Publications


Online archive

    Books  

  1. I. G. Avramidi, 
    Heat Kernel and Quantum Gravity, 
    Lecture Notes in Physics, (Berlin: Springer-Verlag, 2000)
     

    Refereed Publications

  2. I. G. Avramidi and S. Collopy,
    Thermal Yang-Mills Theory in Einstein Universe,
    Journal of Physics A: Mathematical and Theoretical, (2012);
      arXiv:1201.5163 [hep-th], 22pp

  3. I. G. Avramidi and 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;
    arXiv:1012.2414 [hep-th], 40pp

  4. I. G. Avramidi, 
    Non-perturbative effective action in gauge theories and quantum gravity,
    Advances in Theoretical and Mathematical Physics 14 (2010) 309-333.
    arXiv:0903.1295 [hep-th]

  5. I. G. Avramidi, 
    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;
    arXiv:0812.3363 [hep-th], 71pp, by invitation

  6. G. Fucci and I. G. Avramidi,
    On the gravitationally induced Schwinger mechanism,
    In: Proceedings of the International Conference "Quantum Field Theory under the Influence of External Conditions" (QFEXT09). Eds. K. A. Milton and M. Bordag (Singapore: World Scientific, 2010), pp. 485-491

  7.  I. G. Avramidi and G. Fucci,
    Low-energy effective action in non-perturbative electrodynamics in curved spacetime,
    Journal of Mathematical Physics 50 (2009) 102302; DOI:10.1063/1.3239508;
    arXiv:0902.1541 [hep-th]

  8. I. G. Avramidi and G. Fucci,
    A model for the Pioneer anomaly,
    Canadian Journal of Physics 87 (2009) 1089–1093; DOI:10.1139/P09-076;
    arXiv:0811.1573 [gr-qc]

  9. I. G. Avramidi and G. Fucci,
    Non-perturbative heat kernel asymptotics on homogeneous abelian bundles,
    Communications in Mathematical Physics 291 (2009) 543-577, DOI: 10.1007/s00220-009-0804-6;
    arXiv:0810.4889 [math-ph]

  10. I. G. Avramidi and G. Fucci,
     Kinematics in matrix gravity,
    General Relativity and Gravitation, 41 (2009) 1407-1435; DOI: 10.1007/s10714-008-0713-6;

  11.  G. Fucci and I. G. Avramidi,
    Non-commutative corrections in spectral matrix gravity,
    Classical and Quantum Gravity 26 (2009) 045019, 24pp.,  DOI: 10.1088/0264-9381
    arXiv:0802.2557 [gr-qc]

  12. I. G. Avramidi,
    Heat kernel on homogeneous bundles over symmetric spaces,     
    Communications in Mathematical Physics, 288 (2009) 963-1006; DOI: 10.1007/s00220-008-0639-6 

  13. G. Fucci and I. G. Avramidi,
    Non-commutative Einstein equations, 
    Classical and Quantum Gravity, 25 (2008) 025005 

  14. I. G. Avramidi,
    Heat kernel on homogeneous bundles, 
    International Journal of Geometric Methods in Modern Physics, 5 (2008) 1-23

  15. I. G. Avramidi,
    Heat kernel asymptotics on symmetric spaces,
    Proc. Midwest Geometry Conference, Communications in Mathematical Analysis, Conf. 01 (2008) 1–10,
    arXiv:math.DG/0605762

  16. I. G. Avramidi,
    Non-Laplace type operators on manifolds with boundary    ,
    in: `` Analysis, Geometry and Topology of Elliptic Operators, Papers in Honor of Krzysztof P. Wojciechowski, '', Eds. B. Booss-Bavnbek, S. Klimek, M. Lesch and W. Zhang (Singapore: World Scientific, 2006), pp. 119-152; by invitation
    arXiv:math-ph/0509023

  17. I. G. Avramidi,
    Dirac operator in matrix geometry,
    International Journal of Geometric Methods in Modern Physics, 2 (2005) 227-264,   (special issue dedicated to the memory of Dmitri Ivanenko and Vladimir Fock), by invitation

  18. I. G. Avramidi,
    A note on contributions of Prof. Minakshisundaram to mathematical physics,
    Proc. of Andhra Pradesh Akademi of Sciences, , 8 (2004), 247-248 (special issue dedicated to the memory of Subbaramiah Minakshisundaram), by invitation

  19. I. G. Avramidi, 
    Gauged gravity via spectral asymptotics of non-Laplace type operators,
    Journal of High Energy Physics, 07 (2004) 030

  20. I. G. Avramidi, 
    Heat kernel asymptotics of Zaremba boundary value problem,
    Mathematical Physics, Analysis and Geometry, 7 (2004) 9-46

  21. I. G. Avramidi,
    Matrix general relativity: a new look at old problems,
    Classical and Quantum Gravity 20 (2003) 103-120

