arXiv subjects

Ugo Moschella

Publications and source records attributed to Ugo Moschella.

At least 19 recordsLinked to original sources

arXiv2026

Effective potentials for de Sitter and anti de Sitter quantum fields

We derive a systematic treatment of one-loop effective potentials for interacting scalar fields in curved spacetimes, providing a general formula valid in arbitrary geometries and explicit results for de Sitter and anti-de Sitter backgrounds. We then compute the effective potential for a scalar $O(N)$ theory on a de Sitter space in any integer dimension. In $d=3$ and dimensional regularization, we extend the calculation up to two loops and compute the $\beta$-function and the anomalous mass dimension. They coincide exactly with flat-space results, despite dramatic curvature modifications to physical masses/couplings. The flat limit $R\to\infty$ recovers Coleman-Weinberg, confirming consistency. Working in $d=3$ dimensions, we repeat the calculation for $AdS_3$ by using point-splitting regularization, obtaining analogous results for the $\beta$-function and anomalous mass dimension.

hep-th↗

arXiv2025

Two point functions and quantum fields in the anti-de Sitter universe

We construct a manifestly covariant and coordinate-free plane-wave representation of scalar two-point functions in $d$-dimensional anti-de Sitter spacetime. The construction is based on a new class of holomorphic plane waves defined globally on the universal covering of the AdS via chiral cones in the complex null cone. Imposing AdS invariance, locality, positive definiteness and a spectral condition, we obtain integral representations as superpositions over relative homology cycles reproducing the standard maximally analytic solutions in terms of Legendre functions of the second kind. In Poincar\'e coordinates, the two-point functions diagonalize into a Kallen-Lehmann superposition of (d-1)-dimensional Minkowski correlators where the weight is a product of Bessel functions. This diagonalization clarifies the relation between Euclidean and Lorentzian AdS quantum field theory and allows Wick rotation of Euclidean Feynman diagrams to Lorentzian integrals supported on a single Poincare patch while preserving full AdS covariance.

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arXiv2025

Anti-de Sitter, plane waves and quantum field theory

We present a new plane-wave expansion of the Wightman functions of anti de Sitter scalar fields and showcase its conceptual and technical importance in AdS quantum field theory. We deduce from it a new integral representation of the Feynman propagator which helps in clarifying the relation between AdS Euclidean and Lorentzian Feynman diagrams in concrete examples. The plane-wave expansion makes it possible also to demonstrate numerous new nontrivial formulas for Bessel and Legendre functions, and we provide two examples.

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arXiv2024

Plane waves, harmonic analysis in de Sitter and anti de Sitter Quantum Field Theory and the spectral condition

We review the role of the spectral condition as a characteristic feature unifying Minkowski, de Sitter and anti de Sitter Quantum Field Theory. In this context, we highlight the role of an important class of plane waves which are either de Sitter or anti de Sitter covariant and are compatible with the relevant analyticity domains linked to the spectral condition(s). We show again how to expand the two-point functions and propagators in terms of them and some of the advantages of doing so rather than using special coordinate systems and separated variables.

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arXiv2024

Loops in Anti de Sitter space

We discuss general one and two-loop banana diagrams and one-loop diagrams with external lines with arbitrary masses on the anti de Sitter spacetime by using methods of AdS quantum field theory in the dimensional regularization approach. The banana diagrams explicitly computed in this paper are indeed the necessary ingredients for the evaluation of the two-loop effective potential of the Standard Model and can be used to extend the flat space results in in presence of a negative cosmological constant. In the one-loop case we also compute the effective potential for an $O(N)$ model in $d=4$ dimension as an explicit function of the cosmological constant $\Lambda$, both exactly and perturbatively up to order $\Lambda$. In the two-loop case we show the explicit calculation is possible thanks to a remarkable discrete K\"all\'en-Lehmann formula which we found and proved sometimes ago and whose domain of applicability we extend in the present paper.

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arXiv2024

Loops in de Sitter space

We discuss general one and two-loops banana diagrams with arbitrary masses on the de Sitter spacetime by using direct methods of dS quantum field theory in the dimensional regularization approach. In the one-loop case we also compute the effective potential for an $O(N)$ model in $d=4$ dimension as an explicit function of the cosmological constant $Λ$, both exactly and perturbatively up to order $Λ$. For the two-loop case we show that the calculation is made easy thanks to a remarkable Kallen-Lehmann formula that has been in the literature for a while. We discuss the divergent cases at d=3 using a contiguity formula for generalized hypergeometric functions and we extract the dominant term at d=4 proving a general formula to deal with a divergent hypergeometric series.

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arXiv2023

Banana integrals in configuration space

We reconsider the computation of banana integrals at different loops, by working in the configuration space, in any dimension. We show how the 2-loop banana integral can be computed directly from the configuration space representation, without the need to resort to differential equations, and we include the analytic extension of the diagram in the space of complex masses. We also determine explicitly the $\varepsilon$ expansion of the two loop banana integrals, for $d=j-2\varepsilon$, $j=2,3,4$.

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arXiv2022

The massless thermal field and the thermal fermion bosonization in two dimensions

We come back to the issue of bosonization of fermions in two spacetime dimension and give a new costruction in the steady state case where left and right moving particles can coexist at two different temperatures. A crucial role in our construction is played by translation invariant infrared states and the corresponding field operators which are naturally linked to the infrared behaviour of the correlation functions. We present two applications: a simple new derivation in the free relativistic case of a formula by Bernard and Doyon and a full operator solution of the massless Thirring model in the steady state case where the left and right movers have two distinct temperatures.

