Books and Refereed Book Chapters
Heat Kernel Method and Its Applications, (Basel: Birkhauser, 2015)
Mathematical tools for calculation of the effective action in quantum gravity, in: New Paths Towards Quantum Gravity, Ed. B. Booss-Bavnbek, G. Esposito and M. Lesch, (Berlin, Springer, 2010), pp, 193-259; Preprint: arXiv:0812.3363 [hep-th]
Non-Laplace type operators on manifolds with boundary, in: Analysis, Geometry and Topology of Elliptic Operators, Eds. B. Booss-Bavnbek, S. Klimek, M. Lesch and W. Zhang (Singapore: World Scientific, 2006), pp. 119-152 Preprint: arXiv:math-ph/0509023
Reviews
Spectral asymptotics of elliptic operators on manifolds, Reviews in Mathematical Physics (2024), Preprint: arXiv:2301.08728 [math-ph]
Heat kernel approach in quantum field theory, Nuclear Physics B - Proceedings Supplement, 104 (2002) 3-32; Preprint: arXiv:math-ph/0107018
Covariant techniques for computation of the heat kernel, Reviews in Mathematical Physics, 11 (1999), 947-980, Preprint: arXiv:hep-th/9510206
Quantum and Relative Heat Invariants
Heat semigroups on Weyl algebra, Journal of Geometry and Physics, 161 (2021) 104044; Preprint: arXiv:2008.12344[math-ph]
Bogolyubov invariant via relative spectral invariants on manifolds, Journal of Mathematical Physics, 61 (2020) 032303, Preprint: arXiv:1909.09680 [math-ph]
Relative spectral invariants of elliptic operators on manifolds, Journal of Geometry and Physics, 150 (2020) 103599; Preprint: arXiv:1908.01265 [math-ph]
Quantum heat traces, Journal of Geometry and Physics, 112 (2017) 271-288; Preprint: arXiv:1611.03760 [math-ph]
(with B. J. Buckman), Heat determinant on manifolds, Journal of Geometry and Physics, 104 (2016) 64-88; Preprint: arXiv:1408.2265 [math-ph]
Heat Kernel on Homogeneous Bundles
Non-perturbative effective action in gauge theories and quantum gravity, Advances in Theoretical and Mathematical Physics 14 (2010) 309-333; Preprint: arXiv:0903.1295 [hep-th]
(with G. Fucci), Low-energy effective action in non-perturbative electrodynamics in curved spacetime, Journal of Mathematical Physics 50 (2009) 102302 ; Preprint: arXiv:0902.1541 [hep-th]
(with G. Fucci), Non-perturbative heat kernel asymptotics on homogeneous Abelian bundles, Communications in Mathematical Physics 291 (2009) 543-577 Preprint: arXiv:0810.4889 [math-ph]
Heat kernel on homogeneous bundles over symmetric spaces, Communications in Mathematical Physics, 288 (2009) 963-1006; Preprint: arXiv:math.AP/0701489
A new algebraic approach for calculating the heat kernel in quantum gravity, Journal of Mathematical Physics, 37 (1996) 374-394; Preprint: arXiv:hep-th/9406047
The heat kernel on symmetric spaces via integrating over the group of isometries, Physics Letters B, 336 (1994) 171-177; Preprint: arXiv:hep-th/9509079
Covariant algebraic method for calculation of the low-energy heat kernel, Journal of Mathematical Physics, 36 (1995) 5055-5070; Erratum: Journal of Mathematical Physics 39 (1998) 1720; Preprint: arXiv:hep-th/9503132
A new algebraic approach for calculating the heat kernel in gauge theories, Physics Letters B, 305 (1993) 27-34; Preprint
Non-commutative Geometry
(with R. Niardi), MOND via matrix general relativity, Physica Scripta (99) (2024) 034244; Preprint: arXiv:2309.14270 [gr-qc]
(with G. Fucci), Kinematics in matrix gravity, General Relativity and Gravitation, 41 (2009) 1407-1435; Preprint: arXiv:0802.3927 [gr-qc]
(with G. Fucci), Non-commutative corrections in spectral matrix gravity, Classical and Quantum Gravity 26 (2009) 045019 (24pp); Preprint: arXiv:0802.2557 [gr-qc]
(with G. Fucci), Non-commutative Einstein equations, Classical and Quantum Gravity, 25 (2008) 025005; Preprint: arXiv:0709.0015 [gr-qc]
Dirac operator in matrix geometry, International Journal of Geometric Methods in Modern Physics, 2 (2005) 227-264; Preprint: arXiv:math-ph/0502001
