Related papers: Euclidean field theory on a sphere
Soft spheres interacting via a hard core and range of attractive and repulsive "soft-shoulder" potentials self-assemble into clusters forming a variety of mesophases. We combine a mean field theory developed from a lattice model with a…
In a recent pair of papers, Eric DeGiuli has developed a field theory of glasses and granular materials based on the Edwards ensemble, extending our earlier theoretical framework. In this comment, we address a misconception regarding the…
We model the spacetime foam picture by a gas of wormholes in Euclidean field theory. It is shown that at large distances the presence of such a gas leads merely to a renormalization of mass and charge values. We also demonstrate that there…
Algebraic quantum field theory is considered from the perspective of the Hochschild cohomology bicomplex. This is a framework for studying deformations and symmetries. Deformation is a possible approach to the fundamental challenge of…
We consider fermionic fields of higher spin on a four-dimensional de Sitter background. A particular emphasis is placed on the Rarita-Schwinger spin-$\tfrac{3}{2}$ case. Both massive fields and gauge fields are considered, and their…
In this note, we consider generalizations of the Cucker-Smale dynamical system and we derive rigorously in Wasserstein's type topologies the mean-field limit (and propagation of chaos) to the Vlasov-type equation introduced in [12].Unlike…
Unique features of particle orbits produce novel signatures of gravitational observable phenomena, and are quite useful in testing compact astrophysical objects in general relativity or modified theories of gravity. Here we observe a…
We summarize our recently proposed approach to quantum field theory on noncommutative curved spacetimes. We make use of the Drinfel'd twist deformed differential geometry of Julius Wess and his group in order to define an action functional…
Massless interacting scalar fields in de Sitter space have long been known to experience large fluctuations over length scales larger than Hubble distances. A similar situation arises in condensed matter physics in the vicinity of a…
Methodology is provided towards the solution of the minimum enclosing ball problem. This problem concerns the determination of the unique spherical surface of smallest radius enclosing a given bounded set in the d-dimensional Euclidean…
In this paper, we introduce an asymmetric metric on the space of marked Euclidean triangles, and we prove several properties of this metric, including two equivalent definitions of this metric, one of them comparing ratios of functions of…
In this article we study the shape of a compact surface of constant mean curvature of Euclidean space whose boundary is contained in a round sphere. We consider the case that the boundary is prescribed or that the surface meets the sphere…
We study configurations of points on the unit sphere that minimize potential energy for a broad class of potential functions (viewed as functions of the squared Euclidean distance between points). Call a configuration sharp if there are m…
Consequences of Schr\"{o}dinger's antipodal identification on quantum field theory in de Sitter space are investigated. The elliptic $\mathbb{Z}_2$ identification provides observers with complete information. We show that a suitable…
This paper establishes a rigorous geometrical framework for spherical origami, origami using spherical sheets based on spherical geometry. Two settings are treated: origami restricted to the unit sphere ($\mathbb{S}^2$), and…
A frame representation is used to derive a first order quasi-linear symmetric hyperbolic system for a scalar field minimally coupled to gravity. This procedure is inspired by similar evolution equations introduced by Friedrich to study the…
A basic problem in quantizing a field in curved space is the decomposition of the classical modes in positive and negative frequency. The decomposition is equivalent to a choice of a complex structure in the space of classical solutions. In…
This paper describes recent progress in the analysis of relativistic gauge conditions for Euclidean Maxwell theory in the presence of boundaries. The corresponding quantum amplitudes are studied by using Faddeev-Popov formalism and…
The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is presented. The paradigm example studied in this paper is the Euclidean scalar field with a…
The mathematical axiom systems for quantum field theory grew out of Hilbert's sixth problem, that of stating the problems of quantum theory in precise mathematical terms. There have been several competing mathematical systems of axioms, and…