相关论文: The rigorous analyticity-unitarity program and its…

We reinterpret various properties of Noetherian local rings via the existence of some $n$-ary numerical function satisfying certain uniform bounds. We provide such characterizations for seminormality, weak normality, generalized…

The analyticity properties of the S matrix in the physical region are determined by the correspondence principle, which asserts that the predictions of classical physics are generated by taking the classical limit of the predictions of…

In scattering theory the far field pattern describes the directional dependence of a time-harmonic wave scattered by an obstacle or inhomogeneous medium, when observed sufficiently far away from these objects. Considering plane wave…

In this paper, we attempt to derive ``positivity" bounds on Photon and Gluon Effective Field Theories (EFTs) at one loop level. While for the Photon case, the one loop amplitude is IR finite and well defined in the forward limit, earlier…

We prove a lower bound for the modulus of the amplitude for a two-body process at large scattering angle. This is based on the interplay of the analyticity of the amplitude and the positivity properties of its absorptive part. The…

Using a standard definition of fractional powers on the universal cover $\exp:S\to \mathbb{C}^*$ seen as an infinite helicoid embedded in $\mathbb{R}^3$, we study the statistics of pairs from the countable family $\{n^\alpha \, : \, n \in…

In effective field theory, the positivity bounds of higher derivative operators are derived from analyticity, causality, and unitarity. We show that the positivity bounds on some operators of the effective field theory, e.g.,…

Consider a compact Riemannian manifold with boundary endowed with a magnetic field. A path taken by a particle of unit charge, mass, and energy is called a magnetic geodesic. It is shown that if everything is real-analytic, the topology,…

This paper reviews the progress made over the last five years in studying boundary conditions and semiclassical properties of quantum fields about 4-real-dimensional Riemannian backgrounds. For massless spin-${1\over 2}$ fields one has a…

This paper presents the fascinating correspondence between the geometric function theory and the scattering amplitudes with $O(N)$ global symmetry. A crucial ingredient to show such correspondence is a fully crossing symmetric dispersion…

Effective theories are non-local at the scale of the eliminated heavy particles modes. The gradient expansion which represents such non-locality must be truncated to have treatable models. This step leads to the proliferation of the degrees…

We obtain the matter-graviton scattering amplitude in the gravitational theory of quadratic curvature, which has $R_{\mu\nu}^2$ term in the action. Unitarity bound is not satisfied because of the existence of negative norm states, while an…

This letter constructs, making use of the on-shell spinor-helicity formalism, a possible ultraviolet completion of gravity following a "bottom-up" approach. The assumptions of locality, unitarity and causality i) require an infinite tower…

We prove optimal regularity and derive several geometric properties for solutions of a free boundary problem with fractional diffusion. Additionally, we deduce local $C^{1,\alpha}$ regularity results for the corresponding interior and…

Parameters in an effective field theory can be subject to certain positivity bounds if one requires a UV completion that obeys the fundamental principles of quantum field theory. These bounds are relatively straightforward at the tree…

We prove sharp Landau- and Schottky-type theorems for analytic functions which omit the $n$-th roots of unity. The proofs are based on a sharp lower bound for the Poincar\'e metric of the complex plane punctured at the roots of unity.

Aspects of super-planckian gravitational scattering and black hole formation are investigated, largely via a partial-wave representation. At large and decreasing impact parameters, amplitudes are expected to be governed by single graviton…

We propose data-dependent uniform generalization bounds by approaching the problem from a PAC-Bayesian perspective. We first apply the PAC-Bayesian framework on "random sets" in a rigorous way, where the training algorithm is assumed to…

High-statistics data on the $e^+e^-\to \pi^+\pi^-$ cross section and the pion vector form factor have been obtained recently by several collaborations. Unfortunately, there are some tensions between different datasets, especially the most…

We consider a massive, neutral, scalar field theory of mass $m_0$ in a five dimensional flat spacetime. Subsequently, one spatial dimension is compactified on a circle, $S^1$, ofradius $R$. The resulting theory is defined in the manifold,…