Hadamard States From Null Infinity
AbstractFree field theories on a four dimensional, globally hyperbolic spacetime, whose dynamics is ruled by a Green hyperbolic partial differential operator, can be quantized following the algebraic...
View ArticleThe Casimir Effect from the Point of View of Algebraic Quantum Field Theory
AbstractWe consider a region of Minkowski spacetime bounded either by one or by two parallel, infinitely extended plates orthogonal to a spatial direction and a real Klein-Gordon field satisfying...
View ArticleConstructing Hadamard States via an Extended Møller Operator
AbstractWe 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...
View ArticleBoundary-Induced Hadamard States
AbstractIn the introduction to this work, we explained that the algebraic approach to quantum field theory is a two-step procedure. The first consists of the assignment to a physical system of a...
View ArticleGeneral Geometric Setup
AbstractGoal of this section is to discuss the geometric background on which our investigation is based.
View ArticleQuantum Fields in Spacetimes with Null Surfaces
AbstractThe goal of this chapter is twofold. On the one hand we will review how the algebra of observables for a real scalar field on globally hyperbolic spacetimes is built. We will show in addition...
View ArticleWick Polynomials and Extended Observables Algebras
AbstractGoal of this chapter is to discuss the interplays between the bulk-to-boundary correspondence outlined in the previous chapters and the extension of the algebra of observables to include also...
View ArticleIntroduction
AbstractIn the last century, our theoretical knowledge of key physical processes has experienced an impressively large and fast growth thanks to the birth and to the development of new theories.
View ArticleHadamard States for Quantum Abelian Duality
AbstractAbelian duality is realized naturally by combining differential cohomology and locally covariant quantum field theory. This leads to a \(\hbox {C}^*\)-algebra of observables, which encompasses...
View ArticleAlgebraic Quantum Field Theory on Spacetimes with Timelike Boundary
AbstractWe analyze quantum field theories on spacetimes M with timelike boundary from a model-independent perspective. We construct an adjunction which describes a universal extension to the whole...
View ArticleRicci Flow from the Renormalization of Nonlinear Sigma Models in the...
AbstractThe perturbative approach to nonlinear Sigma models and the associated renormalization group flow are discussed within the framework of Euclidean algebraic quantum field theory and of the...
View ArticleFundamental solutions for the wave operator on static Lorentzian manifolds...
AbstractWe consider the wave operator on static, Lorentzian manifolds with timelike boundary, and we discuss the existence of advanced and retarded fundamental solutions in terms of boundary...
View ArticleOn Maxwell’s Equations on Globally Hyperbolic Spacetimes with Timelike Boundary
AbstractWe study Maxwell’s equation as a theory for smooth k-forms on globally hyperbolic spacetimes with timelike boundary as defined by Aké et al. (Structure of globally hyperbolic spacetimes with...
View ArticleAharonov–Bohm superselection sectors
AbstractWe show that the Aharonov–Bohm effect finds a natural description in the setting of QFT on curved spacetimes in terms of superselection sectors of local observables. The extension of the...
View ArticleFundamental solutions and Hadamard states for a scalar field with arbitrary...
AbstractWe consider the Klein-Gordon operator on an n-dimensional asymptotically anti-de Sitter spacetime (M,g) together with arbitrary boundary conditions encoded by a self-adjoint pseudodifferential...
View ArticleLinear bosonic quantum field theories arising from causal variational principles
AbstractIt is shown that the linearized fields of causal variational principles give rise to linear bosonic quantum field theories. The properties of these field theories are studied and compared with...
View ArticleHidden freedom in the mode expansion on static spacetimes
AbstractWe review the construction of ground states focusing on a real scalar field whose dynamics is ruled by the Klein–Gordon equation on a large class of static spacetimes. As in the analysis of the...
View ArticleAn Algebraic and Microlocal Approach to the Stochastic Nonlinear Schrödinger...
AbstractIn a recent work Dappiaggi (Commun Contemp Math 24:2150075, 2022), a novel framework aimed at studying at a perturbative level a large class of nonlinear, scalar, real, stochastic PDEs has been...
View ArticleOn a microlocal version of Young’s product theorem
AbstractA key result in distribution theory is Young’s product theorem which states that the product between two Hölder distributions \(u\in \mathcal {C}^\alpha (\mathbb {R}^d)\) and \(v\in \mathcal...
View ArticleBesov wavefront set
AbstractWe develop a notion of wavefront set aimed at characterizing in Fourier space the directions along which a distribution behaves or not as an element of a specific Besov space. Subsequently we...
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