nLab Leon Takhtajan

Leon A. Takhtajan is a mathematical physicist at SUNY Stony Brook.

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Selected writings

On the FRT construction of quantum groups:

• N. Yu. Reshetikhin, L. A. Takhtajan, L. D. Faddeev, Quantization of Lie groups and Lie algebras, Algebra i analiz 1, 178 (1989) (Russian), English transl. in Leningrad Math. J. 1.

• L. D. Faddeev, N. Yu. Reshetikhin, L. A. Takhtajan, Quantum Groups. Braid Group, Knot Theory and Statistical Mechanics, in: Adv. Ser. Math. Phys. 9, World Sci. 1989, pp. 97–110

Early discussion of Nambu mechanics:

• Leon Takhtajan: On Foundation of the Generalized Nambu Mechanics, Commun. Math. Phys. 160 (1994) 295-316 [arXiv:hep-th/9301111, doi:10.1007/BF02103278]

On relations between quantum field theory and number theory and in particular about the analogy between the Weil reciprocity law for function fields and the Ward identities of quantum field theory:

• Leon Takhtajan: Quantum field theories on algebraic curves and A. Weil reciprocity law [arxiv/0812.0169]

• Leon Takhtajan: : Quantum field theories on an algebraic curve (2000) [pdf]

On quantum mechanics:

• Leon A. Takhtajan: Quantum mechanics for mathematicians, Amer. Math. Soc. (2008) [ISBN:978-0-8218-4630-8]

On solitons:

• Ludwig D. Faddeev, Leon A. Takhtajan: Hamiltonian methods in the theory of solitons, Springer (2007) [doi:10.1007/978-3-540-69969-9]

On Selberg trace formulas via supersymmetric quantum mechanics:

• Changha Choi, Leon A. Takhtajan: Supersymmetry and trace formulas I. Compact Lie groups, Part I. Compact Lie groups. J. High Energ. Phys. 2024 26 (2024) [arXiv:2112.07942, doi:10.1007/JHEP06(2024)026]

• Changha Choi, Leon A. Takhtajan: Supersymmetry and trace formulas II. Selberg trace formula [arXiv:2306.13636]

• Changha Choi, Leon A. Takhtajan: Supersymmetry and trace formulas III. Frenkel trace formula [arXiv:2502.10210]

review:

• Leon A. Takhtajan: Supersymmetry and trace formulas: Selberg trace formula, talk at Integrable Systems and Field Theory, Paris (2023) [pdf]

category: people