Related papers: CONFINEMENT IN RELATIVISTIC POTENTIAL MODELS
Quantizing the gravitational field described by General relativity being a notorious difficult, unsolved and maybe meaningless problem I use in this essay a different strategy: I consider a linear theory in the framework of Special…
Starting from the hypothesis of scaling solutions, the general exact form of the scalar field potential is found. In the case of two fluids, it turns out to be a negative power of hyperbolic sine. In the case of three fluids the analytic…
We discuss a new method for obtaining the WKB approximation to the Dirac equation with a scalar potential and a time-like vector potential. We use the WKB solutions to investigate the scaling behavior of a confining model for quark-hadron…
Gravity theories with non-minimally coupled scalar fields are used as characteristic examples in order to demonstrate the challenges, pitfalls and future perspectives of considering alternatives to general relativity. These lecture notes…
Spontaneous scalarization is an interesting mechanism for modification of gravity by nonminimal coupling of a scalar field to matter or curvature invariants in the context of scalar-tensor theories, and its onset is signaled by linear…
We apply the Dirac factorization method to the nonrelativistic harmonic oscillator and, more in general, to Hamiltonians with a generic potential. It is shown that this procedure naturally leads to a supersymmetric formulation of the…
Dirac-like monopoles are studied in three-dimensional Abelian Maxwell and Maxwell-Chern-Simons models. Their scalar nature is highlighted and discussed through a dimensional reduction of four-dimensional electrodynamics with electric and…
A Taylor variety consists of all fixed order Taylor polynomials of rational functions, where the number of variables and degrees of numerators and denominators are fixed. In one variable, Taylor varieties are given by rank constraints on…
Exact cosmological models for a scalar field in Lyra geometry are studied in the presence of a time-varying effective cosmological term originated from the specific interaction of an auxiliary $\Lambda$ - term with the displacement vector.…
We believe that the difference between time scale systems and ordinary differential equations is not as big as people use to think. We consider linear operators that correspond to linear dynamic systems on time scales. We study solvability…
We discuss the application of a relativistic potential model to the description of the spectrum and radiative transitions in mesons containing at least one heavy quark (b or c). Although the model has a small number of parameters, it is…
We have studied a relativistic electron in the presence of a uniform magnetic field and scalar potential in the cosmic string spacetime. The exact solutions of the Dirac equation with a Coulomb-like scalar potential and linear vector…
Doubly special relativity (DSR) is usually regarded as a low-energy limit of a quantum gravity theory with testable predictions. On the other hand, non-local quantum field theories have been presented as a solution to the inconsistencies…
The relativistic problem of spin- fermions subject to vector hyperbolic (kink-like) potential tanh (kx) is investigated by using the parametric Nikiforov-Uvarov method. The energy eigenvalue equation and the corresponding normalized wave…
Let $\mathbb{F}$ be a field of characteristic different from $2$ and $3$, and let $V$ be a vector space of dimension $2$ over $\mathbb{F}$. The generic classification of homogeneous quadratic maps $f\colon V\to V$ under the action of the…
A system of linear equations over a skew field has properties similar to properties of a system of linear equations over a field. Even noncommutativity of a product creates a new picture the properties of system of linear equations and of…
We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms…
Let $K$ denote a field and let $V$ denote a vector space over $K$ with finite positive dimension. We consider an ordered pair of linear transformations $A:V\to V$ and $A^*:V\to V$ that satisfy conditions (i), (ii) below. (i) There exists a…
Three new models with V-shaped field potentials $U$ are considered: a complex scalar field $X$ in 1+1 dimensions with $U(X)= |X|$, a real scalar field $\Phi$ in 2+1 dimensions with $U(\Phi) = |\Phi|$, and a real scalar field $\phi$ in 1+1…
Null vectors are generalized to the case of indecomposable representations which are one of the main features of logarithmic conformal field theories. This is done by developing a compact formalism with the particular advantage that the…