PUBLICATION LIST - New Mexico Tech

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I. G. Avramidi, Heat Kernel and Quantum Gravity, Lecture Notes in Physics, New ... 9. I. G. Avramidi and G. Fucci, A model for the Pioneer anomaly, Canadian J. Phys. ... 10. I. G. Avramidi and G. Fucci, Non-perturbative heat kernel asymptotics on ... I. G. Avramidi, Non-commutative corrections in spectral matrix gravity, Class.

PUBLICATION LIST Ivan G. Avramidi New Mexico Institute of Mining and Technology

Books and Refereed Book Chapters

1. I. G. Avramidi, Heat Kernel and Quantum Gravity, Lecture Notes in Physics, New Series m: Monographs, LNP:m64 (Berlin-New York: Springer-Verlag 2000) 2. I. G. Avramidi, Heat Kernel: with Applications to Finance, 360 pp. (Springer, 2013). Almost completed. Available upon request. 3. I. G. Avramidi, Mathemathical tools for calculation of the effective action in quantum gravity, in: New Paths Towards Quantum Gravity, Eds. B. Booss-Bavnbek, G. Esposito and M. Lesch, (Berlin, Springer, 2010), pp. 193-259 4. I. G. Avramidi, 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 Refereed Journal Publications 5. I. G. Avramidi and S. Collopy, Thermal Yang-Mills theory in Einstein universe, J. Phys. A: Math. and Theor. 45 (2012) 374009 6. I. G. Avramidi and S. Collopy, Effective action and phase transitions in thermal Yang-Mills theory on spheres, Commun. Math. Phys. 311 (2011) 713-753 7. I. G. Avramidi, Non-perturbative effective action in gauge theories and quantum gravity, Adv. Theor. Math. Phys. 14 (2010) 309-333 8. I. G. Avramidi and G. Fucci, Low-energy effective action in non-perturbative electrodynamics in curved spacetime, J. Math. Phys. 50 (2009) 102302 9. I. G. Avramidi and G. Fucci, A model for the Pioneer anomaly, Canadian J. Phys. 87 (2009) 10891093 10. I. G. Avramidi and G. Fucci, Non-perturbative heat kernel asymptotics on homogeneous Abelian bundles, Commun. Math. Phys. 291 (2009) 543-577 11. I. G. Avramidi and G. Fucci, Kinematics in matrix gravity, Gen. Rel. Grav. 41 (2009) 1407-1435 12. G. Fucci and I. G. Avramidi, Non-commutative corrections in spectral matrix gravity, Class. Quant. Grav. 26 (2009) 045019, 24pp. 13. I. G. Avramidi, Heat kernel on homogeneous bundles over symmetric spaces, Commun. Math. Phys. 288 (2009) 963-1006

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14. I. G. Avramidi, Heat kernel on homogeneous bundles, Int. J. Geom. Methods Mod. Phys. 5 (2008) 1–23 15. G. Fucci and I. G. Avramidi, Non-commutative Einstein equations, Class. Quant. Grav. 25 (2008) 025005, 17 pp. 16. I. G. Avramidi, Dirac operator in matrix geometry, Int. J. Geom. Methods Mod. Phys. 2 (2005), 227–264 17. I. G. Avramidi, Gauged gravity via spectral asymptotics of non-Laplace type operators, J. High Energy Phys. 07 (2004) 030, 36 pp. 18. I. G. Avramidi, Matrix general relativity: a new look at old problems, Class. Quant. Grav. 21 (2004) 103–120 19. I. G. Avramidi, A Noncommutative deformation of general relativity, Phys. Lett. B 576 (2003) 195– 198 20. I. G. Avramidi, Heat kernel asymptotics of Zaremba boundary value problem, Math. Phys., Analysis and Geom. 7 (2004) 9–46 21. I. G. Avramidi and T. Branson, A discrete leading symbol and spectral asymptotics for natural differential operators, J. Funct. Anal. 190 (2002) 292–337 22. I. G. Avramidi and T. Branson, Heat kernel asymptotics of operators with non-Laplace principal part, Rev. Math. Phys. 13 (2001) 847–890 23. I. G. Avramidi and R. Schimming, A new explicit expression for the Korteweg-De Vries hierarchy, Mathematische Nachrichten 219 (2000) 45–64 24. I. G. Avramidi, Covariant techniques for computation of the heat kernel, Rev. Math. Phys. 11 (1999) 947–980 25. I. G. Avramidi and G. Esposito, Gauge theories on manifolds with boundary, Commun. Math. Phys. 200 (1999) 495–543 26. I. G. Avramidi, One-loop effective potential in higher-dimensional Yang-Mills theory, Fortschritte der Physik/Prog. Phys. 47 (1999) 433–455 27. I. G. Avramidi, Green functions of higher-order differential operators, J. Math. Phys. 39 (1998) 2889-2909 28. I. G. Avramidi and G. Esposito, Lack of strong ellipticity in Euclidean quantum gravity, Class. Quant. Grav. 15 (1998) 1141–1152 29. I. G. Avramidi, Singularities of Green functions of the products of the Laplace-type operators, Phys. Lett. B 403 (1997) 280–284 30. I. G. Avramidi and G. Esposito, New invariants in the one-loop divergences on manifolds with boundary, Class. Quant. Grav. 15 (1998) 281–297 31. I. G. Avramidi, G. Esposito and A. Yu. Kamenshchik, Boundary operators in Euclidean quantum gravity, Class. Quant. Grav. 13 (1996) 2361–2373 32. I. G. Avramidi, A new algebraic approach for calculating the heat kernel in quantum gravity, J. Math. Phys. 37 (1996) 374–394

