Temperature in Fermion Systems and the Chiral Fermion Determinant

We give an interpretation to the issue of the chiral determinant in the heatkernel approach. The extra dimension (5-th dimension) is interpreted as (inverse) temperature. The 1+4 dim Dirac equation is naturally derived by the Wick rotation for the temperature. In order to define a “good” temperature, we choose those solutions of the Dirac equation which propagate in a fixed direction in the extra coordinate. This choice fixes the regularization of the fermion determinant. The 1+4 dimensional Dirac mass (M) is naturally introduced and the relation: |4 dim electron momentum| ≪ |M | ≪ ultraviolet cut-off, naturally appears. The chiral anomaly is explicitly derived for the 2 dim Abelian model. Different regularizations appear depending on the choice of propagators. 1 On leave of absence from Department of Physics, University of Shizuoka, Yada 52-1, Shizuoka 422-8526, Japan (Address after Nov.6, 1998). E-mail address: [email protected]