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Quantum field theories on algebraic curves. I. Additive bosons
Using Serre's adelic interpretation of cohomology, we develop a 'differential and integral calculus' on an algebraic curve X over an algebraically closed filed k of constants of characteristic zero, define algebraic analogs of additive multi-valued functions on X and prove corresponding generalized residue theorem. Using the representation theory of the global Heisenberg and lattice Lie algebras, we formulate quantum field theories of additive and charged bosons on an algebraic curve X. Thesedoi:10.1070/im2013v077n02abeh002640 fatcat:tfellfouunez5mxlonqifnfi4y