Related papers: Classical integrable field theories in discrete 2+…
We study the most general form of a three dimensional classical integrable system with axial symmetry and invariant under the axis reflection. We assume that the three constants of motion are the Hamiltonian, $H$, with the standard form of…
The stationary one-dimensional tight-binding Schredinger equation with a weak diagonal long-range correlated disorder in the potential is studied. An algorithm for constructing the discrete binary on-site potential exhibiting a hybrid…
A known general class of superintegrable systems on 2D spaces of constant curvature can be defined by potentials separating in (geodesic) polar coordinates. The radial parts of these potentials correspond either to an isotropic harmonic…
Two field 2-forms on the space-time manifold, in a relationship of duality, are presented and included in the extended phase-space structure used to describe relativistic particles having both electric and magnetic charges. By exterior…
The relations existing between the auxiliary field (einbein field) formalism and the spinless Salpeter equation are studied in the case of two particles with the same mass, interacting via a confining potential. The problem of…
We study general properties of the classical solutions in non-polynomial closed string field theory and their relationship with two dimensional conformal field theories. In particular we discuss how different conformal field theories which…
A rich variety of amorphous solids are found in nature and technology, including ones formed via the vulcanization of long, flexible molecules. A special class -- those featuring a wide gap between the long timescales over which constraints…
In this paper I shall consider field theories in a space of four-dimensions which have field variables consisting of the components of a metric tensor and scalar field. The field equations of these scalar-tensor field theories will be…
A universal model for D=4 spinning particle is constructed with the configuration space chosen as ${\bf R}^{3,1}\times S^2$, where the sphere corresponds to the spinning degrees of freedom. The Lagrangian includes all the possible…
The main fundamental principles characterizing the vacuum field structure are formulated and the modeling of the related vacuum medium and charged point particle dynamics by means of devised field theoretic tools are analyzed. The work is…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
Standard Model with a classical conformal invariance holds the promise to give a better understanding of the hierarchy problem and could pave the way for beyond the standard model physics. So, we give here a mathematical treatment of a…
A Symplectic Effective Field Theory that unveils the observed emergence of symplectic symmetry in atomic nuclei is advanced. Specifically, starting from a simple extension of the harmonic-oscillator Lagrangian, an effective field theory…
Motion of a classical particle in 3-dimensional Lobachevsky and Riemann spaces is studied in the presence of an external magnetic field which is analogous to a constant uniform magnetic field in Euclidean space. In both cases three…
The thermodynamics and dynamics of a one dimensional dimer-forming anharmonic model is studied in the classical limit. This model mimics the behavior of materials with a Peierls instability. Specific heat, correlation length, and order…
Scalar field cosmologies with a generalized harmonic potential are investigated in flat and negatively curved Friedmann-Lema\^itre-Robertson-Walker and Bianchi I metrics. An interaction between the scalar field and matter is considered.…
This article investigates Neel-type states in the anisotropic Heisenberg model with an external field. For arbitrary spin $s$ and arbitrary dimension of the space $d$ we find the expressions relating the angles which define the directions…
New geometric structures that relate the lagrangian and hamiltonian formalisms defined upon a singular lagrangian are presented. Several vector fields are constructed in velocity space that give new and precise answers to several topics…
Models, describing relativistic particles, where Lagrangian densities depend linearly on both the curvature and the torsion of the trajectories, are revisited in D=3 space forms. The moduli spaces of trajectories are completely and…
In this review paper we give a geometrical formulation of the field equations in the Lagrangian and Hamiltonian formalisms of classical field theories (of first order) in terms of multivector fields. This formulation enables us to discuss…