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We consider the heat kernel for higher-derivative and nonlocal operators in $d$-dimensional Euclidean space-time and its asymptotic behavior.
J. Hadamard, Le Problème de Cauchy et les Èquations aux dÉrivées Partielles Linéaires Hyperboliques (Hermann et Cie, Paris, 1932)
1932
Earlier work this paper cites.
E. M. Wright, “The asymptotic expansion of the generalized hypergeometric function,” J. London Math. Soc. 10
1935
Earlier work this paper cites.
V. Fock, “Die Eigenzeit in der Klassischen- und in der Quantennechanik,” Phys. Z. Sowjetunion 12
1937
Earlier work this paper cites.
E. M. Wright, “The asymptotic expansion of the generalized hypergeometric function,” Proc. London Math. Soc. 46
1940
Earlier work this paper cites.
S. Minakshisundaram and A. Pleijel, “Some properties of the eigenfunctions of the Laplace-operator on Riemannian manifolds,” Can. J. Math. 1
1949
Earlier work this paper cites.
J. Schwinger, “On gauge invariance and vacuum polarization,” Phys. Rev. 82
1951
Earlier work this paper cites.
S. Minakshisundaram, “Eigenfunctions on Riemannian manifolds,” J. Indian Math. Soc. 17
1953
Earlier work this paper cites.
R. C. Thorne, “The asymptotic expansion of Legendre function of large degree and order,” Phil. Trans. R. Soc. A 249
1957
Earlier work this paper cites.
B. L. J. Braaksma, “Asymptotic expansions and analytic continuations for a class of Barnes-integrals,” Compositio Math. 15
1964
Earlier work this paper cites.
B. S. DeWitt, Dynamical Theory of Groups and Fields (Gordon and Breach, New York, 1965)
1965
Earlier work this paper cites.
R. T. Seeley, “Complex powers of an elliptic operator,” in Singular Integrals , Proc. Sympos. Pure Math., Vol. 10 (Amer. Math. Soc., Chicago, Ill, 1967) pp. 288–307
1967
Earlier work this paper cites.
P. B. Gilkey, “The spectral geometry of a Riemannian manifold,” J. Differ. Geom. 10
1975
Earlier work this paper cites.
C. DeWitt-Morette, “The semiclassical expansion,” Ann. Phys. (N.Y.) 97
1976
Earlier work this paper cites.
K. S. Stelle, “Renormalization of higher-derivative quantum gravity,” Phys. Rev. D16
1977
Earlier work this paper cites.
G. W. Gibbons, “Quantum field theory in curved spacetime,” in General Relativity. An Einstein Centenary Survey (Cambridge University Press, Cambridge, England, 1979) pp. 639–679
1979
Earlier work this paper cites.
P. B. Gilkey, “Recursion relations and the asymptotic behavior of the eigenvalues of the Laplacian,” Compositio Math. 38
1979
Earlier work this paper cites.
P. B. Gilkey, “The spectral geometry of the higher order Laplacian,” Duke Math. J. 47
1980
Earlier work this paper cites.
E. S. Fradkin and A. A. Tseytlin, “Renormalizable asymptotically free quantum theory of gravity,” Nucl. Phys. B201
1982
Earlier work this paper cites.
O. I. Marichev, Handbook of Integral Transforms of Higher Transcendental Functions: Theory and Algorithmic Tables (Ellis Horwood Limited, Chichester, 1983)
1983
Earlier work this paper cites.
I. Jack and H. Osborn, “Background field calculations in curved spacetime (I). General formalism and application to scalar fields,” Nucl. Phys. B234
1984
Earlier work this paper cites.
H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions (Ellis Horwood Limited, New York, 1984)
1984
Earlier work this paper cites.
I. Jack and L. Parker, “Proof of summed form of proper time expansion for propagator in curved space-time,” Phys. Rev. D31
1985
Earlier work this paper cites.
Choonkyu Lee and Chaiho Rim, “Background Fermi fields and Schwinger–DeWitt proper-time method,” Nucl. Phys. B255
1985
Earlier work this paper cites.
A. O. Barvinsky and G. A. Vilkovisky, “The generalized Schwinger–DeWitt technique in gauge theories and quantum gravity,” Phys. Rep. 119
1985
Earlier work this paper cites.
H. D. Fegan and P. Gilkey, “Invariants of the heat equation,” Pac. J. Math. 117
1985
Earlier work this paper cites.
I. G. Avramidy and A. O. Barvinsky, “Asymptotic freedom in higher-derivative quantum gravity,” Phys. Lett. B159
1985
Earlier work this paper cites.
Hae Won Lee and Pong Youl Pac, “Higher-derivative operators and DeWitt’s WKB ansatz,” Phys. Rev. D33
1986
Cited alongside, same era.
A. O. Barvinsky and G. A. Vilkovisky, “Beyond the Schwinger–DeWitt technique: Converting loops into trees and in-in currents,” Nucl. Phys. B282
1987
Cited alongside, same era.
