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In this paper we review many interesting open problems in mathematical physics which may be attacked with the help of tools from constructive field theory. They could give work for future mathematical physicists trained with the…
We establish a new generalization of an $L^2$ extension theorem of Ohsawa-Takegoshi type. The improvement in the theorem is that it allows the usual curvature assumptions to be significantly weakened in certain favorable settings. The…
In this paper the authors study set expansion in finite fields. Fourier analytic proofs are given for several results recently obtained by Solymosi, Vinh and Vu using spectral graph theory. In addition, several generalizations of these…
We explore the dynamics of assisted quintessence, where more than one scalar field is present with the same potential. For potentials with tracking solutions, the fields naturally approach the same values; in the context of inflation this…
We present a novel scenario where a scalar field acquires a mass which depends on the local matter density: the field is massive on Earth, where the density is high, but is essentially free in the solar system, where the density is low. All…
Survival and percolation probabilities are most important quantities in the theory and in the application of growth models with spreading. We construct field theoretical expressions for these probabilities which are feasible for…
By employing consistent supersymmetric higher derivative terms, we show that the supersymmetric theories may have a sector where the scalar potential does no longer have the conventional form. The theories under consideration contain…
A simple implementation of Noether's theorem for discrete symmetries in relativistic continuum field theories is presented. The associated conserved current is exemplified by charge conjugation and a cyclic symmetry. In addition, the…
The sedenion compounding fields and their quantum interplays can be presented by analogy with the octonionic electromagnetic, gravitational, strong and weak interactions. In sedenion fields which are associated with electromagnetic,…
As the possibility to decouple temporal and spatial variations of the electromagnetic field, leading to a wavelength stretching, has been recognized to be of paramount importance for practical applications, we generalize the idea of…
In connection to the development of the field of Combinatorics on Words, we present a list of open problems and conjectures that were stated during the ten last meetings WORDS. We wish to continually update the present document by adding…
A recent paper \cite{Bousso:2022cun} put forward a theorem showing that hyperentropic surface would result in incomplete null generators for a null hypersurface emanating from the surface provided it satisfies the null curvature condition…
Pairs potential-density in terms of elementary functions that represents flat rings structures are presented. We study structures representing one or several concentric flat rings. Also disks surrounded by concentric flat rings are…
The global behavior of scalar field cosmological models with very hard potential walls is investigated via the simple example of an exponentially steep potential well. It is found that the solutions exhibit a non-trivial oscillatory…
It has been suggested that quantum fluctuations of the gravitational field could give rise in the lowest approximation to an effective noncommutative version of Kaluza-Klein theory which has as extra hidden structure a noncommutative…
Thin elastic sheets appear in systems ranging from graphene to biological membranes, where phenomena such as wrinkling, folding, and thermal fluctuations originate from geometric nonlinearities. These effects are treated within weakly…
The current acceleration of the Universe is one of the most puzzling issues in theoretical physics nowadays. We are far from giving an answer on this letter to its true nature. Yet, with the observations we have at hand, we analyse the…
When supersymmetry is spontaneously broken it will be generically non-linearly realized. A method to describe the non-linear realization of supersymmetry is with constrained superfields. We discuss the basic features of this description and…
We construct here a class of collapsing scalar field models with a non-zero potential, which result in a naked singularity as collapse end state. The weak energy condition is satisfied by the collapsing configuration. It is shown that…
This paper demonstrates that singularities form in the classical $(5+1)$-dimensional, co-rotational Skyrme model. It was recently proven by Chen, Sch\"orkhuber, and the author that the strong field limit of the $(5+1)$-dimensional,…