2003/08/20 by Jae-Suk Park, Park, Jae-Suk
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #hep-th #math.QA
paper · pdf · doi:10.48550/arxiv.hep-th/0308130
LaTeX2e, 53 pages; Dedicated to the Memory of Youngjai Kiem
arxiv created 2003/08/20 · openalex publication_date 2003/08/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Exploiting the path integral approach al la Batalin and Vilkovisky, we show that any anomaly-free Quantum Field Theory (QFT) comes with a family parametrized by certain moduli space M, which tangent space at the point corresponding to the initial QFT is given by the space of all observables. Furthermore the tangent bundle over M is equipped with flat quantum connection, which can be used to determine all correlation functions of the family of QFTs. We also argue that considering family of QFTs is an inevitable step, due to the fact that the products of quantum observables are not quantum observables in general, which leads to a new "global" perspective on quantum world. We also uncover structure of d-algebra in the large class of d-dimensional QFT. This leads to an universal quantization machine for d-algebras decorated by algebro-differential-topology of (d+1)-manifolds as well as a new perspective on differential-topology of low dimensions. This paper is a summary of a forthcoming paper of this author.