Related papers: Minima of Classically Scale-Invariant Potentials
Exact mathematical solution of the minimization conditions of scalar the Higgs potential of the Finite Supersymmetric Grand Unification Theory is proposed and extremal field configurations are found. Types of extrema are investigated and…
The orbit space for a scalar field in a complex square matrix representation obtains a Minkowski space structure from the Cauchy-Schwarz inequality. It can be used to find vacuum stability conditions and minima of the scalar potential. The…
The Gildener-Weinberg models are of particular interest in the context of extensions to the Standard Model of particle physics. These extensions may encompass a variety of theories, including double Higgs models, Grand Unification Theories,…
The existence of compactly supported global minimisers for continuum models of particles interacting through a potential is shown under almost optimal hypotheses. The main assumption on the potential is that it is catastrophic, or not…
After a summary of a recently proposed new type of instant form of dynamics (the Wigner-covariant rest-frame instant form), the reduced Hamilton equations in the covariant rest-frame Coulomb gauge for the isolated system of N scalar…
We study a simplified version of the Standard Electroweak Model and introduce the concept of the physical gauge invariant effective potential in terms of matrix elements of the Hamiltonian in physical states. This procedure allows an…
Using the method of shape invariant potentials, a number of exact solutions of one dimensional effective mass Schrodinger equation are obtained. The solutions with equi-spaced spectrum are discussed in detail.
The questions of the origin of electroweak symmetry breaking and neutrino mass are two major puzzles in particle physics. Neutrino mass generation requires new physics beyond the Standard Model and also suggests reconsideration of physics…
We establish lower semi-continuity and strict convexity of the energy functionals for a large class of vector equilibrium problems in logarithmic potential theory. This in particular implies the existence and uniqueness of a minimizer for…
In the present paper we develop the theory of minimization for energies with multivariate kernels, i.e. energies, in which pairwise interactions are replaced by interactions between triples or, more generally, $n$-tuples of particles. Such…
We perform a systematic analysis of an extension of the Standard Model that includes a complex singlet scalar field and is scale invariant at the tree level. We call such a model the Minimal Scale Invariant extension of the Standard Model…
The effective potential is a widely used phenomenological tool to investigate phase transitions occurring in the early Universe at finite temperature. In the standard perturbative treatment the potential becomes complex in some region of…
Given a positive definite kernel in a locally compact space, we study a minimal energy problem in the presence of an external field over the class of all nonnegative Radon measures that are supported by a given closed noncompact set,…
We consider Brans-Dicke type nonminimally coupled scalar field as a candidate for dark energy. In the conformally transformed Einstein's frame, our model is similar to {\it coupled quintessence} model. In such models, we consider potentials…
Assuming the existence of a local, analytic, unitary UV completion in a Poincar\'{e} invariant scalar field theory with a mass gap, we derive an infinite number of positivity requirements using the known properties of the amplitude at and…
We consider a constrained minimal energy problem with an external field over noncompact classes of infinite dimensional vector measures on a locally compact space. The components are positive measures (charges) that are constrained from…
The problem of defining a gauge invariant effective potential with a strict energetic interpretation is examined in the context of spontaneously broken gauge theories. It is shown that such a potential can be defined in terms of a composite…
Starting from a precise two-nucleon potential, we use the method of unitary transformations to construct an effective potential that involves only momenta less than a given maximal value. We describe this method for an S-wave potential of…
The Shape invariant method has the algebraic structure and its algebras are infinite-dimensional. These algebras are converted into finite-dimensional under conditions. Based on the property of this method we obtain the algebraic structure…
In the semiclassical approximation in which the electric charges of scalar particles are described by Grassmann variables ($Q_i^2=0, Q_iQ_j\ne 0$), it is possible to re-express the Lienard-Wiechert potentials and electric fields in the…