Related papers: Linear Differential Equations for a Fractional Spi…
A simple Lagrangian is proposed that by the choice of the representation of SU(2), gives rise to field equations for arbitrary spin. In explicit examples it is shown, how the Klein-Gordon, the Dirac, and the Proca equation can be obtained…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
This paper studies fractional integral operator for vector fields in weighted $L^1$. Using the estimates on fractional integral operator and Stein-Weiss inequalities, we can give a new proof for a class of Caffarelli-Kohn-Nirenberg…
We describe some field theoretic methods for studying quantum spin systems in one dimension. These include the nonlinear sigma-model approach which is particularly useful for large values of the spin, the idea of Luttinger liquids and…
These lectures discuss the formulation of quantum mechanics with fractional spin and statistics in 2+1 dimensions in a relativistic setting, emphasizing the path-integral approach. The non-relativistic theory is reviewed from a…
Solution of fractional differential equations is an emerging area of present day research because such equations arise in various applied fields. In this paper we have developed analytical method to solve the system of fractional…
We consider a family of quantum loop models in 2+1 spacetime dimensions with marginally long-ranged and statistical interactions mediated by a U$(1)$ gauge field, both purely in 2+1 dimensions and on a surface in a 3+1 dimensional bulk…
We study the interaction of gauge fields of arbitrary half-integer spins with the homogeneous electromagnetic field. We reduce the problem of obtaining the gauge-invariant Lagrangian and transformations of the half-integer spin fields in…
Lagrangian formulation of free massive fields corresponding to irreducible representations of the Poincare group of arbitrary integer and half-integer spins in three-dimensional space-time is presented. A relationship of the theory under…
The new relativistic equations of motion for the particles with spin s=1, s=3/2, s=2 and nonzero mass have been introduced. The description of the relativistic canonical quantum mechanics of the arbitrary mass and spin has been given. The…
We consider a system of nonlinear spinor and scalar fields with minimal coupling in general relativity. The nonlinearity in the spinor field Lagrangian is given by an arbitrary function of the invariants generated from the bilinear spinor…
In the framework of metric-like approach, totally symmetric arbitrary spin bosonic conformal fields propagating in flat space-time are studied. Depending on the values of conformal dimension, spin, and dimension of space-time, we classify…
A universal description of particles with spins j greater or equal one , transforming in (j,0)+(0,j), is developed by means of representation specific second order differential wave equations without auxiliary conditions and in covariant…
Nonholonomic systems are variational models commonly used for mechanical systems with ideal no-slip constraints. This note provides a differential-geometric derivation of the nonholonomic equations of motion for an arbitrary rigid body…
In this paper we describe a method to solve the linear non-homogeneous fractional differential equations (FDE), composed with Jumarie type Fractional Derivative, and describe this method developed by us, to find out Particular Integrals,…
The goal and the main result of the paper is to provide a complete description of the field of rational differential invariants of one class of second order ordinary differential equations with scalar control parameter with respect to Lie…
The nonlinearity of the conformal group is an essential factor that ruins the global conformal invariance for interacting material fields. In this paper we attempt to track such nonlinearity from spacetime transformations to spinor…
A model of a relativistic particle moving in the Liouville field is investigated. Symmetry group of the system is $SL(2,R)/Z_2$. The corresponding dynamical integrals describe full set of classical trajectories. Dynamical integrals are used…
Fermionic continuous spin field propagating in (A)dS space-time is studied. Gauge invariant Lagrangian formulation for such fermionic field is developed. Lagrangian of the fermionic continuous spin field is constructed in terms of triple…
Given a weight of sl(n), we derive a system of variable-coefficient second-order linear partial differential equations that determines the singular vectors in the corresponding Verma module. Moreover, we completely solve the system in a…