Publications (62)
Feynman path integrals on compact Lie groups with bi-invariant Riemannian metrics
Nicoló Drago, Sonia Mazzucchi, Valter Moretti
In this work we consider a suitable generalization of the Feynman path integral on a specific class of Riemannian manifolds consisting of compact Lie groups with bi-invariant Riema…
Certified quantum random number generator based on single-photon entanglement
Nicolò Leone, Stefano Azzini, Sonia Mazzucchi +2
Quantum entanglement represents an ideal resource to guarantee the security of random numbers employed in many scientific and cryptographic applications. However, entanglement-base…
On Wick polynomials of boson fields in locally covariant algebraic QFT
Igor Khavkine, Alberto Melati, Valter Moretti
This work presents some results about Wick polynomials of a vector field renormalization in locally covariant algebraic quantum field theory in curved spacetime. General vector fie…
Frame functions in finite-dimensional Quantum Mechanics and its Hamiltonian formulation on complex projective spaces
Valter Moretti, Davide Pastorello
This work concerns some issues about the interplay of standard and geometric (Hamiltonian) approaches to finite-dimensional quantum mechanics, formulated in the projective space. O…
Tunnelling black-hole radiation with self-interaction: one-loop computation for Rindler Killing horizons
Giovanni Collini, Valter Moretti, Nicola Pinamonti
Tunnelling processes through black hole horizons have recently been investigated in the framework of WKB theory discovering interesting interplay with the Hawking radiation. A more…
On grand canonical Green functions in the Rindler wedge
Valter Moretti
A problem related to some Green functions found by Guimarães and Linet in the manifold of a straight cosmic string continued in the Rindler space is investigated.
Local -functions, stress-energy tensor, field fluctuations, and all that, in curved static spacetime
Valter Moretti
This is a quick review on some technology concerning the local zeta function applied to Quantum Field Theory in curved static (thermal) spacetime to regularize the stress-energy te…
Hadamard States From Light-like Hypersurfaces
Claudio Dappiaggi, Valter Moretti, Nicola Pinamonti
This book provides a rather self-contained survey of the construction of Hadamard states for scalar field theories in a large class of notable spacetimes, possessing a (conformal)…
Modular dynamics in diamonds
Romeo Brunetti, Valter Moretti
We investigate the relation between the actions of Tomita-Takesaki modular operators for local von Neumann algebras in the vacuum for free massive and massless bosons in four dimen…
Proof of the symmetry of the off-diagonal heat-kernel and Hadamard's expansion coefficients in general Riemannian manifolds
Valter Moretti
We consider the problem of the symmetry of the off-diagonal heat-kernel coefficients as well as the coefficients corresponding to the short-distance-divergent part of the Hadamard…
zeta-function regularization and one-loop renormalization of field fluctuations in curved space-times
Valter Moretti, Devis Iellici
A method to regularize and renormalize the fluctuations of a quantum field in a curved background in the -function approach is presented. The method produces finite quantities…
Generation of quantum-certified random numbers using on-chip path-entangled single photons from an LED
Nicolò Leone, Stefano Azzini, Sonia Mazzucchi +7
Single-photon entanglement is a peculiar type of entanglement in which two or more degrees of freedom of a single photon are correlated quantum-mechanically. Here, we demonstrate a…
Spatial Localization of Relativistic Quantum Systems: The Commutativity Requirement and the Locality Principle. Part II: A Model from Local QFT
Valter Moretti
This paper is the second and final part of a two-part study. We construct positive-energy relativistic spatial localization observables in Minkowski spacetime within standard quant…
Local -function techniques vs point-splitting procedure: a few rigorous results
Valter Moretti
Some general properties of local -function procedures to renormalize some quantities in -dimensional (Euclidean) Quantum Field Theory in curved background are rigorously dis…
Distinguished quantum states in a class of cosmological spacetimes and their Hadamard property
Claudio Dappiaggi, Valter Moretti, Nicola Pinamonti
In a recent paper, we proved that a large class of spacetimes, not necessarily homogeneous or isotropous and relevant at a cosmological level, possesses a preferred codimension one…
Achronal localization and representation of the causal logic from a conserved current, application to the massive scalar boson
Domenico P. L. Castrigiano, Carmine De Rosa, Valter Moretti
