arXiv subjects

Marcelo R. Ubriaco

Publications and source records attributed to Marcelo R. Ubriaco.

22 records · Page 2Linked to original sources

arXiv1996

High and low temperature behavior of a quantum group fermion gas

We consider the simplest $SU_{q}(2)$ invariant fermionic hamiltonian and calculate the low and high temperature behavior for the two distinct cases $q>1$ and $q<1$. For low temperatures we find that entropy values for the Fermi case are an upper bound for those corresponding to $q\neq 1$. At high temperatures we find that the sign of the second virial coefficient depends on $q$, and vanishes at $q=1.96$. An important consequence of this fact is that the parameter $q$ connects the fermionic and bosonic regions, showing therefore that $SU_{q}(2)$ fermions exhibit fractional statistics in three spatial dimensions.

hep-th↗

arXiv1996

Thermodynamics of a free $SU_q(2)$ fermionic system

We calculate the partition function, average occupation number and internal energy for a $SU_q(2)$ fermionic system and compare this model at $T=0$ with the ordinary fermionic, $q=1$, case. At low temperatures and $q\gg 1$ we find the chemical potential $μ$ to have the same temperature dependence than the Fermi case. For $q\ll 1$, the function $μ(T)$ has in addition a linear dependence on $T$.

hep-th↗

arXiv1994

Complex $q$-Analysis and Scalar Field Theory on a $q$-Lattice

We develop the basic formalism of complex $q$-analysis to study the solutions of second order $q$-difference equations which reduce, in the $q\rightarrow 1$ limit, to the ordinary Laplace equation in Euclidean and Minkowski space. After defining an inner product on the function space we construct and study the properties of the solutions, and then apply this formalism to the Schrödinger equation and two-dimensional scalar field theory.

hep-th↗

arXiv1993

Quantum Group Schrödinger Field Theory

We show that a quantum deformation of quantum mechanics given in a previous work is equivalent to quantum mechanics on a nonlinear lattice with step size $Δx=~(1-q)x$. Then, based on this, we develop the basic formalism of quantum group Schrödinger field theory in one spatial quantum dimension, and explicitly exhibit the $SU_{q}(2)$ covariant algebras satisfied by the $q$-bosonic and $q$-fermionic Schrödinger fields. We generalize this result to an arbitrary number of fields.

hep-th↗