  22. I. G. Avramidi, 
    A noncommutative deformation of general relativity,
    Physics Letters B 576 (2003) 195-198

  23. I. G. Avramidi, 
    Heat kernel in quantum field theory,
    Nuclear Physics Proc. Suppl 104 (2002) 3-32 

  24. I. G. Avramidi and T. Branson, 
    A discrete leading symbol and spectral asymptotics for natural differential operators ,
    Journal of Functional Analysis, 190 (2002) 292-337

  25. I. G. Avramidi and T. Branson, 
    Heat kernel asymptotics of operators with non-Laplace principal part, 
    Reviews in Mathematical Physics 13 (2001) 847-890

  26. I. G. Avramidi and R. Schimming, 
    A new explicit expression for the Korteweg-De Vries hierarchy,  
    Mathematische Nachrichten, 219 (2000) 45-64

  27. I. G. Avramidi,  
    Covariant techniques for computation of the heat kernel, 
    Reviews in Mathematical Physics, 11 (1999) 947-980

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

  29. I. G. Avramidi,  
    One-loop effective potential in higher-dimensional Yang-Mills theory,  
    Fortschritte der Physik / Progress of Physics, 47 (1999) 4, 433-455

  30. I. G. Avramidi and G. Esposito,  
    Foundational Problems in Quantum Gravity, 
    in: Recent Developments in General Relativity, Eds. A. Masielo et al. (Berlin: Springer, 1999), pp. 395-404

  31. I. G. Avramidi and G. Esposito, 
    Heat kernel asymptotics of Gilkey-Smith boundary value problem,
    in: Trends in Mathematical Physics,  Eds. V. Alexiades and G. Siopsis, AMS/IP Studies in Advanced Mathematics, vol. 13, (American Mathematical Society and International Press, 1999), pp. 15-34, 
    math-ph/9812010

  32. I. G. Avramidi and G. Esposito, 
    On ellipticity and gauge invariance in Euclidean quantum gravity,   
    in: Trends in Mathematical Physics,  Eds. V. Alexiades and G. Siopsis, AMS/IP Studies in Advanced Mathematics, vol. 13, (American Mathematical Society and International Press, 1999), pp. 3-40, 
    hep-th/9810009  

  33. I. G. Avramidi,  
    Green functions of higher-order differential operators,  
    Journal of Mathematical Physics 39 (1998) 2889-2909

  34. I. G. Avramidi and G. Esposito,  
    Lack of strong ellipticity in Euclidean quantum gravity, 
    Classical and Quantum Gravity 15 (1998) 1141-1152

  35. I. G. Avramidi,  
    Nonperturbative methods for calculating the heat kernel, 
    in: Global Analysis, Differential Geometry and Lie Algebras, Ed. G. Tsagas, (Bucharest: Geometry Balkan Press, 1998), pp. 7-21; 
    hep-th/9602169

  36. I. G. Avramidi and G. Esposito, 
    New invariants in the one-loop divergences on manifolds with boundary, 
    Classical and Quantum Gravity 15 (1998) 281-297

  37. I. G. Avramidi,  
    Covariant approximation schemes for calculation of the heat kernel in quantum field theory, 
    in: Quantum Gravity,  Eds. V. A. Berezin, V. A. Rubakov and D. V. Semikoz, (Singapore: World Scientific, 1997), pp. 61-78; 
    hep-th/9509075

  38. I. G. Avramidi,  
    Singularities of Green functions of the products of the Laplace-type operators, 
    Physics Letters B 403 (1997) 280-284

  39. I. G. Avramidi, G. Esposito and A. Yu. Kamenshchik, 
    Axial gauge in Euclidean quantum gravity,
    in: `Constrained Dynamics and Quantum Gravity 1996', Eds: V. de Alfaro, J. E. Nelson, G. Bandelloni, A. Blasi, M. Cavaglia' and A. T. Filippov, Nucl. Physics B Proceedings Supplement 57 (1997), pp. 245-246

  40. I. G. Avramidi, G. Esposito and A. Yu. Kamenshchik, 
    Boundary operators in Euclidean quantum gravity, 
    Classical Quantum Gravity 13 (1996) 2361-2373

  41. I. G. Avramidi,  
    A new algebraic approach for calculating the heat kernel in quantum gravity, 
    Journal of Mathematical Physics 37 (1996) 374-394

  42. I. G. Avramidi and R. Schimming, 
    Algorithms for the calculation of the heat kernel coefficients, 
    in: `Quantum Field Theory under the Influence of External Conditions', Ed. M. Bordag, Teubner-Texte zur Physik, Band 30, (Stuttgart: Teubner, 1996), pp. 150-162; 
    hep-th/9510206  

  43. I. G. Avramidi, Covariant algebraic method for calculation of the low-energy heat kernel, 
    Journal of Mathematical Physics 36 (1995) 5055-5070