Only recently the concept of achronal localization has been developed as the adequate frame for the description of the localizability of a relativistic quantum mechanical system. H…
Mathematical Foundations of Quantum Mechanics: An Advanced Short Course
Valter Moretti
This paper collects and extends the lectures I gave at the "XXIV International Fall Workshop on Geometry and Physics" held in Zaragoza (Spain) August 31 - September 4, 2015. Within…
Rigorous construction and Hadamard property of the Unruh state in Schwarzschild spacetime
Claudio Dappiaggi, Valter Moretti, Nicola Pinamonti
The discovery of the radiation properties of black holes prompted the search for a natural candidate quantum ground state for a massless scalar field theory on Schwarzschild spacet…
On the Stress-Energy Tensor of Quantum Fields in Curved Spacetimes - Comparison of Different Regularization Schemes and Symmetry of the Hadamard/Seeley-DeWitt Coefficients
Thomas-Paul Hack, Valter Moretti
We review a few rigorous and partly unpublished results on the regularisation of the stress-energy in quantum field theory on curved spacetimes: 1) the symmetry of the Hadamard/See…
Optical Approach for the Thermal Partition Function of Photons
Valter Moretti, Devis Iellici
The optical manifold method to compute the one-loop effective action in a static space-time is extended from the massless scalar field to the Maxwell field in any Feynman-like cova…
Mass operator and dynamical implementation of mass superselection rule
Eleonora Annigoni, Valter Moretti
We start reviewing Giulini's dynamical approach to Bargmann superselection rule proposing some improvements. We discuss some general features of the central extensions of the Galil…
Geometric Entropy and Curvature Coupling in Conical Spaces: zeta Function Approach
Valter Moretti
The local function approach is implemented to regularize the natural path integral definition of the geometric entropy in the large mass black hole Euclidean manifold. The cas…
Entropy certification of a realistic QRNG based on single-particle entanglement
Sonia Mazzucchi, Nicolò Leone, Stefano Azzini +2
In single-particle entanglement (SPE) two degrees of freedom of a single particle are entangled. SPE is a resource that can be exploited both in quantum communication protocols and…
Bose-Einstein Condensate and Spontaneous Breaking of Conformal Symmetry on Killing Horizons II
Valter Moretti
In a previous paper (hep-th/0407256) local scalar QFT (in Weyl algebraic approach) has been constructed on degenerate semi-Riemannian manifolds $\bS^1\times Σ$ corresponding to th…
Algebraic QFT in Curved Spacetime and quasifree Hadamard states: an introduction
Igor Khavkine, Valter Moretti
Within this chapter (published as [49]) we introduce the overall idea of the algebraic formalism of QFT on a fixed globally hyperbolic spacetime in the framework of unital -alge…
Thermal partition function of photons and gravitons in a Rindler wedge
Devis Iellici, Valter Moretti
The thermal partition function of photons in any covariant gauge and gravitons in the harmonic gauge, propagating in a Rindler wedge, are computed using a local -function regul…
Representation of the causal logic for the Dirac system and the electron
Domenico P. L. Castrigiano, Carmine De Rosa, Valter Moretti
We construct a covariant representation of the causal logic for the Dirac system and the electron, based on the conserved Dirac probability current and a general current-to-localiz…
Kabat's Surface Terms in the Zeta-Function approach
Devis Iellici, Valter Moretti
The thermal partition functions of photons in any covariant gauge and gravitons in the harmonic gauge, propagating in a Rindler wedge, are computed using a local zeta-function appr…
Analytic Dependence is an Unnecessary Requirement in Renormalization of Locally Covariant QFT
Igor Khavkine, Valter Moretti
Finite renormalization freedom in locally covariant quantum field theories on curved spacetime is known to be tightly constrained, under certain standard hypotheses, to the same te…
The quantization of Proca fields on globally hyperbolic spacetimes: Hadamard states and Møller operators
Valter Moretti, Simone Murro, Daniele Volpe
This paper deals with several issues concerning the algebraic quantization of the real Proca field in a globally hyperbolic spacetime and the definition and existence of Hadamard s…
Thermal Wightman Functions and Renormalized Stress Tensors in the Rindler Wedge
Valter Moretti, Luciano Vanzo
The Wightman functions in the Rindler portion of Minkowski space-time are presented for any value of the temperature and for massless spin fields up to s=1 and the renormalized str…
