Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-12-16
Annals Phys. 250 (1996) 1-50
Physics
High Energy Physics
High Energy Physics - Theory
Plain TeX, 48 pages
Scientific paper
10.1006/aphy.1996.0086
We use the $\zeta$-function regularization and an integral representation of the complex power of a pseudo differential operator, to give an unambiguous definition of the determinant of the Dirac operator. We bring this definition to a workable form by making use of an asymmetric Wigner representation. The expression so obtained is amenable to several treatments of which we consider in detail two, the inverse mass expansion and the gradient expansion, with concrete examples. We obtain explicit closed expressions for the corresponding Seeley-DeWitt coefficients to all orders. The determinant is shown to be vector gauge invariant and to posses the correct axial and scale anomalies. The main virtue of our approach is that it is conceptually simple and systematic and can be extended naturally to more general problems (bosonic operators, gravitational fields, etc). In particular, it avoids defining the real and imaginary parts of the effective action separately. In addition, it does not reduce the problem to a bosonic one to apply heat kernel nor performs further analytical rotations of the fields to make the Dirac operator Hermitian. We illustrate the flexibility of the method by studying some interesting cases.
Arriola Enrique Ruiz
Salcedo L. L.
No associations
LandOfFree
Wigner transformation for the determinant of Dirac operators does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Wigner transformation for the determinant of Dirac operators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Wigner transformation for the determinant of Dirac operators will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-46362