Related papers: CONFINEMENT IN RELATIVISTIC POTENTIAL MODELS
We propose a scalar-tensor representation of $f(R)$ theories with use of conformal transformations. In this representation, the model takes the form of the Brans-Dicke model with a potential function and a non-zero kinetic term for the…
The Pauli-Villars regularization scheme is often used for evaluating parton distributions within the framework of the chiral quark soliton model with inclusion of the vacuum polarization effects. Its simplest version with a single…
We construct a theory of real scalar fields that interpolates between two different theories: a Lee-Wick theory with $N$ propagator poles, including $N-1$ Lee-Wick partners, and a nonlocal infinite-derivative theory with kinetic terms…
I suggest wave equations for the scalar, pseudoscalar, vector, and pseudovector fields with different masses for spin zero and one states. Tensor, matrix, and quaternion formulations of fields with two mass and spin states are considered.…
Variational (Rayleigh-Ritz) methods are applied to local quantum field theory. For scalar theories the wave functional is parametrized in the form of a superposition of Gaussians and the expectation value of the Hamiltonian is expressed in…
We construct the relativistic particle model without Grassmann variables which meets the following requirements. A) Canonical quantization of the model implies the Dirac equation. B) The variable which experiences {\it Zitterbewegung},…
We show how logarithmic terms may arise in the correlators of fields which belong to the representation of the Schrodinger-Virasoro algebra (SV) or the affine Galilean Conformal Algebra (GCA). We show that in GCA, only scaling operator can…
Applications of the Dirac equation with an anomalous magnetic moment are considered for description of characteristics of electrons, muons and quarks. The Dirac equation with four-dimensional scalar and vector potentials is reduced to a…
General algebraic properties of the algebras of vector fields over quantum linear groups $GL_q(N)$ and $SL_q(N)$ are studied. These quantum algebras appears to be quite similar to the classical matrix algebra. In particular, quantum…
We study quadratic integrability of systems with velocity dependent potentials in three-dimensional Euclidean space. Unlike in the case with only scalar potential, quadratic integrability with velocity dependent potentials does not imply…
We present a variational approach to a general Lienard-type equation in order to linearize it and, as an example, the Van der Pol oscillator is discussed. The new equation which is almost linear is factorized. The point symmetries of the…
We discuss a model for the study of quark-hadron duality in inclusive electron scattering based on solving the Dirac equation numerically for a scalar confining linear potential and a vector color Coulomb potential. We qualitatively…
The field theory quantized on the {\it light-front} is compared with the conventional equal-time quantized theory. The arguments based on the {\it microcausality} principle imply that the light-front field theory may become nonlocal with…
A class of three-dimensional models which satisfy supersymmetric intertwining relations with the simplest - oscillator-like - variant of shape invariance is constructed. It is proved that the models are not amenable to conventional…
Nuclear matter and surface properties are carefully studied for a model based on an effective hadronic lagrangian with vector-vector and scalar-vector self-interactions. The results of the model are compared with those of the successful…
We study vector valued solutions to non-linear elliptic partial differential equations with $p$-growth. Existence of a solution is shown in case the right hand side is the divergence of a function which is only $q$ integrable, where $q$ is…
The present paper is devoted to consideration and discussion of a number of contradictions that take place in fundamental electrodynamics researches. A concept of the scalar-vector potential is introduced that allows us to avoid a number of…
The paper concerns the solvability by quadratures of linear differential systems, which is one of the questions of differential Galois theory. We consider systems with regular singular points as well as those with (non-resonant) irregular…
The subleading term of the heavy quark potential (the analogue of the Luscher term) is computed in a string model for the case of three quarks. It turns out to be positive in 2+1 dimensions, making the potential non-concave as a function of…
We consider $(2+1)$ dimensional massless Dirac equation in the presence of complex vector potentials. It is shown that such vector potentials (leading to complex magnetic fields) can produce bound states and the Dirac Hamiltonians are…