Gauged gravity via spectral asymptotics of non-Laplace type operators, Journal of High Energy Physics, 07 (2004) 030; Preprint: arXiv:hep-th/0406026
Matrix general relativity: a new look at old problems, Classical and Quantum Gravity, 21 (2004) 103-120; Preprint: arXiv:hep-th/0307140
A noncommutative deformation of general relativity, Physics Letters B, 576 (2003) 195-198; Preprint: arXiv:hep-th/0310009
Non-Laplace Type Differential Operators
(with T. Branson), A discrete leading symbol and spectral asymptotics for natural differential operators, Journal of Functional Analysis, 190 (2002) 292-337; Preprint: arXiv:hep-th/0109181
(with T. Branson), Heat kernel asymptotics of operators with non-Laplace principal part, Reviews in Mathematical Physics, 13 (2001) 847-890; Preprint: arXiv:math-ph/9905001
Heat Kernel on Manifolds with Boundary
Heat kernel asymptotics of Zaremba boundary value problem, Mathematical Physics, Analysis and Geometry, 7 (2004) 9-46, Preprint: arXiv:math-ph/0110020
(with G. Esposito), Gauge theories on manifolds with boundary, Communications in Mathematical Physics, 200 (1999) 495-543; Preprint: arXiv:hep-th/9710048
(with G. Esposito), Lack of strong ellipticity in Euclidean quantum gravity, Classical and Quantum Gravity, 15 (1998) 1141-1152; Preprint: arXiv:hep-th/9708163
Heat Kernel Asymptotics
A covariant technique for the calculation of the one-loop effective action, Nuclear Physics B, 355 (1991) 712-754; Preprint; Erratum: Nuclear Physics B, 509 (1998) 557-558; Preprint
The covariant technique for calculation of the heat kernel asymptotic expansion, Physics Letters B, 238 (1990) 92-97; Preprint
The nonlocal structure of one-loop effective action via partial summation of asymptotic expansion, Physics Letters B, 236 (1990) 443-449, Preprint
Higher-Order Differential Operators
Green functions of higher-order differential operators, Journal of Mathematical Physics, 39 (1998) 2889-2909; Preprint: arXiv:hep-th/9707040
Singularities of Green functions of the products of the Laplace-type operators, Physics Letters B, 403 (1997) 280-284; Preprint: hep-th/9703005
Korteweg-de Vries Hierarchy
Heat trace and functional determinant in one dimension, Journal of Mathematical Physics 55 (2014) 123501; Preprint: arXiv:1406.1499
(with R. Schimming), A new explicit expression for the Korteweg-de Vries hierarchy, Mathematische Nachrichten, 219 (2000) 45-64; Preprint: arXiv:solv-int/9710009
(with R. Schimming), Heat kernel coefficients to the matrix Schroedinger operator, Journal of Mathematical Physics, 36 (1995) 5042-5054; Preprint: arXiv:hep-th/9501026
Yang-Mills Theory
(with S. Collopy), Thermal Yang-Mills Theory in Einstein Universe, Journal of Physics A:Mathematical and Theoretical, 45 (2012) 374009; Preprint: arXiv:1201.5163, 23pp
(with S. Collopy), Effective Action and Phase Transitions in Thermal Yang-Mills Theory on Spheres, Communications in Mathematical Physics, 311 (2012) 713-753; Preprint: arXiv:1012.2414 [hep-th]
A model of stable chromomagnetic vacuum in higher-dimensional Yang-Mills theory, Fortschritte der Physik / Progress of Physics, 47 (1999) 433-455; Preprint: arXiv:hep-th/9604160
Covariant algebraic calculation of the one-loop effective potential in non-Abelian gauge theory and a new approach to stability problem, Journal of Mathematical Physics, 36 (1995) 1557-1571; Preprint: arXiv:gr-qc/9403035
Quantum Gravity
(with S. Collopy), One-loop quantum gravity in Einstein Universe, Journal of High Energy Physics, 11 (2015) 193, Preprint: arXiv:1509.00929 [hep-th], 50pp.
Asymptotic behaviour of the quantum theory of gravity with higher order derivatives, Yadernaya Fizika, 44 (1986) 255-263, [in Russian]; Soviet Journal of Nuclear Physics, 44 (1986) 160-164 [in English]