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IVAN AVRAMIDI
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    • Math 132: Calculus II
    • MATH 231: Calculus III
    • MATH 332: Vector Analysis
    • MATH 335: Ordinary Differential Equations
    • MATH 352: Basic Concepts of Mathematics
    • MATH 372: Basic Concepts of Analysis
    • MATH 435: Complex Analysis
    • MATH 436: Complex Analysis
    • MATH 442: Introduction to Differential Geometry
    • MATH 454: Linear Algebra
    • MATH 471: Real Analysis
    • MATH 535: Methods of Mathematical Physics
    • MATH 536: Methods of Mathematical Physics
    • MATH 542: Topics in Differential Geometry
    • MATH 581: Introduction to Quantum Field Theory
    • Academic Honesty Policy
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IVAN AVRAMIDI
  • Home
  • CV
    • CV
    • Academic Profile
    • Publication List
    • Research Statement
    • Research Proposal
    • Teaching Statement
  • Research
    • Research
    • Interests
    • Conferences
    • Colloquia
    • Seminars
    • Citations
  • Books
  • Publications
    • Publications
    • Complete List
    • Notes
    • LaTeX
  • Advising
  • Teaching
    • Teaching
    • Math 132: Calculus II
    • MATH 231: Calculus III
    • MATH 332: Vector Analysis
    • MATH 335: Ordinary Differential Equations
    • MATH 352: Basic Concepts of Mathematics
    • MATH 372: Basic Concepts of Analysis
    • MATH 435: Complex Analysis
    • MATH 436: Complex Analysis
    • MATH 442: Introduction to Differential Geometry
    • MATH 454: Linear Algebra
    • MATH 471: Real Analysis
    • MATH 535: Methods of Mathematical Physics
    • MATH 536: Methods of Mathematical Physics
    • MATH 542: Topics in Differential Geometry
    • MATH 581: Introduction to Quantum Field Theory
    • Academic Honesty Policy
    • Homework Policy
  • Networks
  • Schedule
  • More
    • Home
    • CV
      • CV
      • Academic Profile
      • Publication List
      • Research Statement
      • Research Proposal
      • Teaching Statement
    • Research
      • Research
      • Interests
      • Conferences
      • Colloquia
      • Seminars
      • Citations
    • Books
    • Publications
      • Publications
      • Complete List
      • Notes
      • LaTeX
    • Advising
    • Teaching
      • Teaching
      • Math 132: Calculus II
      • MATH 231: Calculus III
      • MATH 332: Vector Analysis
      • MATH 335: Ordinary Differential Equations
      • MATH 352: Basic Concepts of Mathematics
      • MATH 372: Basic Concepts of Analysis
      • MATH 435: Complex Analysis
      • MATH 436: Complex Analysis
      • MATH 442: Introduction to Differential Geometry
      • MATH 454: Linear Algebra
      • MATH 471: Real Analysis
      • MATH 535: Methods of Mathematical Physics
      • MATH 536: Methods of Mathematical Physics
      • MATH 542: Topics in Differential Geometry
      • MATH 581: Introduction to Quantum Field Theory
      • Academic Honesty Policy
      • Homework Policy
    • Networks
    • Schedule

Publications

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. 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]

  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

 Reviews 

  1. Spectral asymptotics of elliptic operators on manifolds, Reviews in Mathematical Physics, 36 (2024) No 5, 2450007, Preprint: arXiv:2301.08728 [math-ph] 

  2. Heat kernel approach in quantum field theory, Nuclear Physics B - Proceedings Supplement, 104 (2002) 3-32; Preprint: arXiv:math-ph/0107018

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

SUSY Quantum Mechanics 

  1. On zero energy states in SUSY quantum mechanics on manifolds, Preprint: arXiv:2502.09040[math-ph] 

 Quantum and Relative Heat Invariants 

  1. Heat semigroups on Weyl algebra, Journal of Geometry and Physics, 161 (2021) 104044; Preprint: arXiv:2008.12344[math-ph]

  2. Bogolyubov invariant via relative spectral invariants on manifolds, Journal of Mathematical Physics, 61 (2020) 032303, Preprint: arXiv:1909.09680 [math-ph]

  3. Relative spectral invariants of elliptic operators on manifolds, Journal of Geometry and Physics, 150 (2020) 103599; Preprint: arXiv:1908.01265 [math-ph]

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

  5. (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 Warped Products

  1. Heat kernel on warped products, Preprint: arXiv:2506.0765[math-ph] 

Heat Kernel on Homogeneous Bundles

  1. 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]

  2. (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] 

  3. (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]

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

  5. 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

  6. 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

  7. 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

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

Non-commutative Geometry

  1. (with R. Niardi), MOND via matrix general relativity, Physica Scripta (99) (2024) 034244; Preprint: arXiv:2309.14270 [gr-qc]   

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

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

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

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

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

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

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

Non-Laplace Type Differential Operators

  1. (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

  2. (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 

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

  2. (with G. Esposito), Gauge theories on manifolds with boundary, Communications in Mathematical Physics, 200 (1999) 495-543;  Preprint: arXiv:hep-th/9710048

  3. (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

  1. 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 

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

  3. 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 

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

  2. 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 

  1. Heat trace and functional determinant in one dimension, Journal of Mathematical Physics 55 (2014) 123501; Preprint: arXiv:1406.1499

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

  3. (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 

  1. (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

  2. (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]

  3. 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

  4. 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 

  1. (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. 

  2. 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]

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

Quantum Mechanics

  1. (with R. Niardi), Geometric deformation of quantum mechanics, Preprint: arXiv:2412.08007 [quant-ph] 

Higher Spin Fields  

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


Copyright © Ivan G. Avramidi; Contact: Department of Mathematics, New Mexico Tech, Socorro, NM 87801, USA; Phone: +1 (575)-835-5638; Fax: +1 (575)-835-5366; Email: ivan.avramidi@nmt.edu
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