ALGEBRAIC QUANTUM FIELD THEORY

By E. NAVIK

STRUCTURE THE NET OBSERVABLE ALGEBRAS NONLOCALITY AND OPEN SYSTEMS AQFT PROSPECTS FOR PARTICLES THE PROBLEM VALUE-DEFINITENESS AQFT QUANTUM FIELDS AND SPACETIME POINTS THE PROBLEM INEQUIVALENT REPRESENTATIONS THE CATEGORY LOCALIZED TRANSPORTABLE ENDO- MORPHISMS FROM FIELDS REPRESENTATIONS FROM REPRESENTATIONS FIELDS FOUNDATIONAL IMPLICATIONS OF THE RECONSTRUCTION THE- OREM ALGEBRAIC QUANTUM FIELD THEORY? ABSTRACT ALGEBRAIC QUANTUM ?ELD THEORY PROVIDES A GENERAL, MATHEMATICALLY PRECISE DESCRIPTION OF THE STRUCTURE OF QUANTUM ?ELD THEORIES, AND THEN DRAWS OUT CONSE- QUENCES OF THIS STRUCTURE BY MEANS OF VARIOUS MATHEMATICAL TOOLS — THE THEORY OF OPERATOR ALGEBRAS, CATEGORY THEORY, ETC GIVEN THE RIGOR AND GENERALITY OF AQFT, IT IS A PARTICULARLY APT TOOL FOR STUDYING THE FOUNDATIONS OF QFT THIS PAPER IS A SURVEY OF AQFT, WITH AN ORIENTATION TOWARDS FOUNDATIONAL TOPICS IN ADDITION TO COVERING THE BASICS OF THE THEORY, WE DISCUSS ISSUES RELATED TO NONLOCALITY, THE PARTICLE CONCEPT, THE ?ELD CONCEPT, AND INEQUIVALENT REPRESEN- TATIONS WE ALSO PROVIDE A DETAILED ACCOUNT OF THE ANALYSIS OF SUPERSELECTION RULES BY DOPLICHER, HAAG, AND ROBERTS (DHR); AND WE GIVE AN ALTERNATIVE PROOF OF DOPLICHER AND ROBERT’S RECONSTRUCTION OF ?ELDS AND GAUGE GROUP FROM THE CATEGORY OF PHYSICAL REPRESENTATIONS OF THE OBSERVABLE ALGEBRA THE LATTER IS BASED ON UNPUBLISHED IDEAS DUE TO J E ROBERTS AND THE ABSTRACT DUALITY THEO- REM FOR SYMMETRIC TENSOR ?-CATEGORIES, A SELF-CONTAINED PROOF OF WHICH IS GIVEN IN THE APPENDIX