Heat kernel asymptotics of operators with non-laplace principal part

Reviews in Mathematical Physics

Volumn 13, Issue 7, 2001, Pages 847-890

  Avramidi, Ivan G ^a,b   Branson, Thomas ^a  

^a UNIVERSITY OF IOWA   (United States)

^b NEW MEXICO INSTITUTE OF MINING AND TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035596191     PISSN: 0129055X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129055X01000892     Document Type: Article

References (19)

1. S. Alexandrov and D. Vassilevich, "Heat kernel for nonminimal operators on a Kaehler manifold", J. Math. Phys. 37 (1996) 5715-5718.
2. I. G. Avramidi, "A covariant technique for the calculation of the one-loop efective action", Nucl. Phys. B355 (1991) 712-754.
3. I. G. Avramidi, "Green functions of higher-order differential operators", J. Math. Phys. 39 (1998) 2889-2909.
4. I. G. Avramidi, "Covariant techniques for computation of the heat kernel", Rev. Math. Phys. 11 (1999) 947-980.
5. I. G. Avramidi, Heat Kernel and Quantum Gravity, Lecture Notes in Physics, Series Monographs, LNP: m64. Berlin, New York, Springer-Verlag, 2000.
6. I. G. Avramidi and T. Branson, "A discrete leading symbol and spectral asymptotics for natural differential operators", Irvin Segal memorial volume (2001), to appear.
7. I. G. Avramidi and G. Esposito, "Gauge theories on manifolds with boundary", Comm. Math. Phys. 200 (1999) 495-543.
8. N. Berline, E. Getzler and M. Vergne, Heat Kernels and Dirac Operators, Berlin, New York, Springer-Verlag, 1992.
9. T. P. Branson, P. B. Gilkey and A. Pierzchalski, "Heat equation asymptotics of elliptic differential operators with non-scalar leading symbol", Math. Nachr. 166 (1994) 207-215.
10. H. T. Cho and R. Kantowski, "ζ-functions for nonminimal operators", Phys. Rev. D52 (1995) 4588-4599.
11. B. D. De Witt, "The spacetime approach to quantum field theory", pp. 383-738 in Relativity, Groups and Topology II, eds. B. S. De Witt and R. Stora, Amsterdam, North Holland, 1984.
12. P. B. Gilkey, Invariance Theory, the Heat Equation and the Atiyah-Singer Index Theorem, Boca Raton, CRC Press, 1995.
13. P. B. Gilkey, T. P. Branson and S. A. Fulling, "Heat equation asymptotics of 'nonminimal' operators on differential forms", J. Math. Phys. 32 (1991) 2089-2091.
14. V. P. Gusynin, "Asymptotics of the heat kernel for nonminimal differential operators", Ukrainian Math. Zh. 43 (1991) 1541-1551.
15. V. P. Gusinyn, "Heat kernel technique for nonminimal operators", pp. 65-86 in Heat Kernel Techniques and Quantum Gravity, eds. S. A. Fulling, Proceedings, Winnipeg, Manitoba, 1994. Discourses in Mathematics and Its Applications, vol. 4, College Station, Texas, Texas A&M University, 1995.
16. 4 for nonminimal operator on curved manifolds", Fund. Appl. Math. 5 (1999) 649-674.
17. J. Hadamard, "Lectures on Cauchy's problem", in Linear Partial Differential Equations, New Haven, Yale University Press, 1923.
18. V. D. Kupradze, Potential Methods in the Theory of Elasticity, Jerusalem, Israel program of Scientific Translation, 1965.
19. V. P. Maslov and M. V. Fedoriuk, Semi-classical Approximation in Quantum Mechanics, Boston, D. Reidel Pub. Co., 1981.