  44. I. G. Avramidi and R. Schimming,  
    Heat kernel coefficients to the matrix Schroedinger operator, 
    Journal of Mathematical Physics 36 (1995) 5042-5054

  45. I. G. Avramidi,  
    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 

  46. I. G. Avramidi,  
    New algebraic methods for calculating the heat kernel and the effective action in quantum gravity and gauge theories, 
    in: `Heat Kernel Techniques and Quantum Gravity', Ed. S. A. Fulling, Discourses in Mathematics and Its Applications, (College Station, Texas: Department of Mathematics, Texas A& M University, 1995), pp. 115-140; 
    hep-th/9408028  

  47. I. G. Avramidi,  
    The heat kernel on symmetric spaces via integrating over the group of isometries, 
    Physics Letters B 336 (1994) 171-177 

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

  49. I. G. Avramidi,  
    A method for calculating the heat kernel for manifolds with boundary,  
    Yadernaya Fizika 56 (1993) 245-252, [Russian]; 
    Physics of Atomic Nucleus 56 (1993) 138-142 [English] 

  50. I. G. Avramidi,  
    A covariant technique for the calculation of the one-loop effective action, 
    Nuclear Physics B 355 (1991) 712-754 

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

  52. I. G. Avramidi,  
    The covariant technique for calculation of the heat kernel asymptotic expansion, 
    Physics Letters B 238 (1990) 92-97 

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

  54. I. G. Avramidi,  
    Covariant methods of studying the nonlocal structure of an effective action, 
    Yadernaya Fizika, 49 (1989) 1185-1192, [Russian]; 
    Soviet Journal of Nuclear Physics , 49 (1989) 735-739 [English] 

  55. I. G. Avramidi,  
    Background field calculations in quantum field theory (vacuum polarization), 
    Teoreticheskaya i Matematicheskaya Fizika, 79 (1989) 219-231, [Russian];
    Theoretical and Mathematical Physics 79 (1989) 494-502 [English] 

  56. I. G. Avramidi,  
    Asymptotic behavior of the quantum theory of gravity with higher order derivatives, 
    Yadernaya Fizika, 44 (1986) 255-263, [Russian]; 
    Soviet Journal of Nuclear Physics, 44 (1986) 160-164 [English] 

  57. I. G. Avramidi and A. O. Barvinsky, 
    Asymptotic freedom in higher - derivative quantum gravity, 
    Physics Letters B 159 (1985) 269-274 

  58. I. G. Avramidi, B. G. Barabashov and G. G. Vertogradov, 
    A method of reducing the effect of multipath propagation on the accuracy of determining the angles of arrival of radiowaves,  
    Radiotekhnika, 9 (1983) 69-72, [Russian]; 
    Telecommunications and Radioengineering 9 (1983) 111-113 [English] 

    Preprints, Reports and Thesis
     

  59. I. G. Avramidi, 
    Analytic and Geometric Aspects of Heat Kenel Applications in Finance,   NATIXIS Corporate and Investment Bank, Paris, France, (2007), 249 pp.

  60. I. G. Avramidi and G. Esposito, 
    Universal Functions in Euclidean Quantum Gravity, 
    hep-th/9702150, 8 pp. 

  61. I. G. Avramidi,  
    The heat kernel approach for calculating the effective action in quantum field theory and quantum gravity, 
    University Greifswald (June, 1994), 
    hep-th/9509077, 21 pp. 

  62. I. G. Avramidi,  
    Covariant methods for calculating the low-energy effective action in quantum field theory and quantum gravity, 
    University of Greifswald (March, 1994), 
    gr-qc/9403036, 48 pp. 

  63. I. G. Avramidi,  
    Covariant Methods for the Calculation of the Effective Action in Quantum Field Theory and Investigation of Higher-Derivative Quantum Gravity, 
    PhD Thesis, Moscow State University (1986), Universal Decimal Code (UDC) 530.12:531.51, 178 pp. [Russian]; 
    hep-th/9510140, 159 pp. [English] 

  64. I. G. Avramidi,  
    Background field method in quantum theory,
    Moscow State University (1984), Deposited at VINITI (Soviet Institute for Scientific and Technical Information), No 1512-85 Dep., VINITI, Moscow, (1985), 41 pp., [in Russian]

     

    Conference Abstracts
     

  65. I. G. Avramidi,
    Noncommutative deformation of general relativity,
    in: International Congress of Mathematical Physics 2003, Lisbon, Book of Abstracts, (Lisbon, Portugal, 2003) 

  66. I. G. Avramidi,
    Heat kernel asymptotics of Zaremba boundary value problem,
    in: International Congress of Mathematicians, Beijing 2002, Aug. 20-28, Abstracts of Short Communications and Poster Sessions}, (Beijing: Higher Education Press, 2002), pp.~208--209  

