A Closed Formula for the Riemann Normal Coordinate Expansion

We derive an integral representation whichencodes all coefficients of the Riemann normalcoordinate expansion and also a closed formula for thosecoefficients.

[1]  I. Khriplovich,et al.  Normal coordinates along a geodesic , 1983 .

[2]  V. K. Patodi,et al.  On the heat equation and the index theorem , 1973 .

[3]  M. Shifman.  Wilson Loop in Vacuum Fields , 1980 .

[4]  P. Amsterdamski,et al.  b 8 'Hamidew' coefficient for a scalar field , 1989 .

[5]  D. Perret-Gallix,et al.  New computing techniques in physics research IV : proceedings of the Fourth international Workshop on Software Engineering, Artificial Intelligence, and Expert Systems in High Energy and Nuclear Physics, April 3-8, 1995, Pisa, Italy , 1995 .

[6]  C. Schubert,et al.  The Higher Derivative Expansion of the Effective Action by the String Inspired Method, II , 1997, hep-th/9707189.

[7]  Julian Schwinger,et al.  On gauge invariance and vacuum polarization , 1951 .

[8]  A. V. D. Ven,et al.  Renormalization of generalized two-dimensional nonlinear σ models , 1986 .

[9]  A. V. D. Ven.  Index-free heat kernel coefficients , 1997, hep-th/9708152.

[10]  On the Calculation of Effective Actions by String Methods , 1993, hep-th/9309055.

[11]  M Lüscher,et al.  Dimensional regularisation in the presence of large background fields , 1982 .

[12]  G. Herglotz.  Über die Bestimmung eines Linienelementes in Normalkoordinaten aus dem Riemannschen Krümmungstensor , 1925 .

[13]  I. Holopainen.  Riemannian Geometry , 1927, Nature.

[14]  B. M. Fulk.  MATH , 1992 .

[15]  D. Friedan,et al.  Nonlinear models in 2 + ε dimensions☆ , 1985 .

[16]  Trace anomalies from quantum mechanics , 1992, hep-th/9208059.

[17]  D. Freedman,et al.  The background field method and the ultraviolet structure of the supersymmetric nonlinear σ-model , 1981 .

[18]  Ivan G. Avramidi,et al.  The Covariant Technique for Calculation of One Loop Effective Action , 1991 .