Hae Won Lee, Pong Youl Pac, and Hyun Kuk Shin, “New algorithm for asymptotic expansions of the heat kernel,” Phys. Rev. D35
1987
Cited alongside, same era.
M. V. Fedoryuk, Asymptotics: Integrals and Series (Nauka, Moscow, 1987) (in Russian)
1987
Cited alongside, same era.
V. P. Gusynin, “New algorithm for computing the coefficients in the heat kernel expansion,” Phys. Lett. B225
1989
Cited alongside, same era.
R. Gorenflo, Y. Luchko, and F. Mainardi, “Wright functions as scale-invariant solutions ot the diffusion-wave equation,” Journal of computational and applied mathematics 118
2000
Later among the works it cites.
F. Mainardi, Y. Luchko, and G. Pagnini, “The fundamental solution of the space-time fractional diffusion equation,” Fractional Calculus Appl. Anal. 4
2001
Later among the works it cites.
I. G. Avramidi, “Heat kernel approach in quantum field theory,” Nucl. Phys. B, Proc. Suppl. 104
2002
Later among the works it cites.
A. A. Kilbas, M. Saigo, and J. J. Trujillo, “On the generalized Wright function,” Fractional Calculus Appl. Anal. 5
2002
Later among the works it cites.
A. O. Barvinsky, Yu. V. Gusev, V. F. Mukhanov, and D. V. Nesterov, “Nonperturbative late time asymptotics for the heat kernel in gravity theory,” Phys. Rev. D68
2003
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A. O. Barvinsky and G. A. Vilkovisky, “Covariant perturbation theory (II). Second order in the curvature. General algorithms,” Nucl. Phys. B333
1990
Cited alongside, same era.
V. P. Gusynin, “Seeley–Gilkey coefficients for fourth-order operators on a Riemannian manifold,” Nucl. Phys. B333
1990
Cited alongside, same era.
P. B. Gilkey, Th. P. Branson, and S. A. Fulling, “Heat equation asymptotics of “nonminimal” operators on differential forms,” J. Math. Phys. (N.Y.) 32
1991
Cited alongside, same era.
V. P. Gusynin, “Asymptotics of the heat kernel for nonminimal differential operators,” Ukr. Math. J. 43
1991
Cited alongside, same era.
V. P. Gusynin and E. V. Gorbar, “Local heat kernel asymptotics for nonminimal differential operators,” Phys. Lett. B270
1991
Cited alongside, same era.
V. P. Gusynin, E. V. Gorbar, and V. V. Romankov, “Heat kernel expansion for nonminimal differential operations and manifolds with torsion,” Nucl. Phys. B362
1991
Cited alongside, same era.
1993
Cited alongside, same era.
Later among the works it cites.
D. V. Vassilevich, “Heat kernel expansion: user’s manual,” Phys. Rep. 388
2003
Later among the works it cites.
P. B. Gilkey, Asymptotic Formulae in Spectral Geometry (Chapman and Hall/CRC, Boca Raton, London, New York, Washington, DC, 2003)
2003
Later among the works it cites.
C. Bär and S. Moroianu, “Heat kernel asymptotics for roots of generalized Laplacians,” Int. J. Math. 14
2003
Later among the works it cites.
M. A. Luty, M. Porrati, and R. Rattazzi, “Strong interactions and stability in the DGP model,” J. High Energy Phys. , 029 (2003) , arXiv:0303116 [hep-th]
2003
Later among the works it cites.
A. A. Kilbas and M. Saigo, H H -Transforms: Theory and Applications (Chapman and Hall/CRC, Boca Raton, London, New York, Washington, DC, 2004)
2004
Later among the works it cites.
A. V. Pskhu, Partial Differential Equations of Fractional Order (Nauka, Moscow, 2005) (in Russian)
2005
Later among the works it cites.
A. A. Kilbas, “Fractional calculus of the generalized Wright function,” Fractional Calculus Appl. Anal. 8
2005
Later among the works it cites.
A. O. Barvinsky and D. V. Nesterov, “Quantum effective action in spacetimes with branes and boundaries,” Phys. Rev. D73
2006
Later among the works it cites.
2010
Later among the works it cites.
A. M. Mathai, R. K. Saxena, and H. J. Haubold, The H H -Function: Theory and Applications (Springer, New York, Dordrecht, Heidelberg, London, 2010)
2010
Later among the works it cites.
2010
Later among the works it cites.
V. E. Tarasov, Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media (Springer, Heidelberg, Dordrecht, London, New York, 2010)
2010
Later among the works it cites.
L. Modesto, “Super-renormalizable multidimensional quantum gravity,” Astron. Rev. 8
2013
Later among the works it cites.
2014
Later among the works it cites.
2014
Later among the works it cites.
2015
Later among the works it cites.
2017
Later among the works it cites.
2017
Later among the works it cites.
2017
Later among the works it cites.
V. E. Tarasov, “Fractional Derivative Regularization in QFT,” Adv. High Energy Phys. 2018
2018
Later among the works it cites.