RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Izv. RAN. Ser. Mat.: Year: Volume: Issue: Page: Find

 Izv. RAN. Ser. Mat., 2013, Volume 77, Issue 2, Pages 165–196 (Mi izv7923)

Quantum field theories on algebraic curves. I. Additive bosons

L. A. Takhtajanab

a Department of Mathematics, Stony Brook University
b Euler International Mathematical Institute

Abstract: Using Serre's adelic interpretation of cohomology, we develop a ‘differential and integral calculus’ on an algebraic curve $X$ over an algebraically closed field $k$ of constants of characteristic zero, define algebraic analogues of additive multi-valued functions on $X$ 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 $X$. These theories are naturally connected with the algebraic de Rham theorem. We prove that an extension of global symmetries (Witten's additive Ward identities) from the $k$-vector space of rational functions on $X$ to the vector space of additive multi-valued functions uniquely determines these quantum theories of additive and charged bosons.

Keywords: algebraic curves and algebraic functions, adèles, additive multi-valued functions, additive Ward identities, Heisenberg algebra, current algebra on an algebraic curve, generalized residue theorem, Fock spaces, quantum theories of free bosons on an algebraic curve, expectation value functional.

 Funding Agency Grant Number National Science Foundation DMS-0204628DMS-0705263DMS-1005769

DOI: https://doi.org/10.4213/im7923

Full text: PDF file (676 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2013, 77:2, 378–406

Bibliographic databases:

UDC: 512.626+512.772+512.815.8+530.145
MSC: 81R10, 14H81
Revised: 19.04.2012

Citation: L. A. Takhtajan, “Quantum field theories on algebraic curves. I. Additive bosons”, Izv. RAN. Ser. Mat., 77:2 (2013), 165–196; Izv. Math., 77:2 (2013), 378–406

Citation in format AMSBIB
\Bibitem{Tak13} \by L.~A.~Takhtajan \paper Quantum field theories on algebraic curves. I.~Additive bosons \jour Izv. RAN. Ser. Mat. \yr 2013 \vol 77 \issue 2 \pages 165--196 \mathnet{http://mi.mathnet.ru/izv7923} \crossref{https://doi.org/10.4213/im7923} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3097571} \zmath{https://zbmath.org/?q=an:06170776} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2013IzMat..77..378T} \elib{http://elibrary.ru/item.asp?id=20359176} \transl \jour Izv. Math. \yr 2013 \vol 77 \issue 2 \pages 378--406 \crossref{https://doi.org/10.1070/IM2013v077n02ABEH002640} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000318276000007} \elib{http://elibrary.ru/item.asp?id=20442704} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84877025976}