Path integral approach to the nonextensive canonical density matrix

Feynman's path integral is herein generalized to the nonextensive canonical density matrix based on Tsallis entropy. This generalization is done in tw o ways by using unnormalized and normalized constraints. Firstly, we consid er the path integral formulation with unnormalized constraints, and this ge neralization is worked out through two different ways, which are shown to b e equivalent. These formulations with unnormalized constraints are solution s to the two generalized Bloch equations proposed in this work. The first f orm of the generalized Bloch equation is linear, but with a temperature-dep endent effective Hamiltonian; the second form is nonlinear and resembles th e anomalous correlated diffusion equation (porous medium equation). Further more, we can extend these results to the prescription of field theory using integral representations. The second development is dedicated to analyzing the path integral formulation with normalized constraints. To illustrate t he methods introduced here, we analyze the free particle case and a non-int eracting scalar field. The results herein obtained are expected to be usefu l in the discussion of generic nonextensive contexts. (C) 2000 Elsevier Sci ence B.V. All rights reserved.