Effective action, quantum action, heat kernel, proper time method, cutoff regularization in the coordinate representation, regularization by averaging, quasi-local theory, renormalization, scalar model, Yang–Mills theory, non-linear sigma model, principal chiral field model.
Subject:
The main research activities are related to the theory of generalized functions, the theory of regularization and renormalization, quantum field theory, as well as the application of the theat kernel method in various fields of quantum and classical physics. The following topics can be identified as relevant today:
1) cutoff regularization in the coordinate representation and its properties;
2) structure of singularities in various theories (scalar model, Yang–Mills theory, sigma model);
3) dependence of theory data on regularization and the renormalization process;
4) quasi-local theories and their properties.
Main publications:
A. V. Ivanov, “Effective actions, cutoff regularization, quasi-locality, and gluing of partition functions”, J. Phys. A: Math. Theor., 58 (2025), 135401
A. V. Ivanov, “Three-loop renormalization of the quantum action for a four-dimensional scalar model with quartic interaction with the usage of the background field method and a cutoff regularization”, Nuclear Physics B, 1006 (2024), 116647
A. V. Ivanov, N. V. Kharuk, “Special functions for heat kernel expansion”, Eur. Phys. J. Plus, 137 (2022), 1060
A. V. Ivanov, “Explicit Cutoff Regularization in Coordinate Representation”, J. Phys. A: Math. Theor., 45 (2022), 495401
A. V. Ivanov, N. V. Kharuk, “Two-loop cutoff renormalization of 4-D Yang–Mills effective action”, J. Phys. G: Nucl. Part. Phys., 48 (2020), 015002
Aleksandr Ivanov, “An applicability condition of a cutoff regularization in the coordinate representation”, Funct. Anal. Appl., 59:1 (2025), 3–12
2.
A. V. Ivanov, “Effective actions, cutoff regularization, quasi-locality, and gluing of partition functions”, J. Phys. A: Math. Theor., 58 (2025), 135401 , arXiv: 2411.13857 (http://www.pdmi.ras.ru/preprint/2024/24-11.html)
2024
3.
A. V. Ivanov, “Three-loop renormalization of the quantum action for a four-dimensional scalar model with quartic interaction with the usage of the background field method and a cutoff regularization”, Nuclear Physics B, 1006 (2024), 116647 , 60 pp., arXiv: 2402.14549 (https://www.pdmi.ras.ru/preprint/2024/24-02.html)
A. V. Ivanov, N. V. Kharuk, “Three-loop renormalization of the quantum action for a five-dimensional scalar cubic model with the usage of the background field method and a cutoff regularization”, The European Physical Journal Plus, 139 (2024), 849 , 15 pp., arXiv: 2404.07513 (https://www.pdmi.ras.ru/preprint/2024/24-05.html)
5.
A. V. Ivanov, “Applicability condition of a cutoff in two-dimensional models”, Questions of quantum field theory and statistical physics. Part 30, Zap. Nauchn. Sem. POMI, 532, POMI, St. Petersburg, 2024, 153–168
6.
A. V. Ivanov, “Local heat kernel”, Questions of quantum field theory and statistical physics. Part 30, Zap. Nauchn. Sem. POMI, 532, POMI, St. Petersburg, 2024, 136–152
7.
A. V. Ivanov, N. V. Kharuk, “Three-loop divergences in effective action of $4$-dimensional Yang–Mills theory with cutoff regularization: $\Gamma_4^2$-contribution”, J. Math. Sci. (N. Y.), 284:5 (2024), 681–699
2023
8.
A. V. Ivanov, N. V. Kharuk, “Ordered Exponential and Its Features in Yang–Mills Effective Action”, Communications in Theoretical Physics, 75 (2023), 085202 , 9 pp., arXiv: 2301.10514
P. V. Akacevich, A. V. Ivanov, “On Two-Loop Effective Action of 2D Sigma Model”, The European Physical Journal C, 83 (2023), 653 (2023) , 8 pp., arXiv: 2304.02374
A. V. Ivanov, M. A. Kurkov, D. V. Vassilevich, “Heat Kernel, Spectral Functions and Anomalies in Weyl Semimetals”, J. Phys. A: Math. Theor., 55 (2022), 224004 , arXiv: 2111.11493
A. V. Ivanov, N. V. Kharuk, “Formula for two-loop divergent part of 4-D Yang–Mills effective action”, Eur. Phys. J. C, 82 (2022), 997 , arXiv: 2203.07131
A. V. Ivanov, M. A. Russkikh, “Quantum field theory on the example of the simplest cubic model”, Questions of quantum field theory and statistical physics. Part 28, Zap. Nauchn. Sem. POMI, 509, POMI, St. Petersburg, 2021, 123–152 , arXiv: 2107.14488
16.
