nLab Leon Takhtajan

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

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Selected writings

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 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

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