Spatial Localization of Relativistic Quantum Systems: The Commutativity Requirement and the Locality Principle. Part I: A General Analysis
Valter Moretti
We investigate whether commutativity is necessary to represent relativistic locality for localization observables of relativistic quantum systems in Minkowski spacetime. A well kno…
On the Relativistic Spatial Localization for massive real scalar Klein-Gordon quantum particles
Valter Moretti
I rigorously analyze a proposal, introduced by D.R.Terno, about a spatial localization observable for a Klein-Gordon massive real particle in terms of a Poincaré-covariant family…
On the global Hadamard parametrix in QFT and the signed squared geodesic distance defined in domains larger than convex normal neighbourhoods
Valter Moretti
We consider the global Hadamard condition and the notion of Hadamard parametrix whose use is pervasive in algebraic QFT in curved spacetime (see refences in the main text). We poin…
Bulk-boundary asymptotic equivalence of two strict deformation quantizations
Valter Moretti, Christiaan J. F van de Ven
The existence of a strict deformation quantization of , the state space of the matrices which is canonically a compact Poi…
Proof of the symmetry of the off-diagonal Hadamard/Seeley-deWitt's coefficients in Lorentzian manifolds by a local Wick rotation
Valter Moretti
Completing the results obtained in a previous paper, we prove the symmetry of Hadamard/Seeley-deWitt off-diagonal coefficients in smooth -dimensional Lorentzian manifolds. To th…
Spectral representations of normal operators via Intertwining Quaternionic Projection Valued Measures
Riccardo Ghiloni, Valter Moretti, Alessandro Perotti
The possibility of formulating quantum mechanics over quaternionic Hilbert spaces can be traced back to von Neumann's foundational works in the thirties. The absence of a suitable…
Comments on the Stress-Energy Tensor Operator in Curved Spacetime
Valter Moretti
Hollands and Wald's technique based on *-algebras of Wick products of field operators is strightforwardly generalized to define the stress-energy tensor operator in curved globally…
Hessling's Quantum Equivalence Principle and the Temperature of an Extremal Reissner-Nordström Black Hole
Valter Moretti
The Hessling improvement of the Haag, Narnhofer and Stein principle is analysed in the case of a massless scalar field propagating outside of an extremal R-N black hole. It is foun…
The interplay of the polar decomposition theorem and the Lorentz group
Valter Moretti
It is shown that the polar decomposition theorem of operators in (real) Hilbert spaces gives rise to the known decomposition in boost and spatial rotation part of any matrix of the…
Euclidean Thermal Green Functions of Photons in Generalized Euclidean Rindler Spaces for any Feynman-like Gauge
Valter Moretti
The thermal Euclidean Green functions for Photons propagating in the Rindler wedge are computed employing an Euclidean approach within any covariant Feynman-like gauge. This is don…
Direct -function approach and renormalization of one-loop stress tensors in curved spacetimes
Valter Moretti
A method which uses a generalized tensorial -function to compute the renormalized stress tensor of a quantum field propagating in a (static) curved background is presented. The…
Continuous slice functional calculus in quaternionic Hilbert spaces
Riccardo Ghiloni, Valter Moretti, Alessandro Perotti
The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical spectrum of a normal…
Topological features of massive bosons on two dimensional Einstein space-time
Romeo Brunetti, Lorenzo Franceschini, Valter Moretti
In this paper we tackle the problem of constructing explicit examples of topological cocycles of Roberts' net cohomology, as defined abstractly by Brunetti and Ruzzi. We consider t…
One-loop stress-tensor renormalization in curved background: the relation between -function and point-splitting approaches, and an improved point-splitting procedure
Valter Moretti
We conclude the rigorous analysis of a previous paper concerning the relation between the (Euclidean) point-splitting approach and the local -function procedure to renormalize…
The classical limit of Schrödinger operators in the framework of Berezin quantization and spontaneous symmetry breaking as emergent phenomenon
Valter Moretti, Christiaan J. F. van de Ven
The algebraic properties of a strict deformation quantization are analysed on the classical phase space $\bR^{2n}$. The corresponding quantization maps enable us to take the limit…
The correct formulation of Gleason's theorem in quaternionic Hilbert spaces
Valter Moretti, Marco Oppio
From the viewpoint of the theory of orthomodular lattices of elementary propositions, Quantum Theories can be formulated in real, complex or quaternionic Hilbert spaces as establis…