  67. I. G. Avramidi,
    Heat kernel asymptotics of a non-smooth boundary-value problem,
    in: International Congress of Mathematical Physics 2000, London, Book of Abstracts}, (London, UK, 2000), p.~98  

  68. I. G. Avramidi,  
    Heat kernel asymptotics of a non-smooth boundary-value problem, 
    in: Abstracts of the International Conference `Workshop in Spectral Geometry', University of Bristol, Bristol, UK, 2000  

  69. I. G. Avramidi,  
    Heat kernel asymptotics of operators with non-Laplace principl part, 
    in: Abstracts of the International Conference `Workshop in Partial Differential Equations', University of Potsdam, Potsdam, Germany, 1999  

  70. I. G. Avramidi,  
    Heat kernel asymptotics of the Gilkey-Smith boundary value problem,
    in: Abstracts of `8th Intrnational Conference on Differential Equations and Mathematical Phyics', University of Alabama, Birmingham, Alabama, 1999  

  71. I. G. Avramidi,  
    Heat kernel as the basis for the functional integration in quantum field theory, 
    in: Functional Integration: Basics and Applications, Eds: C. DeWitt-Morette, P. Cartier and A. Folacci, NATO ASI Series, Series B: Vol. 361, (New York: Plenum Press, 1997), p. 413-413  

  72. I. G. Avramidi,  
    Effective potential in Yang-Mills theory and the stability of the chromomagnetic vacuum, 
    in: `Quantum Field Theory under the Influence of External Conditions', Ed. M. Bordag, Teubner-Texte zur Physik, Band 30, (Stuttgart: Teubner, 1996), pp. 168-169  

  73. I. G. Avramidi,  
    The low energy heat kernel and the effective action in semiclassical quantum gravity, 
    Abstracts of 14th International Conference General "Relativity and Gravitation", Florence, August 6-12, 1995, 2 pp.  

  74. I. G. Avramidi,  
    One-loop approximation in quantum theory of scalar, spinor and vector fields in external gravitational background field, 
    in: Modern theoretical and experimental problems of general relativity and gravitation, Abstracts of VIth Soviet Gravitational Conference, Ed. V. N. Ponomarev (Moscow: Moscow State Pedagogical Institute (MGPI), 1984), pp. 199-201, [in Russian] 


    Lecture Notes 

  75. I. G. Avramidi, Introduction to Differential Geometry, Lecture Notes for MATH 442, New Mexico Tech, 2005  

  76. I. G. Avramidi, Lecture Notes on Linear Algebra and Vector Analysis, (can be used for MATH 332, MATH 454, MATH 442), New Mexico Tech, 2005, 118 pp. 

  77. I. G. Avramidi, Methods of Mathematical Physics, Lecture Notes for MATH 535/536, New Mexico Tech, 2005, 165 pp. (in progress) 

  78. I. G. Avramidi, Basic Concepts of Analysis, Lecture Notes for MATH 372, New Mexico Tech, 2004, 127 pp. 

  79. I. G. Avramidi, Basic Concepts of Mathematics, Lecture Notes for MATH 352, New Mexico Tech, 2004, 110 pp. 

  80. I. G. Avramidi, Lecture Notes in Mathematical Physics, New Mexico Tech, 2000, 67 pp. 

  81. I. G. Avramidi, Effective Action Approach to Quantum Field Theory, New Mexico Tech, 2000, 90 pp. 

  82. I. G. Avramidi, Notes on Special Relativity and Quantum Fields, New Mexico Tech, 2000, 27 pp. 

  83. I. G. Avramidi, Notes on Lie Groups, New Mexico Tech, 2000, 14 pp. 

  84. I. G. Avramidi, Notes on Hilbert Spaces, New Mexico Tech, 2000, 17 pp. 

  85. I. G. Avramidi, Notes on Asymptotic Expansions, New Mexico Tech, 2000, 34 pp. 

  86. I. G. Avramidi, Notes on Differential Forms, New Mexico Tech, 2003, 13 pp. 

  87. I. G. Avramidi, Elementary Notes on Tensors, New Mexico Tech, 2001, 9 pp. 


    Books in preparation
     

  88. I. G. Avramidi,  
    Analytic and Geometric Methods for Heat Kernel Applications in Finance,

  89. I. G. Avramidi,  
    Heat Kernel in Mathematical Physics,
      

    Papers in preparation
     

  90. I. G. Avramidi,  
    Modified heat kernel asymptotics on Kaehler manifolds,  

  91. I. G. Avramidi,  
    On positivity of the spectrum of a certain class of differential operators,  

  92. I. G. Avramidi,
    Equivariant spectral asymptotics
 
Ivan Avramidi
http://www.nmt.edu/~iavramid
iavramid@nmt.edu