The q-deformed statistics for fermions arising within the non-extensive thermostatistical formalism has been applied to the study of various quantum many-body systems recently. The aim of the present note is to point out some subtle difficulties presented by this approach in connection with the problem of thermodynamic consistency. Different possible ways to apply the q-deformed quantum distributions in a thermodynamically consistent way are considered.

Boundary conditions on an extra-dimensional interval can be chosen to break bulk gauge symmetries and to reduce the rank of the gauge group. We consider this mechanism in models with gauge trinification. We determine the boundary conditions necessary to break the trinified gauge group directly down to that of the standard model. Working in an effective theory for the gauge symmetry-breaking parameters on a boundary, we examine the limit in which the GUT-breaking sector is Higgsless and show how one may obtain the low-energy particle content of the minimal supersymmetric standard model. We find that gauge unification is preserved in this scenario, and that the differential gauge coupling running is logarithmic above the scale of compactification. We compare the phenomenology of our model to that of four-dimensional trinified theories.

Recently a version of Lorentz-conserving noncommutative field theory (NCFT) has been suggested. The underlying Lie algebra of the theory is the same as that of Doplicher, Fredenhagen, and Roberts. In Lorentz-conserving NCFT the matrix parameter θ µν which characterizes the canonical NCFT's is promoted to an operatorθ µν that transforms as a Lorentz tensor. In this paper, we calculate phenomenological consequences of the QED version of this theory by looking at various collider processes. In particular we calculate modifications to Møller scattering, Bhabha scattering, e + e − → µ + µ − and e + e − → γγ. We obtain bounds on the noncommutativity scale from the existing experiments at LEP and make predictions for what may be seen in future collider experiments.

The generalized non-extensive statistics proposed by Tsallis have been successfully utilized in many systems where long range interactions are present. For high density quark matter an attractive long range interaction arising from single gluon exchange suggests the formation of a diquark condensate. We study the effects on this color superconducting phase for two quark flavors due to a change to Tsallis statistics. By numerically solving the gap equation we obtain a generalization of the universality condition, 2φ 0 T C ≈ 3.52 and determine the temperature dependence of the gap. For the Tsallis parameter q ≈ 1 the specific heat is exponential becoming more linear as q increases. This suggests that for larger values of q s-wave color superconductors behave like high T c superconductors rather than weak superconductors.