Abstract:We discuss the quantization of linearized gravity on globally hyperbolic, asymptotically flat, vacuum spacetimes and the construction of distinguished states which are both of Hadamard form and invariant under the action of all bulk isometries. The procedure, we follow, consists of looking for a realization of the observables of the theory as a sub-algebra of an auxiliary, non-dynamical algebra constructed on future null infinity ℑ + . The applicability of this scheme is tantamount to proving that a solution o… Show more
In this paper it is given an explicit construction of the algebraic quantization of a massless scalar field on two prototypical examples of spacetime with boundary, usually related to the Casimir effect. This paper is based on Ref.[1].
In this paper it is given an explicit construction of the algebraic quantization of a massless scalar field on two prototypical examples of spacetime with boundary, usually related to the Casimir effect. This paper is based on Ref.[1].
“…To conclude this section we stress that, although in this book, we will only focus on real scalar fields, the methods devised can be used also to discuss other scenarios, such as Dirac fields [DHP11] free electromagnetism [DS13,Si11] or linearised gravity [BDM14].…”
Section: Bulk To Boundary Correspondence and Construction Of Hadamardmentioning
“…[SDH14, BDS14, BDHS14, FL16, Ben16, BSS16], but there also exist similar developments for e.g. linearized gravity [FH13,BDM14,Kha16,Kha18] and linearized supergravity [HS13]. In addition to such non-interacting models, examples of perturbatively interacting quantum gauge theories were constructed in [Hol08, FR12, FR13, TZ18] by means of an appropriate adaption of the BRST/BV formalism to AQFT.…”
It is observed that the shifted Poisson structure (antibracket) on the solution complex of Klein-Gordon and linear Yang-Mills theory on globally hyperbolic Lorentzian manifolds admits retarded/advanced trivializations (analogs of retarded/advanced Green's operators). Quantization of the associated unshifted Poisson structure determines a unique (up to equivalence) homotopy algebraic quantum field theory (AQFT), i.e. a functor that assigns differential graded * -algebras of observables and fulfills homotopical analogs of the AQFT axioms. For Klein-Gordon theory the construction is equivalent to the standard one, while for linear Yang-Mills it is richer and reproduces the BRST/BV field content (gauge fields, ghosts and antifields).
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