Temperature in Fermion Systems and the Chiral Fermion Determinant

Details Temperature in Fermion Systems and the Chiral Fermion Determinant Temperature in Fermion Systems and the Chiral Fermion Determinant

1998-11-10

arxiv.org/abs/hep-th/9811094v5

Phys.Rev. D61 (2000) 055001

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, some figures, to be published in Phys.Rev.D

Scientific paper

10.1103/PhysRevD.61.055001

We give an interpretation to the issue of the chiral determinant in the heat-kernel 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: $|$4 dim electron momentum$|$ $\ll$ $|M|$ $\ll$ ultraviolet cut-off, naturally appears. The chiral anomaly is explicitly derived for the 2 dim Abelian model. Typically two different regularizations appear depending on the choice of propagators. One corresponds to the chiral theory, the other to the non-chiral (hermitian) theory.

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