A. V. Ivanov, “On Gustafson integrals for the group $\mathrm{SL}(2,\mathbb{R})$”, Questions of quantum field theory and statistical physics. Part 28, Zap. Nauchn. Sem. POMI, 509, POMI, St. Petersburg, 2021, 113–122
17.
S. E. Derkachev, A. V. Ivanov, “Racah coefficients for the group $\mathrm{SL}(2,\mathbb{R})$”, Questions of quantum field theory and statistical physics. Part 28, Zap. Nauchn. Sem. POMI, 509, POMI, St. Petersburg, 2021, 99–112
18.
A. V. Ivanov, “Index Theorem for Domain Walls”, J. Phys. A: Math. Theor., 54 (2021), 095203 , arXiv: 2008.02058
A. V. Ivanov, N. V. Kharuk, “Heat kernel: Proper-time method, Fock–Schwinger gauge, path integral, and Wilson line”, Theoret. and Math. Phys., 205:2 (2020), 1456–1472 , arXiv: 1906.04019
2022
20.
S. E. Derkachev, A. V. Ivanov, L. A. Shumilov, “Mellin–Barnes Transformation for Two-Loop Master-Diagram”, J. Math. Sci., 264:3 (2022), 298–312
2020
21.
A. V. Ivanov, D. V. Vassilevich, “Atiyah-Patodi-Singer Index Theorem for Domain Walls”, J. Phys. A: Math. Theor., 53 (2020), 305201 , arXiv: 2003.06674
A. V. Ivanov, N. V. Kharuk, “Two-loop cutoff renormalization of 4-D Yang–Mills effective action”, J. Phys. G: Nucl. Part. Phys., 48 (2020), 015002 , arXiv: 2004.05999
A. V. Ivanov, “Diagram technique for the heat kernel of the covariant Laplace operator”, Theoret. and Math. Phys., 198:1 (2019), 100–117 , arXiv: 1905.05455
24.
A. V. Ivanov, N. V. Kharuk, “Quantum equation of motion and two-loop cutoff renormalization for $\phi^3$ model”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 26, Zap. nauchn. sem. POMI, 487, POMI, SPb., 2019, 151–166 , arXiv: 2203.04562; A. V. Ivanov, N. V. Kharuk, “Quantum Equation of Motion and Two-Loop Cutoff Renormalization for $\phi^3$ Model”, J. Math. Sci., 257:4 (2021), 526–536 , arXiv: 2203.04562
A. V. Ivanov, “Notes on functional integration”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 26, Zap. nauchn. sem. POMI, 487, POMI, SPb., 2019, 140–150; A. V. Ivanov, “Notes on Functional Integration”, J. Math. Sci., 257:4 (2021), 518–525
A. V. Ivanov, “On the completeness of projectors for tensor product decomposition of continuous series representations groups $SL (2,\mathbb{R})$”, J. Math. Sci., 242:5 (2019), 692–700
28.
A. V. Ivanov, “On the application of matrix formalism of heat kernel to the number theory”, J. Math. Sci., 242:5 (2019), 683–691 , arXiv: 1808.08103
2018
29.
A. V. Ivanov, “About renormalized effective action for the Yang–Mills theory in four-dimensional space-time”, EPJ Web Conf., 191, XXth International Seminar on High Energy Physics (QUARKS-2018) (2018), 06001 , 7 pp.
S. È. Derkachev, A. V. Ivanov, L. D. Faddeev, “Renormalization scenario for the quantum Yang–Mills theory in four-dimensional space–time”, Theoret. and Math. Phys., 192:2 (2017), 1134–1140
2019
31.
A. V. Ivanov, “On dimensional regularization on an example from Yang–Mills theory”, J. Math. Sci., 238:6 (2019), 862–869
2017
32.
A. V. Ivanov, “About renormalization of the Yang–Mills theory and the approach to calculation of the heat kernel”, EPJ Web Conf., 158, The XXIII International Workshop “High Energy Physics and Quantum Field Theory” (QFTHEP 2017) (2017), 07004 , 5 pp.
Ordered exponential and its features in Yang–Mills effective action N. V. Kharuk, A. V. Ivanov III International Conference “Mathematical Physics, Dynamical Systems, Infinite-Dimensional Analysis”, dedicated to the 100th anniversary of V.S. Vladimirov, the 100th anniversary of L.D. Kudryavtsev and the 85th anniversary of O.G. Smolyanov July 11, 2023 15:35
2025
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