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Super Theta Vectors and Super Quantum Theta Operators

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Theta functions are the sections of line bundles on a complex torus. Noncommutative versions of theta functions have appeared as theta vectors and quantum theta operators. In this paper we describe a super version of theta vectors and quantum theta operators. This is the natural unification of Manin’s result on bosonic operators, and the author’s previous result on fermionic operators.

Abstract

Theta functions are the sections of line bundles on a complex torus. Noncommutative versions of theta functions have appeared as theta vectors and quantum theta operators. In this paper we describe a super version of theta vectors and quantum theta operators. This is the natural unification of Manin’s result on bosonic operators, and the author’s previous result on fermionic operators.

참고문헌 (10)

  1. M. Bergvelt, "Supercurves, their Jacobians, and super KP equations", Duke Math. J, 98(1), pp.1~57 (1999)
  2. A. Connes, "Noncommutative geometry and matrix theory", J. High Energy Phys., JHEP, 9802, pp.35~ (1998)
  3. 김호일, "Quantum Super Theta Vectors and Theta Functions", Kyungpook Mathematical Journal, 56(1), pp.249~256 (2016), 경북대학교 자연과학대학 수학과
  4. Y. Manin, "Theta functions, quantum tori and Heisenberg Groups", Lett. Math. Phys, 56(3), pp.295~320 (2001)
  5. Y. Manin, "Functional equations for quantum theta functions", Publ. Res. Inst. Math. Sci, 40(3), pp.605~624 (2004)
  6. D. Mumford, "Tata lectures on theta III" (1991), Birkhauser
  7. M. Rieffel, "Projective modules over higher dimensional noncommutative tori", Canad. J. Math, 40(2), pp.257~338 (1988)
  8. A. Schwarz, "Theta functions on noncommutative tori", Lett. Math. Phys, 58, pp.81~90 (2001)
  9. Y. Tsuchimoto, "On super theta functions", J. Math. Kyoto Univ, 34(3), pp.641~694 (1994)
  10. A. Tyurin, "Quantization and "theta functions"", arXiv:math

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