integrable systems,
quantum groups,
Yang–Baxter equations,
analitical evaluations in quantum field theory.
UDC:
512.552
Subject:
Several papers (in collaboration with A.I. Molev and O.V. Ogievetsky) are devoted to the devolopment of the representation theory of (affine) Hecke and Birman–Murakami–Wenzl algebras. In collaboration with P.P. Kulish, reflection equations for factorizable scattering of strings were constructed. The operator method of the analytical evaluation of multi-loop Feynman integrals was developed.
Main publications:
A. P. Isaev, “Multi-loop Feynman integrals and conformal quantum mechanics”, Nucl. Phys. B, 662 (2003), 461–475
A. P. Isaev, P.N. Pyatov, “Spectral extension of the quantum group cotangent bundle”, Comm. Math. Phys., 288 (2009), 1137–1179
D. Chicherin, S. Derkachov, A. P. Isaev, “Conformal group: R-matrix and star-triangle relation”, JHEP, 1304 (2013), 020
A. P. Isaev, A. I. Molev, O. V. Ogievetsky, “Idempotents for Birman–Murakami–Wenzl algebras and reflection equation”, Adv.Theor.Math.Phys, 18 (2014), 1-25
A.P.Isaev, A.N.Kirillov and V.O.Tarasov, “Bethe subalgebras in affine Birman–Murakami–Wenzl algebras and flat connections for q-KZ equations”, J. Phys. A: Math. Theor, 49 (2016), 204002
A. P. Isaev, A. A. Provorov, “$3$-split Casimir operator of the $sl(M|N)$ and $osp(M|N)$
simple Lie superalgebras in the representation $\operatorname{ad}^{\otimes 3}$ and the Vogel
parameterization”, TMF, 221:1 (2024), 154–175; Theoret. and Math. Phys., 221:1 (2024), 1726–1743
2023
2.
I. L. Buchbinder, A. P. Isaev, M. A. Podoynitsyin, S. A. Fedoruk, “Generalization of the Bargmann–Wigner construction for infinite-spin fields”, TMF, 216:1 (2023), 76–105; Theoret. and Math. Phys., 216:1 (2023), 973–999
A. P. Isaev, A. A. Provorov, “Split Casimir operator and solutions of the Yang–Baxter equation for the $osp(M|N)$ and $s\ell(M|N)$ Lie superalgebras, higher Casimir operators, and the Vogel parameters”, TMF, 210:2 (2022), 259–301; Theoret. and Math. Phys., 210:2 (2022), 224–260
A. P. Isaev, A. A. Provorov, “Projectors on invariant subspaces of representations $\operatorname{ad}^{\otimes2}$ of Lie algebras $so(N)$ and $sp(2r)$ and Vogel parameterization”, TMF, 206:1 (2021), 3–22; Theoret. and Math. Phys., 206:1 (2021), 1–18
I. L. Buchbinder, A. P. Isaev, S. A. Fedoruk, “Massless Infinite Spin (Super)particles and Fields”, Trudy Mat. Inst. Steklova, 309 (2020), 54–65; Proc. Steklov Inst. Math., 309 (2020), 46–56
A. P. Isaev, M. A. Podoynitsyin, “Polarization tensors for massive arbitrary-spin particles and the Behrends–Fronsdal projection operator”, TMF, 198:1 (2019), 101–112; Theoret. and Math. Phys., 198:1 (2019), 89–99
A. P. Isaev, M. A. Podoinicin, “Unitary representations of the Wigner group $ISL(2,\mathbb C)$ and a two-spinor description of massive particles with an arbitrary spin”, TMF, 195:3 (2018), 331–361; Theoret. and Math. Phys., 195:3 (2018), 779–806
P. A. Valinevich, S. E. Derkachov, A. P. Isaev, A. V. Komisarchuk, “Orthogonal polynomials, $6j$-symbols and statistical weights of SOS models”, Zap. Nauchn. Sem. POMI, 465 (2017), 105–134; J. Math. Sci. (N. Y.), 238:6 (2019), 834–853
P. A. Valinevich, S. E. Derkachov, A. P. Isaev, “SOS-representation for the $SL(2,\mathbb C)$-invariant $R$-operator and Feynman diagrams”, Zap. Nauchn. Sem. POMI, 465 (2017), 82–104; J. Math. Sci. (N. Y.), 238:6 (2019), 819–833
A. P. Isaev, A. I. Molev, “Fusion procedure for the Brauer algebra”, Algebra i Analiz, 22:3 (2010), 142–154; St. Petersburg Math. J., 22:3 (2011), 437–446
A. P. Isaev, “Functional equations for transfer-matrix operators in open Hecke chain models”, TMF, 150:2 (2007), 219–236; Theoret. and Math. Phys., 150:2 (2007), 187–202
A. P. Isaev, O. V. Ogievetskii, P. N. Pyatov, “On R-Matrix Representations of Birman–Murakami–Wenzl Algebras”, Trudy Mat. Inst. Steklova, 246 (2004), 147–153; Proc. Steklov Inst. Math., 246 (2004), 134–141
V. G. Gorbunov, A. P. Isaev, O. V. Ogievetskii, “BRST Operator for Quantum Lie Algebras: Relation to the Bar Complex”, TMF, 139:1 (2004), 29–44; Theoret. and Math. Phys., 139:1 (2004), 473–485
A. P. Isaev, O. V. Ogievetskii, “BRST Operator for Quantum Lie Algebras and Differential Calculus on Quantum Groups”, TMF, 129:2 (2001), 298–316; Theoret. and Math. Phys., 129:2 (2001), 1558–1572
A. T. Filippov, A. P. Isaev, A. B. Kurdikov, “Paragrassmann differential calculus”, TMF, 94:2 (1993), 213–231; Theoret. and Math. Phys., 94:2 (1993), 150–165
E. A. Ivanov, A. P. Isaev, “The Green–Schwarz superstring as an asymmetric model of a chiral field”, TMF, 81:3 (1989), 420–433; Theoret. and Math. Phys., 81:3 (1989), 1304–1313
S. G. Gorishnii, A. P. Isaev, “An approach to the calculation of many-loop massless Feynman integrals”, TMF, 62:3 (1985), 345–358; Theoret. and Math. Phys., 62:3 (1985), 232–240
V. V. Bazhanov, A. P. Isaev, “Equations for path mean values in non-Abelian gauge theory”, TMF, 49:3 (1981), 307–319; Theoret. and Math. Phys., 49:3 (1981), 1049–1057
2021
21.
V. V. Belokurov, E. E. Boos, M. I. Vysotsky, M. V. Danilov, A. P. Isaev, V. D. Kekelidze, N. V. Krasnikov, V. A. Matveev, I. N. Meshkov, V. A. Novikov, V. A. Rubakov, G. V. Trubnikov, “Dmitrii Igorevich Kazakov (on his 70th birthday)”, UFN, 191:12 (2021), 1403–1404; Phys. Usp., 64:12 (2021), 1326–1327
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