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arXiv2021

New dynamical features of pure k-essential cosmologies

We come back on the dynamical properties of k-essential cosmological models and show how the interesting phenomenological features of those models are related to the existence of boundaries in the phase surface. We focus our attention to the branching points where the energy density has an extremum and the effective speed of sound diverges. We discuss the behaviour of solutions of a general class of cosmological models exhibiting such curves and give two possible interpretations; the most interesting possibility regards the arrow of time that is reversed in trespassing the branching curve. This study teaches to us something new about general FLRW cosmologies where the fluids driving the cosmic evolution have equations of state that are multivalued functions of the energy density and other thermodynamical quantities.

gr-qc↗

arXiv2020

QFT and topology in two dimensions: $SL(2,{\Bbb R})$-symmetry and the de Sitter universe

We study bosonic Quantum Field Theory on the double covering $\widetilde{dS}_{2}$ of the 2-dimensional de Sitter universe, identified to a coset space of the group $SL(2,{\Bbb R})$. The latter acts effectively on $\widetilde{dS}_{2}$ and can be interpreted as it relativity group. The manifold is locally identical to the standard the Sitter spacetime ${dS}_2$; it is globally hyperbolic, geodesically complete and an inertial observer sees exactly the same bifurcate Killing horizons as in the standard one-sheeted case. The different global Lorentzian structure causes however drastic differences between the two models. We classify all the $SL(2,{\Bbb R})$-inveriant two-point functions and show that: 1) there is no Hawking-Gibbons temperature; 2) there is no covariant field theory solving the Klein-Gordon equation with mass less than $1/2R$ , i.e. the complementary fields go away.

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arXiv2019

Topological surprises in de Sitter QFT in two-dimensions

Motivated by the study of soluble models of quantum field theory, we illustrate a new type of topological effect by comparing the constructions of canonical Klein-Gordon quantum fields on the two-dimensional de Sitter spacetime as opposed to its double covering. We show that the while commutators of the two fields coincide locally, the global topological differences make the theories drastically different. Many of the well-known features of de Sitter quantum field theory disappear. In particular there is nothing like a Bunch-Davies vacuum. Correspondingly, even though the local horizon structure is the same for the two universes there is no Hawking - Gibbons thermal state. Finally, there is no complementary series of fields.

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arXiv2018

Ultraviolet phenomena in AdS self-interacting quantum field theory

We study the one-loop corrections to the four-point function in the Anti de Sitter space-time for a $ϕ^4$ field theory. Our calculation shows the existence of non-local counterterms which however respect the AdS isometry. Our arguments are quite general and applicable to other (non-conformal) AdS field theories. We also explain why calculations in Euclidean and Lorentzian signatures should differ even at the leading order in non globaly hyperbolic manifolds.

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arXiv2016

de Sitter symmetry of Neveu-Schwarz spinors

We study the relations between Dirac fields living on the 2-dimensional Lorentzian cylinder and the ones living on the double-covering of the 2-dimensional de Sitter manifold, here identified as a certain coset space of the group $SL(2,R)$. We show that there is an extended notion of de Sitter covariance only for Dirac fields having the Neveu-Schwarz anti-periodicity and construct the relevant cocycle. Finally, we show that the de Sitter symmetry is naturally inherited by the Neveu-Schwarz massless Dirac field on the cylinder.

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arXiv2014

de Sitter tachyons and related topics

We present a complete study of a family of tachyonic scalar fields living on the de Sitter universe. We show that for an infinite set of discrete values of the negative squared mass the fields exhibit a gauge symmetry and there exists for them a fully acceptable local and covariant quantization similar to the Feynman-Gupta-Bleuler quantization of free QED. For general negative squares masses we also construct positive quantization where the de Sitter symmetry is spontaneously broken. We discuss the sense in which the two quantizations may be considered physically inequivalent even when there is a Lorentz invariant subspace in the second one.

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arXiv2013

Doubly elliptic strings on the (anti-)de Sitter manifold

We present a new class of elliptic-like strings on two-dimensional manifolds of constant curvature. Our solutions are related to a class of identities between Jacobi theta functions and to the geometry of the lightcone in one (spacelike) dimension more.

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arXiv2012

Infrared surprises in the de Sitter universe

We describe a few unexpected features of de Sitter Quantum Field Theory that have no Minkowskian counterparts. These phenomena show that even when the cosmological constant is tiny a Minkowskian way of fast thinking about de Sitter can lead to mistakes and that de Sitter QFT is essentially different from standard relativistic (Minkowskian) QFT.

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arXiv2011

Anti de Sitter quantum field theory and a new class of hypergeometric identities

We use Anti-de Sitter quantum field theory to prove a new class of identities between hypergeometric functions related to the Källén-Lehmann representation of products of two Anti-de Sitter two-point functions. A rich mathematical structure emerges. We apply our results to study the decay of unstable Anti-de Sitter particles. The total amplitude is in this case finite and Anti-de Sitter invariant.

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arXiv2010

Scalar tachyons in the de Sitter universe

We provide a construction of a class of local and de Sitter covariant tachyonic quantum fields which exist for discrete negative values of the squared mass parameter and which have no Minkowskian counterpart. These quantum fields satisfy an anomalous non-homogeneous Klein-Gordon equation. The anomaly is a covariant field which can be used to select the physical subspace (of finite codimension) where the homogeneous tachyonic field equation holds in the usual form. We show that the model is local and de Sitter invariant on the physical space. Our construction also sheds new light on the massless minimally coupled field, which is a special instance of it.

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