Claudio Dappiaggi

Bio: Claudio Dappiaggi is an academic researcher from University of Pavia. The author has contributed to research in topics: Quantum field theory & Spacetime. The author has an hindex of 30, co-authored 124 publications receiving 2438 citations. Previous affiliations of Claudio Dappiaggi include University of Vienna & Istituto Nazionale di Fisica Nucleare.

Rigorous steps towards holography in asymptotically flat spacetimes

Abstract: Scalar QFT on the boundary ℑ+ at future null infinity of a general asymptotically flat 4D spacetime is constructed using the algebraic approach based on Weyl algebra associated to a BMS-invariant symplectic form. The constructed theory turns out to be invariant under a suitable strongly-continuous unitary representation of the BMS group with manifest meaning when the fields are interpreted as suitable extensions to ℑ+ of massless minimally coupled fields propagating in the bulk. The group theoretical analysis of the found unitary BMS representation proves that such a field on ℑ+ coincides with the natural wave function constructed out of the unitary BMS irreducible representation induced from the little group Δ, the semidirect product between SO(2) and the two-dimensional translations group. This wave function is massless with respect to the notion of mass for BMS representation theory. The presented result proposes a natural criterion to solve the long-standing problem of the topology of BMS group. Indeed the found natural correspondence of quantum field theories holds only if the BMS group is equipped with the nuclear topology rejecting instead the Hilbert one. Eventually, some theorems towards a holographic description on ℑ+ of QFT in the bulk are established at level of C*-algebras of fields for asymptotically flat at null infinity spacetimes. It is proved that preservation of a certain symplectic form implies the existence of an injective *-homomorphism from the Weyl algebra of fields of the bulk into that associated with the boundary ℑ+. Those results are, in particular, applied to 4D Minkowski spacetime where a nice interplay between Poincare invariance in the bulk and BMS invariance on the boundary at null infinity is established at the level of QFT. It arises that, in this case, the *-homomorphism admits unitary implementation and Minkowski vacuum is mapped into the BMS invariant vacuum on ℑ+.

Rigorous construction and Hadamard property of the Unruh state in Schwarzschild spacetime

Abstract: 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 the Schwarzschild spacetime. Among the several available proposals in the literature, an important physical role is played by the so-called Unruh state which is supposed to be appropriate to capture the physics of a real spherically symmetric black hole formed by collapsing matter. One of the aims of this paper, referring to a massless Klein-Gordon field, is to rigorously construct that state globally, i.e. on the algebra of Weyl observables localized in the union of the static external region, the future event horizon and the non-static black hole region. The Unruh state is constructed following the traditional recipe that it is the vacuum state with respect to the affine parameter U of the geodesic forming the whole past horizon whereas it is the vacum state with respect to the Schwarzschild Killing time t on the past light infinity, interpreting these data within our algebraic formalism. Eventually, making use of the microlocal-analysis approach, we prove that the Unruh state built up following our procedure fulfills the so-called Hadamard condition everywhere it is defined and, hence, it is perturbatively stable, realizing the natural candidate with which one could study purely quantum phenomena such as the role of the back reaction of Hawking's radiation. The achieved results are obtained by means of a bulk-to-boundary reconstruction technique which exploits the Killing (horizon) structure and the conformal asymptotic structure of the underlying background, employing Hormander's theorem on propagation of singularities, some recent results about passive state extended to our case, and a careful analysis of the remaining part of the wavefront set of the state. A crucial technical role is played by the recent results due to Dafermos and Rodnianski on the peeling behaviour of the solutions of Klein-Gordon equations in Schwarzschild spacetime.

Advances in algebraic quantum field theory

Abstract: Structural aspects of quantum field theory.- Introduction to Algebraic Quantum Field Theory.- Algebraic Quantum Field Theory on curved backgrounds.- QED and infrared sectors.- Applicative aspects of algebraic quantum field theory.- Hadamard States and Microlocal Analysis.- Applications of algebraic quantum field theory to cosmology.- Conformal Field Theory and its applications.- Supersymmetric algebraic quantum field theory.- Interacting field theories.- Perturbative Algebraic Quantum Field Theory.- Integrable models and construction of interacting quantum field theories.- Kitaev's Toric Code model.- Algebraic quantum field theory on non commutative spacetimes.

Stable cosmological models driven by a free quantum scalar field

Abstract: In the mathematically rigorous analysis of semiclassical Einstein equations, the renormalization of the stress-energy tensor plays a crucial role. We address such a topic in the case of a scalar field with both arbitrary mass and coupling with gravity in the hypothesis that the underlying algebraic quantum state is of the Hadamard type. Particularly, if we focus on highly symmetric solutions of the semiclassical Einstein equations, the envisaged method displays a de Sitter-type behavior even without an a priori introduced cosmological constant. As a further novel result, we shall show that these solutions turn out to be stable.

Phd by thesis

Abstract: Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Aspects of the BMS/CFT correspondence

Abstract: After a review of symmetries and classical solutions involved in the AdS3/CFT2 correspondence, we apply a similar analysis to asymptotically flat spacetimes at null infinity in 3 and 4 dimensions. In the spirit of two dimensional conformal field theory, the symmetry algebra of asymptotically flat spacetimes at null infinity in 4 dimensions is taken to be the semi-direct sum of supertranslations with infinitesimal local conformal transformations and not, as usually done, with the Lorentz algebra. As a first application, we derive how the symmetry algebra is realized on solution space. In particular, we work out the behavior of Bondi’s news tensor, mass and angular momentum aspects under local conformal transformations.

Bulk Locality and Quantum Error Correction in AdS/CFT

Abstract: We point out a connection between the emergence of bulk locality in AdS/CFT and the theory of quantum error correction. Bulk notions such as Bogoliubov transformations, location in the radial direction, and the holographic entropy bound all have natural CFT interpretations in the language of quantum error correction. We also show that the question of whether bulk operator reconstruction works only in the causal wedge or all the way to the extremal surface is related to the question of whether or not the quantum error correcting code realized by AdS/CFT is also a “quantum secret sharing scheme”, and suggest a tensor network calculation that may settle the issue. Interestingly, the version of quantum error correction which is best suited to our analysis is the somewhat nonstandard “operator algebra quantum error correction” of Beny, Kempf, and Kribs. Our proposal gives a precise formulation of the idea of “subregion-subregion” duality in AdS/CFT, and clarifies the limits of its validity.

Symmetries of asymptotically flat four-dimensional spacetimes at null infinity revisited.

Abstract: It is shown that the symmetry algebra of asymptotically flat spacetimes at null infinity in 4 dimensions should be taken as the semidirect sum of supertranslations with infinitesimal local conformal transformations and not, as usually done, with the Lorentz algebra. As a consequence, two-dimensional conformal field theory techniques will play as fundamental a role in this context of direct physical interest as they do in three-dimensional anti-de Sitter gravity.

Fourier Integral Operators

Abstract: The theory of pseudo differential operators, discussed in § 1, is well suited for investigating various problems connected with elliptic differential equations. However, this theory fails to be adequate for studying equations of hyperbolic type, and one is then forced to examine a wider class of operators, the so-called Fourier integral operators (Egorov [1975], Hormander [1968, 1971, 1983, 1985], Kumano-go [1982], Shubin [1978], Taylor [1981], Treves [1980]).