Algebraic Structures of Quantum Projective Field Theory Related to Fusion and Braiding. Hidden Additive Weight
نویسنده
چکیده
The interaction of various algebraic structures, describing fusion, braiding and group symmetries in quantum projective field theory, is an object of an investigation in the paper. Structures of projective Zamolodchikov algebras, their representations, spherical correlation functions, correlation characters and envelopping QPFT–operator algebras, projective Ẅ–algebras, shift algebras, infinite dimensional R–matrices Rproj(u) and R ∗ proj(u) of the QPFT, braiding admissible QPFT– operator algebras and projective G–hypermultiplets are explored.
منابع مشابه
/ 00 01 12 9 v 1 2 0 Ja n 20 00 Algebraic Quantum Field Theory , Perturbation Theory , and the Loop Expansion
The perturbative treatment of quantum field theory is formulated within the framework of algebraic quantum field theory. We show that the algebra of interacting fields is additive, i.e. fully determined by its subalgebras associated to arbitrary small subregions of Minkowski space. We also give an algebraic formulation of the loop expansion by introducing a projective system A of observables “u...
متن کاملAlgebraic Quantum Field Theory, Perturbation Theory, and the Loop Expansion
The perturbative treatment of quantum field theory is formulated within the framework of algebraic quantum field theory. We show that the algebra of interacting fields is additive, i.e. fully determined by its subalgebras associated to arbitrary small subregions of Minkowski space. We also give an algebraic formulation of the loop expansion by introducing a projective system A(n) of observables...
متن کاملQuantum Field Theories on Algebraic Curves and A. Weil Reciprocity Law
Using Serre’s adelic interpretation of the cohomology, we develop “differential and integral calculus” on an algebraic curve X over an algebraically closed constant field k of characteristic zero, define an algebraic analogs of additive and multiplicative multi-valued functions on X, and prove corresponding generalized residue theorem and A. Weil reciprocity law. Using the representation theory...
متن کاملRings of Singularities
This paper is a slightly revised version of an introduction into singularity theory corresponding to a series of lectures given at the ``Advanced School and Conference on homological and geometrical methods in representation theory'' at the International Centre for Theoretical Physics (ICTP), Miramare - Trieste, Italy, 11-29 January 2010. We show how to associate to a triple of posit...
متن کاملAlgebraic Topology Foundations of Supersymmetry and Symmetry Breaking in Quantum Field Theory and Quantum Gravity: A Review
A novel algebraic topology approach to supersymmetry (SUSY) and symmetry breaking in quantum field and quantum gravity theories is presented with a view to developing a wide range of physical applications. These include: controlled nuclear fusion and other nuclear reaction studies in quantum chromodynamics, nonlinear physics at high energy densities, dynamic Jahn–Teller effects, superfluidity, ...
متن کامل