Constructing Hadamard states via an extended Møller operator

Abstract

We consider real scalar field theories whose dynamics is ruled by normally hyperbolic operators differing only by a smooth potential $V$. By means of an extension of the standard definition of Møller operator, we construct an isomorphism between the associated spaces of smooth solutions and between the associated algebras of observables. On the one hand such isomorphism is non-canonical since it depends on the choice of a smooth time-dependant cut-off function. On the other hand, given any quasi-free Hadamard state for a theory with a given $V$, such isomorphism allows for the construction of another quasi-free Hadamard state for a different potential. The resulting state preserves also the invariance under the action of any isometry, whose associated Killing field commutes with the vector field built out of the normal vectors to a family of Cauchy surfaces, foliating the underlying manifold. Eventually we discuss a sufficient condition to remove on static spacetimes the dependence on the cut-off via a suitable adiabatic limit.

27 pages, published version

References in corpus (3)

• Cosmological horizons and reconstruction of quantum field theories
• States of Low Energy on Robertson-Walker Spacetimes
• The time slice axiom in perturbative quantum field theory on globally hyperbolic spacetimes

Cited by in corpus (9)

• Hadamard property of the in and out states for Klein-Gordon fields on asymptotically static spacetimes
• The algebra of Wick polynomials of a scalar field on a Riemannian manifold
• On the adiabatic limit of Hadamard states
• On Wick polynomials of boson fields in locally covariant algebraic QFT
• A new class of Fermionic Projectors: Møller operators and mass oscillation properties
• Ricci Flow from the Renormalization of Nonlinear Sigma Models in the Framework of Euclidean Algebraic Quantum Field Theory
• Intertwining operators for symmetric hyperbolic systems on globally hyperbolic manifolds
• Equilibrium states in Thermal Field Theory and in Algebraic Quantum Field Theory
• Thermal state with quadratic interaction