Nonrelativistic fermions in magnetic fields: a quantum field theory approach

The statistical mechanics of nonrelativistic fermions in a constant magneti c field is considered from the quantum field theory point of view. The ferm ionic determinant is computed using a general procedure that is compatible with the all reasonable regularization procedures. The nonrelativistic gran d-potential can be expressed in terms polylogarithm functions, whereas the partition function in 2 + 1 dimensions and vanishing chemical potential can be compactly written in terms of the Dedekind eta function. The strong and weak magnetic fields limits are easily studied in the latter case by using the duality properties of the Dedekind function. (C) 2001 Elsevier Science B.V. All rights reserved.