Paracausal deformations of Lorentzian metrics and Møller isomorphisms in algebraic quantum field theory
Valter Moretti, Simone Murro, Daniele Volpe
Given a pair of normally hyperbolic operators over (possibily different) globally hyperbolic spacetimes on a given smooth manifold, the existence of a geometric isomorphism, called…
The notion of observable and the moment problem for *-algebras and their GNS representations
Nicolò Drago, Valter Moretti
We address some usually overlooked issues concerning the use of -algebras in quantum theory and their physical interpretation. If is a -algebra describing a qu…
Quantum theory in quaternionic Hilbert space: How Poincaré symmetry reduces the theory to the standard complex one
Valter Moretti, Marco Oppio
We extend some results of group representation theory and von Neumann algebras to the quaternionic Hilbert space case, proving the double commutant theorem (whose quaternionic proo…
Uniqueness theorem for BMS-invariant states of scalar QFT on the null boundary of asymptotically flat spacetimes and bulk-boundary observable algebra correspondence
Valter Moretti
Scalar BMS-invariant QFT defined on the causal boundary $\scri$ of an asymptotically flat spacetime is discussed. (a)(i) It is noticed that the natural invariant pure quasifr…
Strict deformation quantization of the state space of with applications to the Curie-Weiss model
Klaas Landsman, Valter Moretti, Christiaan J. F. van de Ven
Increasing tensor powers of the matrices are known to give rise to a continuous bundle of -algebras over …
Quantum particle localization observables on Cauchy surfaces of Minkowski spacetime and their causal properties
Carmine De Rosa, Valter Moretti
We introduce and study a general notion of spatial localization on spacelike smooth Cauchy surfaces of quantum systems in Minkowski spacetime. The notion is constructed in terms of…
Quantum theory in real Hilbert space: How the complex Hilbert space structure emerges from Poincaré symmetry
Valter Moretti, Marco Oppio
As established by Solèr, Quantum Theories may be formulated in real, complex or quaternionic Hilbert spaces only. Stückelberg provided physical reasons for ruling out real Hilber…
Generalized Complex Spherical Harmonics, Frame Functions, and Gleason Theorem
Valter Moretti, Davide Pastorello
Consider a finite dimensional complex Hilbert space $\cH$, with $dim(\cH) \geq 3$, define $\bS(\cH):= \{x\in \cH \:|\: ||x||=1\}$, and let $ν_\cH$ be the unique regular Borel posi…
A review on recent results of the -function regularization procedure in curved spacetime
Valter Moretti
Some recent (1997-1998) theoretical results concerning the -function regularization procedure used to renormalize, at one-loop, the effective Lagrangian, the field fluctuations…
Chernoff approximations of Feller semigroups in Riemannian manifolds
Sonia Mazzucchi, Valter Moretti, Ivan Remizov +1
Chernoff approximations of Feller semigroups and the associated diffusion processes in Riemannian manifolds are studied. The manifolds are assumed to be of bounded geometry, thus i…
State independence for tunneling processes through black hole horizons and Hawking radiation
Valter Moretti, Nicola Pinamonti
Tunneling processes through black hole horizons have recently been investigated in the framework of WKB theory discovering interesting interplay with the Hawking radiation. In this…
An operational construction of the sum of two non-commuting observables in quantum theory and related constructions
Nicolò Drago, Sonia Mazzucchi, Valter Moretti
The existence of a real linear-space structure on the set of observables of a quantum system -- i.e., the requirement that the linear combination of two generally non-commuting obs…
Some recent results in scalar quantum field theory in globally hyperbolic asymptotically flat spacetimes
Valter Moretti
Some recent results obtained by the author and collaborators about QFT in asymptotically flat spacetimes at null infinity are summarized and reviewed. In particular it is focused o…
Spectral properties of compact normal quaternionic operators
Riccardo Ghiloni, Valter Moretti, Alessandro Perotti
General, especially spectral, features of compact normal operators in quaternionic Hilbert spaces are studied and some results are established which generalize well-known propertie…
A Bisognano-Wichmann-like Theorem in a Certain Case of a Non Bifurcate Event Horizon related to an Extreme Reissner-Nordström Black Hole
Valter Moretti, Stefan Steidl
Thermal Wightman functions of a massless scalar field are studied within the framework of a ``near horizon'' static background model of an extremal R-N black hole. This model is bu…