arXiv subjects

Stefano Galanda

Publications and source records attributed to Stefano Galanda.

9 recordsLinked to original sources

arXiv2026

Equilibrium states for non relativistic Bose gases and the Gross-Pitaevskii limit

In this paper, we present the construction of equilibrium states for a gas of weakly interacting non-relativistic bosons, focusing on the case of a non-trivial background field in infinitely extended space. Building upon a method introduced by Araki and further developed by Fredenhagen and Lindner, we derive the generating function of the correlation functions of the theory as a suitable series. By applying a Hubbard-Stratonovich transformation, we rewrite this quantity into a more mathematically tractable form, allowing us to establish the convergence of the corresponding loop vertex expansion in certain intermediate regimes. Furthermore, we isolate the tree diagrams that produce the scattering length in the dispersion relations of the two-point function of the state within the Gross-Pitaevskii regime. Finally, we use this scattering length to renormalise the background and the two-point function of the fluctuations and we discuss convergence of the generating function of the connected correlation functions of the renormalised theory in the limit of vanishing temperature.

math-ph↗

arXiv2026

The Semiclassical Einstein-Klein-Gordon System: Asymptotic Analysis of Minkowski Spacetime

We establish the linear instability of the semiclassical Einstein-Klein-Gordon system linearised about the Minkowski vacuum spacetime. The proof relies on formulating a forcing problem for both metric and state perturbations within the space of past-compact sections. This geometric framework admits a unique tensor decomposition which, in conjunction with the quantum M{\o}ller operator, enables the decoupling of the linearised system into two distinct Cauchy problems. Consequently, the metric perturbations are shown to be governed by a higher-order, nonlocal hyperbolic partial differential equation. By relegating the nonlocal contributions to subleading order, we establish the well-posedness of this forcing problem. Furthermore, we provide a rigorous asymptotic analysis for physically admissible choices of the renormalisation constants. We prove that the system exhibits a late-time linear instability: the metric perturbations grow exponentially, bounded strictly by a universal scale H, thereby indicating a quantum backreaction-driven transition toward a de Sitter cosmological spacetime. Provided the parameters governing the system are restricted to a physically relevant regime, this universal scale is compatible with the measured expansion of our universe.

math-ph↗

arXiv2026

Haag Duality in the Thermal Sector

We prove that the net of localised von Neumann algebras associated with a real scalar field propagating on Minkowski spacetime, in the KMS representation, satisfies a generalised version of Haag duality. Our proof combines ideas from existing arguments for the ground-state representation with purification techniques.

math-ph↗

arXiv2025

Equilibrium states for non relativistic Bose gases with condensation

In this paper we present the construction of the equilibrium states at positive temperature in the presence of a condensation phase for a Gas of non relativistic Bose particles on an infinite space interacting through a localised two body interaction. We use methods of quantum field theory in the algebraic formulation to obtain this result and in order to prove convergence of the partition function and of the generating function of the correlation functions, we introduce an auxiliary stochastic Gaussian field which mediates the interaction of the Bose particles (Hubbard-Stratonovich transformation). The construction of the equilibrium state and of the partition function in the presence of the condensate, treating the auxiliary stochastic field as external potential, can be achieved using and adapting ideas and methods of Araki. Explicit formulas for the relative entropy of the equilibrium state with the external potential with respect to the equilibrium state of the free theory are obtained adapting known Feynman-Kac formulas for the propagators of the theory. If the two-body interaction is sufficiently weak, the proof of the convergence of the partition function after evaluation of the external stochastic field on a suitable Gaussian state can be given utilizing the properties of the relative entropy mentioned above. Limits where the localisation of the two-body interaction is removed are eventually discussed in combination of the limits of vanishing temperature and or in the weakly interacting regime.

math-ph↗

arXiv2024

Perturbative Construction of Equilibrium States for Interacting Fermionic Field Theories

In this paper, we aim to extend to interacting massive and massless fermionic theories the recent perturbative construction of equilibrium states developed within the framework of perturbative algebraic quantum field theory on Lorentzian spacetime. We analyze the case of interactions which depend on time by a smooth switch-on function and on space by a suitably bounded function that multiplies an interaction Lagrangian density constructed with the field of the theory. The construction is achieved by first considering the case of compact support and, in a second step, by removing the space cutoff with a suitable limit (adiabatic limit). As an application, we consider a Dirac field interacting with a classical stationary background electromagnetic potential, and we compute at first perturbative order (linear response) the expectation value of the conserved current on the equilibrium state for the interacting theory. The resulting expectation value is written as a convolution, in the space coordinates, between the electromagnetic potential and an integral kernel which, at vanishing conjugate momentum, gives the inverse of the square Debye screening length at finite temperature. The corresponding Debye screening effect is visible in the backreaction treated semiclassically of this current on the classical background electromagnetic potential sourced by a classical external current.

