A non covariant fermionic determinant and its connection to Luttinger systems

ANÍBAL IUCCI, CARLOS M. NAÓN

JOURNAL OF PHYSICS. A - MATHEMATICAL AND GENERAL

IOP

Lugar: Bristol, UK; Año: 2005 vol. 38 p. 749 - 758

0305-4470

We consider a fermionic determinant associated to a non covariant Quantum Field Theory used to describe a non relativistic system in (1+1) dimensions. By exploiting the freedom that arises when Lorentz invariance is not mandatory, we determine the heat-kernel regulating operator so as to reproduce the correct dispersion relations of the bosonic excitations. We also derive the Hamiltonian of the functionally bosonized model and the corresponding currents. In this way we were able to establish the precise heat-kernel regularization that yields complete agreement between the path-integral and operational approaches to the bosonization of the Tomonaga-Luttinger model.