Books and Refereed Book Chapters

  1. Heat Kernel Method and Its Applications, (Basel: Birkhauser, 2015)

  2. Heat Kernel and Quantum Gravity, (Berlin:  Springer,  2000)

  3. Mathemathical 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], 71pp,

  4. 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 

  5. Reviews

  6. Heat kernel approach in quantum field theory,
    Nuclear Physics B - Proceedings Supplement, 104 (2002) 3-32

    Preprint: arXiv:math-ph/0107018, 67pp

  7. Covariant techniques for computation of the heat kernel,
    Reviews in Mathematical Physics, 11 (1999), 947-980
    Preprint: arXiv:hep-th/9510206

  8. Asymptotics of Generalized Heat Invariants

  9. Quantum heat traces, Journal of Geometry and Physics, 112 (2017) 271-288;
  10. Preprint: arXiv:1611.03760 [math-ph], 33 pp

  11. (with B. J. Buckman),
    Heat determinant on manifolds, Journal of Geometry and Physics, 104 (2016) 64-88, DOI: 10.1016/j.geomphys.2016.02.004
    Preprint: arXiv:1408.2265 [math-ph], 41 pp

  12. Heat Kernel Asymptotics on Manifolds without Boundary

  13. A covariant technique for the calculation of the one-loop effective action,
    Nuclear Physics B, 355 (1991) 712-754;

    Erratum: Nuclear Physics B, 509 (1998) 557-558;

  14. The covariant technique for calculation of the heat kernel asymptotic expansion,
    Physics Letters B, 238 (1990) 92-97;


  15. Non-perturbative Heat Kernel Asymptotics on Homogeneous Bundles

  16. (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], 45 pp,

  17. (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] , 42pp

  18. Leading Derivatives in Heat Kernel Coefficients and Asymptotic Form of Zeta Determinant

  19. The nonlocal structure of one-loop effective action via partial summation of asymptotic expansion, 
    Physics Letters B, 236 (1990) 443-449


  20. Zaremba Boundary Value Problem

  21. Heat kernel asymptotics of Zaremba boundary value problem, 
    Mathematical Physics, Analysis and Geometry, 7 (2004) 9-46,
    Preprint: arXiv:math-ph/0110020, 

  22. Oblique Boundary Value Problem

  23. (with G. Esposito),
    Gauge theories on manifolds with boundary,
    Communications in Mathematical Physics, 200 (1999) 495-543

    Preprint: arXiv:hep-th/9710048

  24. (with G. Esposito),
    Lack of strong ellipticity in Euclidean quantum gravity,  
    Classical and Quantum Gravity, 15 (1998) 1141-1152;
    Preprint: arXiv:hep-th/9708163

  25. Higher-Order Differential Operators

  26. Green functions of higher-order differential operators,
    Journal of Mathematical Physics, 39 (1998) 2889-2909; 
    Preprint: arXiv:hep-th/9707040

  27. Singularities of Green functions of the products of the Laplace-type operators,
    Physics Letters B, 403 (1997) 280-284;
    Preprint: hep-th/9703005

  28. Korteweg-de Vries Hierarchy

  29. Heat trace and functional determinant in one dimension,
    Journal of Mathematical Physics 55 (2014) 123501; DOI: 10.1063/1.4902379;

    Preprint: arXiv:1406.1499, 25pp

  30. (with R. Schimming), 
    A new explicit expression for the Korteweg-de Vries hierarchy,
    Mathematische Nachrichten, 219 (2000) 45-64;
    Preprint: arXiv:solv-int/9710009

  31. (with R. Schimming), 
    Heat kernel coefficients to the matrix Schroedinger operator, 
    Journal of Mathematical Physics, 36 (1995) 5042-5054;
    Preprint: arXiv:hep-th/9501026

  32. Non-Laplace Type Differential Operators on Manifolds without Boundary

  33. (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

  34. (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

  35. Non-commutative Riemannian Geometry and General Relativity

  36. (with G. Fucci),
     Kinematics in matrix gravity,
    General Relativity and Gravitation, 41 (2009) 1407-1435
    Preprint: arXiv:0802.3927 [gr-qc], 31pp

  37. (with G. Fucci),
    Non-commutative corrections in spectral matrix gravity, 
    Classical and Quantum Gravity 26 (2009) 045019 (24pp)
    Preprint: arXiv:0802.2557 [gr-qc] , 32pp

  38. (with G. Fucci),
    Non-commutative Einstein equations, 
    Classical and Quantum Gravity, 25 (2008) 025005
    Preprint: arXiv:0709.0015 [gr-qc] , 17pp

  39. Dirac operator in matrix geometry,
    International Journal of Geometric Methods in Modern Physics, 2 (2005) 227-264
    Preprint: arXiv:math-ph/0502001, 45pp 

  40. Gauged gravity via spectral asymptotics of non-Laplace type operators,
    Journal of High Energy Physics, 07 (2004) 030
    Preprint: arXiv:hep-th/0406026 , 41pp

  41. Matrix general relativity: a new look at old problems, 
    Classical and Quantum Gravity, 21 (2004) 103-120
    Preprint: arXiv:hep-th/0307140 

  42. A noncommutative deformation of general relativity, 
    Physics Letters B, 576 (2003) 195-198
    Preprint: arXiv:hep-th/0310009 

  43. Heat Kernel on Homogeneous Bundles over Symmetric Spaces

  44. 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], 26pp

  45. Heat kernel on homogeneous bundles over symmetric spaces, 
    Communications in Mathematical Physics, 288 (2009) 963-1006
    Preprint: arXiv:math.AP/0701489

  46. 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

  47. 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

  48. 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

  49. A new algebraic approach for calculating the heat kernel in gauge theories,
    Physics Letters B, 305 (1993) 27-34;

  50. Yang-Mills Theory

  51. (with S. Collopy),
    Thermal Yang-Mills Theory in Einstein Universe,
    Journal of Physics A:Mathematical and Theoretical, 45 (2012) 374009; DOI:10.1088/1751-8113/45/37/374009
    Preprint:  arXiv:1201.5163, 23pp

  52. (with S. Collopy),
    Effective Action and Phase Transitions in Thermal Yang-Mills Theory on Spheres,
    Communications in Mathematical Physics, 311 (2012) 713-753, DOI: 10.1007/s00220-012-1418-y;
    Preprint: arXiv:1012.2414 [hep-th], 40pp

  53. 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, 24 pp.

  54. 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

  55. Quantum Gravity

  56. (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.

  57. 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]

  58. (with A. O. Barvinsky),
    Asymptotic freedom in higher-derivative quantum gravity,
    Physics Letters B, 159 (1985) 269-274


  59. Higher Spin Fields 

  60. Gauge invariant theory of higher spin fields in curved space, 
    International Journal of Modern Physics A, 6 (1991) 1693-1700;

Ivan Avramidi