arXiv subjects

Beatrice Costeri

Publications and source records attributed to Beatrice Costeri.

5 recordsLinked to original sources

arXiv2026

A perturbative approach to the Wetterich equation for Bosonic and Fermionic interacting fields

We study the Lorentzian Wetterich Renormalization Group (RG) flow equation for interacting quantum fields on curved backgrounds within the framework of perturbative Algebraic Quantum Field Theory (pAQFT). Specifically, we consider two classes of models: two mutually interacting scalar fields on globally hyperbolic spacetimes without boundary and, under the further assumption that the underlying background is spin, self-interacting Dirac fields. In both cases, we derive the corresponding RG flow equations within a Local Potential Approximation and compute the beta functions for the relevant couplings. For the scalar model, we also discuss an asymmetric interaction potential which is formally reminiscent of the Martin-Siggia-Rose description of a stochastic dynamics, thereby indicating a possible connection between Lorentzian algebraic RG methods [DDP+24] and stochastic field-theoretic models, [Duc25]. In addition, we address the local well-posedness of the resulting flow equations. Adapting the strategy detailed in [DP23] and based on the the Nash-Moser theorem, we prove local existence and uniqueness of solutions for both the scalar and the Dirac models.

math-ph↗

arXiv2026

Schauder estimates for germs of distributions on smooth manifolds

We discuss germs of distributions on $d-$dimensional smooth Riemannian manifolds and, in particular, we derive \emph{multi-level Schauder estimates} without making any further assumptions on the underlying geometry. As a preliminary step, we define the notions of coherence and homogeneity for germs of distributions on open subsets of $\mathbb{R}^d$, $d \ge 1$. Subsequently, we formulate both the reconstruction theorem, cf., [CZ20], and the Schauder estimates, cf., [BCZ24], in this setting. Leveraging the properties of the exponential map, we extend these results to Riemannian manifolds. Specifically, we devise a counterpart of the reconstruction theorem previously established in the literature [RS21], while additionally proving the regularity of the reconstructed distribution in suitable H\"older-Zygmund spaces. Finally, by introducing a novel concept of $\beta$-regularizing kernels on Riemannian manifolds, we establish Schauder estimates for coherent and homogeneous germs in this context.

math-ph↗

arXiv2025

Spectral asymmetry via pseudodifferential projections: the massless Dirac operator

A new approach to the study of spectral asymmetry for systems of partial differential equations (PDEs) on closed manifolds was proposed in a recent series of papers by the first author and collaborator. They showed that information on spectral asymmetry can be encoded within and recovered from a negative order pseudodifferential operator -- the asymmetry operator -- constructed from appropriately defined pseudodifferential (spectral) projections. In this manuscript we apply these techniques to the study of the massless Dirac operator; in particular, we compute the principal symbol of the asymmetry operator, accounting for the underlying gauge invariance.

math-ph↗

arXiv2024

Conservation Law and Trace Anomaly for the Stress Energy Tensor of a Self-Interacting Scalar Field

We consider a self-interacting, massive, real scalar field on a four-dimensional globally hyperbolic spacetime and the associated stress-energy tensor. Using techniques proper of the algebraic approach to perturbative quantum field theory, we study the associated, Wick-ordered, quantum observable. In particular we generalize a construction, first developed in the free field theory scenario by Moretti in [Mor03], aimed at exploiting the existing freedoms in the definition of the classical stress-energy tensor, in order to define a quantum counterpart which is divergence free. We focus on Minkowski spacetime proving that this procedure can be adapted also to cubic or quartic self-interactions, at least up to order $\mathcal{O}(\lambda^3)$ in perturbation theory. We remark that this result can be extended to arbitrary globally hyperbolic spacetimes, although, in this case one needs to exploit the existing regularization freedom in the construction of the Wick ordered stress-energy tensor.

math-ph↗

arXiv2024

A microlocal investigation of stochastic partial differential equations for spinors with an application to the Thirring model

On a $d$-dimensional Riemannian, spin manifold $(M,g)$ we consider non-linear, stochastic partial differential equations for spinor fields, driven by a Dirac operator and coupled to an additive Gaussian, vector-valued white noise. We extend to the case in hand a procedure, introduced in [DDRZ20] for the scalar counterpart, which allows to compute at a perturbative level the expectation value of the solutions as well as the associated correlation functions accounting intrinsically for the underlying renormalization freedoms. This framework relies strongly on tools proper of microlocal analysis and it is inspired by the algebraic approach to quantum field theory. As a concrete example we apply it to a stochastic version of the Thirring model proving in particular that it lies in the subcritical regime if $d\leq 2$.

math-ph↗