The thermal coupling constant and the gap equation in the λϕD4\lambda\phi^{4}_{D} model

By the concurrent use of two different resummation methods, the composite operator formalism and the Dyson-Schwinger equation, we re-examinate the behavior at finite temperature of the O(N)-symmetric $\lambda\phi^{4}$ model in a generic D-dimensional Euclidean space. In the cases D=3 and D=4, an analysis of the thermal behavior of the renormalized squared mass and coupling constant are done for all temperatures. It results that the thermal renormalized squared mass is positive and increases monotonically with the temperature. The behavior of the thermal coupling constant is quite different in odd or even dimensional space. In D=3, the thermal coupling constant decreases up to a minimum value diferent from zero and then grows up monotonically as the temperature increases. In the case D=4, it is found that the thermal renormalized coupling constant tends in the high temperature limit to a constant asymptotic value. Also for general D-dimensional Euclidean space, we are able to obtain a formula for the critical temperature of the second order phase transition. This formula agrees with previous known values at D=3 and D=4.Comment: 23 pages, 4 figure

Dimensional Reduction of Fermions in Brane Worlds of the Gross-Neveu Model

We study the dimensional reduction of fermions, both in the symmetric and in the broken phase of the 3-d Gross-Neveu model at large N. In particular, in the broken phase we construct an exact solution for a stable brane world consisting of a domain wall and an anti-wall. A left-handed 2-d fermion localized on the domain wall and a right-handed fermion localized on the anti-wall communicate with each other through the 3-d bulk. In this way they are bound together to form a Dirac fermion of mass m. As a consequence of asymptotic freedom of the 2-d Gross-Neveu model, the 2-d correlation length \xi = 1/m increases exponentially with the brane separation. Hence, from the low-energy point of view of a 2-d observer, the separation of the branes appears very small and the world becomes indistinguishable from a 2-d space-time. Our toy model provides a mechanism for brane stabilization: branes made of fermions may be stable due to their baryon asymmetry. Ironically, our brane world is stable only if it has an extreme baryon asymmetry with all states in this ``world'' being completely filled.Comment: 26 pages, 7 figure

Bessel Process and Conformal Quantum Mechanics

Different aspects of the connection between the Bessel process and the conformal quantum mechanics (CQM) are discussed. The meaning of the possible generalizations of both models is investigated with respect to the other model, including self adjoint extension of the CQM. Some other generalizations such as the Bessel process in the wide sense and radial Ornstein- Uhlenbeck process are discussed with respect to the underlying conformal group structure.Comment: 28 Page