Quantum field theories on algebraic curves. I. Additive bosons

  title={Quantum field theories on algebraic curves. I. Additive bosons},
  author={Leon A. Takhtajan},
  journal={Izvestiya: Mathematics},
  pages={378 - 406}
  • L. Takhtajan
  • Published 30 November 2008
  • Mathematics
  • Izvestiya: Mathematics
Using Serre's adelic interpretation of cohomology, we develop a ‘differential and integral calculus’ on an algebraic curve over an algebraically closed field of constants of characteristic zero, define algebraic analogues of additive multi-valued functions on and prove the corresponding generalized residue theorem. Using the representation theory of the global Heisenberg algebra and lattice Lie algebra, we formulate quantum field theories of additive and charged bosons on an algebraic curve… 
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