math-ph↗

arXiv2024

Entropy-area law and temperature of de Sitter horizons from modular theory

We derive an entropy-area law for the future horizon of an observer in diamonds inside the static patch of de Sitter spacetime, taking into account the backreaction of quantum matter fields. We prove positivity and convexity of the relative entropy for coherent states using Tomita--Takesaki modular theory, from which the QNEC for diamonds follows. Furthermore, we show that the generalized entropy conjecture holds. Finally, we reveal that the local temperature which is measured by an observer at rest exhibits subleading quantum corrections with respect to the well-known cosmological horizon temperature $H/(2π)$.

hep-th↗

arXiv2023

Secular growths and their relation to equilibrium states in perturbative QFT

In the perturbative treatment of interacting quantum field theories, if the interaction Lagrangian changes adiabatically in a finite interval of time, secular growths may appear in the truncated perturbative series also when the interaction Lagrangian density is returned to be constant. If this happens, the perturbative approach does not furnish reliable results in the evaluation of scattering amplitudes or expectation values. In this paper we show that these effects can be avoided for adiabatically switched-on interactions, if the spatial support of the interaction is compact and if the background state is suitably chosen. We start considering equilibrium background states and show that, when thermalisation occurs (interaction Lagrangian of spatial compact support), secular effects are avoided. Furthermore, no secular effects pop up if the limit where the Lagrangian is supported everywhere in space is taken after thermalisation (large time limit), in contrast to the reversed order. This result is generalized showing that if the interaction Lagrangian is spatially compact, secular growths are avoided for generic background states which are only invariant under time translation and to states whose explicit dependence of time is not too strong. Finally, as an application, the presented theorems are used to study a complex scalar and a Dirac field, on a background KMS state, in a classical external electromagnetic potential and the contribution to the two point-function given by a generic loop diagram arising from a second order perturbative expansion.

math-ph↗

arXiv2023

Relative Entropy of Fermion Excitation States on the CAR Algebra

The relative entropy of certain states on the algebra of canonical anticommutation relations (CAR) is studied in the present work. The CAR algebra is used to describe fermionic degrees of freedom in quantum mechanics and quantum field theory. The states for which the relative entropy is investigated are multi-excitation states (similar to multi-particle states) with respect to KMS states defined with respect to a time-evolution induced by a unitary dynamical group on the one-particle Hilbert space of the CAR algebra. If the KMS state is quasifree, the relative entropy of multi-excitation states can be explicitly calculated in terms of 2-point functions, which are defined entirely by the one-particle Hilbert space defining the CAR algebra and the Hamilton operator of the dynamical group on the one-particle Hilbert space. This applies also in the case that the one-particle Hilbert space Hamilton operator has a continuous spectrum so that the relative entropy of multi-excitation states cannot be defined in terms of von Neumann entropies. The results obtained here for the relative entropy of multi-excitation states on the CAR algebra can be viewed as counterparts of results for the relative entropy of coherent states on the algebra of canonical commutation relations (CCR) which have appeared recently. It turns out to be useful to employ the setting of a self-dual CAR algebra introduced by Araki.

math-ph↗

arXiv2022

Relative Entropy for Fermionic Quantum Field Theory

We study the relative entropy, in the sense of Araki, for the representation of a self-dual CAR algebra $\mathfrak{A}_{SDC}(\mathcal{H},Γ)$. We notice, for a specific choice of $f \in \mathcal{H}$, that the associated element in $\mathfrak{A}_{SDC}(\mathcal{H},Γ)$ is unitary. As a consequence, we explicitly compute the relative entropy between a quasifree state over $\mathfrak{A}_{SDC}(\mathcal{H},Γ)$ and an excitation of it with respect to the abovely mentioned unitary element. The generality of the approach, allows us to consider $\mathcal{H}$ as the Hilbert space of solutions of the classical Dirac equation over globally hyperbolic spacetimes, making our result, a computation of relative entropy for a Fermionic Quantum Field Theory. Our result extends those of Longo and Casini et al. for the relative entropy between a quasifree state and a coherent excitation for a free Scalar Quantum Field Theory, to the case of fermions. As a first application, we computed such a relative entropy for a Majorana field on an ultrastatic spacetime.

math-ph↗