Related papers: Coordinate singularities of self-interacting vecto…
This paper is concerning the inverse conductive scattering of acoustic waves by a bounded inhomogeneous object with possibly embedded obstacles inside. A new uniqueness theorem is proved that the conductive object is uniquely determined by…
The two-dimensional case occupies a special position in the theory of critical phenomena due to the exact results provided by lattice solutions and, directly in the continuum, by the infinite-dimensional character of the conformal algebra.…
We consider a neutral self-interacting massive scalar field defined in a d-dimensional Euclidean space. Assuming thermal equilibrium, we discuss the one-loop perturbative renormalization of this theory in the presence of rigid boundary…
Gibbs fields with continuous spins are studied, the underlying graphs of which can be of unbounded vertex degree and the spin-spin pair interaction potentials are random and unbounded. A high-temperature uniqueness of such fields is proved…
We consider the role that gauge symmetry breaking terms play on the continuum limit of gauge theories in three dimensions. As a paradigmatic example we consider scalar electrodynamics in which $N_f$ complex scalar fields interact with a…
Scale invariant theories which contain (in $4-D$) a four index field strength are considered. The integration of the equations of motion of these $4-index$ field strength gives rise to scale symmetry breaking. The phenomena of mass…
We introduce a classical field theory based on a concept of extended causality that mimics the causality of a point-particle Classical Mechanics by imposing constraints that are equivalent to a particle initial position and velocity. It…
Energy-minimizing constraint maps are a natural extension of the obstacle problem within a vectorial framework. Due to inherent topological constraints, these maps manifest a diverse structure that includes singularities similar to harmonic…
We show that if the $\alpha$-attractor model is realized by the spontaneous breaking of the scale symmetry, then the stability and the dynamics of the vector field that gauges the scale symmetry can severely constrain the $\alpha$-parameter…
These notes address two problems. First, we investigate the question of ``how many'' are (in Baire sense) vector fields in $L^1_t L^q_x$, $q \in [1, \infty)$, for which existence and/or uniqueness of local, distributional solutions to the…
We survey rigorous, formal, and numerical results on the formation of point-like singularities (or blow-up) for a wide range of evolution equations. We use a similarity transformation of the original equation with respect to the blow-up…
If a bulk gravitational path integral can be identified with an average of partition functions over an ensemble of boundary quantum theories, then a corresponding moment problem can be solved. We review existence and uniqueness criteria for…
We extend our study of deriving the local gauge invariance with spontaneous symmetry breaking in the context of an effective field theory by considering self-interactions of the scalar field and inclusion of the electromagnetic interaction.…
Given a finite set of data generated by an unknown ordinary differential equation it is impossible to exactly determine the associated vector field, and hence, bifurcation theory tells us that it is impossible, in general, to correctly…
We show there exist UV-complete field-theoretic models in general dimension, including $2+1$, with the spontaneous breaking of a global symmetry, which persists to the arbitrarily high temperatures. Our example is a conformal vector model…
Treating the gravitational field as a dynamical field, we study the spontaneous symmetry breaking induced by a scalar field under its self-interaction and non-minimal interaction with gravity in four dimensional space-time. In particular,…
Running couplings can be understood as arising from the spontaneous breaking of an exact scale invariance in appropriate effective theories with no dilatation anomaly. Any ordinary quantum field theory, even if it has massive fields, can be…
In this paper, we explore the possibility of constructing the quantum chromodynamics of a massive color-octet vector field without introducing higher structures like extended gauge symmetries, extra dimensions or scalar fields. We show that…
For isolated complex hypersurface singularities with real defining equation we show the existence of a monodromy vector field such that complex conjugation intertwines the local monodromy diffeomorphism with its inverse. In particular, it…
Gravitational properties of a hedge-hog type topological defect in two extra dimensions are considered in General Relativity employing a vector as the order parameter. All previous considerations were done using the order parameter in the…