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33. I. G. Avramidi, Covariant algebraic method for calculation of the low-energy heat kernel, J. Math. Phys. 36 (1995) 5055–5070 34. I. G. Avramidi and R. Schimming, Heat kernel coefficients to the matrix Schr¨odinger operator, J. Math. Physics, 36 (1995) 5042–5054 35. I. G. Avramidi, Covariant algebraic calculation of the one-loop effective potential in non-Abelian gauge theory and a new approach to stability problem, J. Math. Phys. 36 (1995) 1557–1571 36. I. G. Avramidi, The heat kernel on symmetric spaces via integrating over the group of isometries, Phys. Lett. B 336 (1994) 171–177 37. I. G. Avramidi, A new algebraic approach for calculating the heat kernel in gauge theories, Phys. Lett. B 305 (1993) 27–34 38. I. G. Avramidi, A method for calculating the heat kernel for manifolds with boundary, Yadernaya Fizika 56 (1993) 245–252, [Russian]; Phys. Atom. Nucl. 56 (1993) 138–142 [English] 39. I. G. Avramidi, A covariant technique for the calculation of the one-loop effective action, Nucl. Phys. B 355 (1991) 712–754 40. I. G. Avramidi, Gauge invariant theory of higher spin fields in curved space, Int. J. Mod. Phys. A 6 (1991) 1693–1700 41. I. G. Avramidi, The covariant technique for calculation of the heat kernel asymptotic expansion, Phys. Lett. B 238 (1990) 92–97 42. I. G. Avramidi, The nonlocal structure of one-loop effective action via partial summation of asymptotic expansion, Phys. Lett. B 236 (1990) 443–449 43. I. G. Avramidi, Covariant methods of studying the nonlocal structure of an effective action, Yadernaya Fizika 49 (1989) 1185–1192, [Russian]; Soviet J. Nucl. Phys. 49 (1989) 735–739 [English] 44. I. G. Avramidi, Background field calculations in quantum field theory (vacuum polarization), Teoreticheskaya i Matematicheskaya Fizika 79 (1989) 219–231, [Russian]; Theor. Math. Phys. 79 (1989) 494–502 [English] 45. I. G. Avramidi, Asymptotic behavior of the quantum theory of gravity with higher order derivatives, Yadernaya Fizika 44 (1986) 255–263, [Russian]; Soviet J. Nucl. Phys. 44 (1986) 160–164 [English] 46. I. G. Avramidy and A. O. Barvinsky, Asymptotic freedom in higher-derivative quantum gravity, Phys. Lett. B 159 (1985) 269–274 47. 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] Conference Proceedings 48. 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 49. I. G. Avramidi, Heat kernel asymptotics on symmetric spaces, Proc. Midwest Geometry Conference, Commun. Math. Anal. 01 (2008) 110

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50. I. G. Avramidi, Heat kernel approach in quantum field theory, Nucl. Phys. Proc. Suppl. 104 (2002) 3–32 51. I. G. Avramidi and G. Esposito, Foundational problems in quantum gravity, in: Recent Developments in General Relativity, Eds. D. Fortunato, A. Masiello, B. Casciaro and M. Francaviglia, (Berlin: Springer, 1999), pp. 353–362 52. I. G. Avramidi and G. Esposito, Heat Kernel Asymptotics of the Gilkey-Smith Boundary Value Problem, in: “Trends in Mathematical Physics”, Eds: V. Alexiades and G. Siopsis, AMS/IP Studies in Advanced Mathematics, vol. 13, (AMS and International Press, 1999), pp. 15–34 53. 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, (AMS and International Press, 1999), pp. 33–40 54. I. G. Avramidi, Nonperturbative methods for calculating the heat kernel, in: “Global Analysis, Differential Geometry and Lie Algebras”, Ed. G. Tsagas, (Bucharest, Geometry Balcan Press, 1998), pp. 7-21; 55. 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, 1998), pp. 61–78 56. 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. Phys. Proc. Suppl. B 57 (1997), pp. 245–246 57. 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 58. 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 Preprints and Reports 59. I. G. Avramidi and G. Esposito, Universal functions in Euclidean quantum gravity, arXiv:hep-th/9702150, 8 pp. 60. I. G. Avramidi, The heat kernel approach for calculating the effective action in quantum field theory and quantum gravity, arXiv:hep-th/9509077, 21 pp. 61. I. G. Avramidi, Covariant methods for calculating the low-energy effective action in quantum field theory and quantum gravity, arXiv:gr-qc/9403036, 48 pp. 62. 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), UDC 530.12:531.51, 178 pp. [Russian]; Available at: arXiv:hep-th/9510140, 159 pp. [English]

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63. 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., [Russian] Lecture Notes 64. I. G. Avramidi, Complex Analysis, Lecture Notes for MATH 435/436, New Mexico Tech, 2011, 65 pp 65. I. G. Avramidi, Ordinary Differential Equations, Lecture Notes for MATH 335, New Mexico Tech, 2010, 126 pp 66. I. G. Avramidi, Introduction to Differential Geometry, Lecture Notes for MATH 442, New Mexico Tech, 2005, 210 pp 67. I. G. Avramidi, Methods of Mathematical Physics, Lecture Notes for MATH 535/536, New Mexico Tech, 2005, 165 pp 68. I. G. Avramidi, Basic Concepts of Analysis, Lecture Notes for MATH 372, New Mexico Tech, 2004, 127 pp 69. I. G. Avramidi, Basic Concepts of Mathematics, Lecture Notes for MATH 352, New Mexico Tech, 2004, 110 pp 70. 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. 71. I. G. Avramidi, Effective Action Approach to Quantum Field Theory, New Mexico Tech, 2000, 90 pp. Reviews 72. I. G. Avramidi, A note on contributions of Prof. Minakshisundaram to mathematical physics, Proc. of Andhra Pradesh Akademi of Sciences, 8 (2004), 247–248