Books and Refereed Book Chapters
Heat Kernel on Lie Groups and Maximally Symmetric Spaces, Frontiers in Mathematics (Springer, 2023)
Heat Kernel Method and Its Applications, (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 gravity, Physica Scripta (2024), DOI 10.1088/1402-4896/ad28a2; 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]