LEADER 03808nam 2200493 450 001 9910793296903321 005 20220822045616.0 010 $a1-4704-4941-2 035 $a(CKB)4100000007133844 035 $a(MiAaPQ)EBC5571093 035 $a(Au-PeEL)EBL5571093 035 $a(OCoLC)1065020893 035 $a(RPAM)20684076 035 $a(PPN)233023917 035 $a(EXLCZ)994100000007133844 100 $a20220527d2018 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aTopology and quantum theory in interaction $eNSF-CBMS Regional Conference in the Mathematical Sciences, Topological and Geometric Methods in QFT, July 31-August 4, 2017, Montana State University, Bozeman, Montana /$fDavid Ayala, Daniel S. Freed, Ryan E. Grady, editors 210 1$a[Place of publication not identified] :$cAmerican Mathematical Society,$d[2018] 210 4$dİ2018 215 $a1 online resource (274 pages) 225 1 $aContemporary mathematics,$v718$x0271-4132 311 $a1-4704-4243-4 320 $aIncludes bibliographical references. 327 $tGeometry and physics: an overview /$rDavid R. Morrison --$tAn introduction to spin systems for mathematicians /$rIngmar Saberi --$tThe Arf-Brown TQFT of pin? surfaces /$rArun Debray and Sam Gunningham --$tA guide for computing stable homotopy groups /$rAgnes Beaudry and Jonathan A. Campbell --$tFlagged higher categories /$rDavid Ayala and John Francis --$tHow to derive Feynman diagrams for nite-dimensional integrals directly from the BV formalism /$rOwen Gwilliam and Theo Johnson-Freyd --$tHomotopy RG flow and the non-linear -model /$rRyan E. Grady and Brian Williams --$tThe holomorphic bosonic string /$rOwen Gwilliam and Brian Williams. 330 $aThis volume contains the proceedings of the NSF-CBMS Regional Conference on Topological and Geometric Methods in QFT, held from July 31-August 4, 2017, at Montana State University in Bozeman, Montana. In recent decades, there has been a movement to axiomatize quantum field theory into a mathematical structure. In a different direction, one can ask to test these axiom systems against physics. Can they be used to rederive known facts about quantum theories or, better yet, be the framework in which to solve open problems? Recently, Freed and Hopkins have provided a solution to a classification problem in condensed matter theory, which is ultimately based on the field theory axioms of Graeme Segal. Papers contained in this volume amplify various aspects of the Freed-Hopkins program, develop some category theory, which lies behind the cobordism hypothesis, the major structure theorem for topological field theories, and relate to Costello's approach to perturbative quantum field theory. Two papers on the latter use this framework to recover fundamental results about some physical theories: two-dimensional sigma-models and the bosonic string. Perhaps it is surprising that such sparse axiom systems encode enough structure to prove important results in physics. These successes can be taken as encouragement that the axiom systems are at least on the right track toward articulating what a quantum field theory is. 410 0$aContemporary mathematics (American Mathematical Society).$v718$x0271-4132 606 $aQuantum field theory$xMathematics$vCongresses 615 0$aQuantum field theory$xMathematics 676 $a530.143 702 $aAyala$b David$f1982- 702 $aFreed$b Daniel S. 702 $aGrady$b Ryan E.$f1985- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910793296903321 996 $aTopology and quantum theory in interaction$93797939 997 $aUNINA