Modern Physics Letters A

An approach is proposed enabling to effectively describe the behavior of a bosonic system. The approach uses the quantum group GL_p,q(2) formalism. Indeed, considering a bosonic Hamiltonian in terms of the GL_p,q(2) generators, it is shown that its thermodynamic properties are connected to deformation parameters p and q. For instance, the average number of particles and the pressure have been computed. If p is fixed to be the same value for q, our approach coincides perfectly with some results developed recently in this subject. The ordinary results, of the present system, can be found when we take the limit p = q = 1.

After a brief review of classical probability theory (measure theory), we present an observation (due to Sorkin) concerning an aspect of probability in quantum mechanics. Following Sorkin, we introduce a generalized measure theory based on a hierarchy of "sum-rules". The first sum-rule yields classical probability theory, and the second yields a generalized probability theory that includes quantum mechanics as a special case. We present some algebraic relations involving these sum-rules. This may be useful for the study of the higher-order sum-rules and possible generalizations of quantum mechanics. We conclude with some open questions and suggestions for further work.

The formalism of space–time dependent Lagrangians developed in Ref. 1 is applied to the sine-Gordon and massive Thirring models. It is shown that the well-known equivalence of these models (in the context of weak–strong duality) can be understood in this approach from the same considerations as described in Ref. 1 for electromagnetic duality. A further new result is that all these can naturally be linked to the fact that the holographic principle has analogues at length scales much larger than quantum gravity. There is also the possibility of noncommuting coordinates residing on the boundaries.

The relation between BRST cohomology and the N = 1 supersymmetric Yang–Mills action in four dimensions is discussed. In particular, it is shown that both off- and on-shell N = 1 SYM actions are related to a lower-dimensional field polynomial by solving the descent equations, which is obtained from the cohomological analysis of linearized Slavnov–Taylor operator ℬ, in the framework of algebraic renormalization. Furthermore we show that off- and on-shell solutions differ only by a ℬ-exact term, which is a consequence of the fact that the cohomology of both cases are the same.

We perform Monte–Carlo simulations of a three-dimensional spin system with a Hamiltonian which contains only four-spin interaction term. This system describes random surfaces with extrinsic curvature – gonihedric action. We study the anisotropic model when the coupling constants β_S for the space-like plaquettes and β_T for the transverse-like plaquettes are different. In the two limits β_S = 0 and β_T = 0 the system has been solved exactly and the main interest is to see what happens when we move away from these points towards the isotropic point, where we recover the original model. We find that the phase transition is of first order for β_T = β_S ≈ 0.25, while away from this point it becomes weaker and eventually turns to a crossover. The conclusion which can be drawn from this result is that the exact solution at the point β_S = 0 in terms of 2D-Ising model should be considered as a good zero-order approximation in the description of the system also at the isotropic point β_S = β_T and clearly confirms the earlier findings that at the isotropic point the original model shows a first-order phase transition.