Large Mass Invariant Asymptotics of the Effective Action

Details Large Mass Invariant Asymptotics of the Effective Action Large Mass Invariant Asymptotics of the Effective Action

2001-06-25

arxiv.org/abs/hep-th/0106226v2

Phys.Rev. D64 (2001) 087701

Physics

High Energy Physics

High Energy Physics - Theory

5 pages, revtex, no figures

Scientific paper

10.1103/PhysRevD.64.087701

We study the large mass asymptotics of the Dirac operator with a nondegenerate mass matrix m={diag}(m_1,m_2,m_3) in the presence of scalar and pseudoscalar background fields taking values in the Lie algebra of the U(3) group. The corresponding one-loop effective action is regularized by the Schwinger's proper-time technique. Using a well-known operator identity, we obtain a series representation for the heat kernel which differs from the standard proper-time expansion, if m_1\ne m_2\ne m_3. After integrating over the proper-time we use a new algorithm to resum the series. The invariant coefficients which define the asymptotics of the effective action are calculated up to the fourth order and compared with the related Seeley-DeWitt coefficients for the particular case of a degenerate mass matrix with m_1=m_2=m_3.

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