Abstract
This paper investigates the relationship between algebraic quantum field theories and factorization algebras on globally hyperbolic Lorentzian manifolds. Functorial constructions that map between these two types of theories in both directions are developed under certain natural hypotheses, including suitable variants of the local constancy and descent axioms. The main result is an equivalence theorem between (Cauchy constant and additive) algebraic quantum field theories and (Cauchy constant, additive and time-orderable) prefactorization algebras. A concept of *-involution for the latter class of prefactorization algebras is introduced via transfer. This involves Cauchy constancy explicitly and does not extend to generic (time-orderable) prefactorization algebras.
Highlights
Introduction and SummaryFactorization algebras and algebraic quantum field theory are two mathematical frameworks to axiomatize the algebraic structure of observables in a quantum field theory.While from a superficial point of view these two approaches look similar, there are subtle differences
This paper investigates the relationship between algebraic quantum field theories and factorization algebras on globally hyperbolic Lorentzian manifolds
(2) We investigate in detail uniqueness, associativity, naturality and Einstein causality of the multiplications μM : F(M)⊗F(M) → F(M) determined by a Cauchy constant additive prefactorization algebra F, which requires rather sophisticated arguments from Lorentzian geometry
Summary
Factorization algebras and algebraic quantum field theory are two mathematical frameworks to axiomatize the algebraic structure of observables in a quantum field theory. Our main result is an equivalence theorem between (Cauchy constant and additive) algebraic quantum field theories and (Cauchy constant, additive and time-orderable) prefactorization algebras, cf Theorem 5.1. 3 we construct a functor A : PFAadd,c → AQFTadd,c that assigns a Cauchy constant additive algebraic quantum field theory A[F] to each Cauchy constant additive prefactorization algebra F, see Theorem 3.11 for the main result. F : AQFT → tPFA that assigns a time-orderable prefactorization algebra F[A] to each algebraic quantum field theory A, see Theorem 4.7 for the main result. 3 factors through the forgetful functor PFAadd,c → tPFAadd,c, thereby defining a functor A : tPFAadd,c → AQFTadd,c that assigns a Cauchy constant additive algebraic quantum field theory to each Cauchy constant additive time-orderable prefactorization algebra. Theorem 5.1 to transfer ∗-involutions from algebraic quantum field theories to Cauchy constant additive time-orderable prefactorization algebras. We observe as in [GR17] that the corresponding time-orderable prefactorization algebra FKG ∈ tPFAadd,c describes the time-ordered products from perturbative algebraic quantum field theory, cf. [FR13,Rej16]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
