Conference on General Relativity and Gravitational Physics, Roma, September 23-27, 1996. 1 Quantizing gravity The subject of this talk are several more or less deve...

Commutators originated over 100 years ago as a by-product of computing group characters of nonabelian groups. They are now an established and immensely useful tool in all of group theory. Commutators became objects of interest in their own right soon after their introduction. In particular, the phenomenon that the set of commutators does not necessarily form a subgroup has been well documented ...