Related papers: Nonlocal Lagrangian fields and the second Noether …
We show by some counterexamples that Lagrangian sysytems with nonlocality of finite extent are not necessarily unstable.
In this review, the fundamental concepts of group theory and representation theory are introduced. Special emphasis is placed on the unitary irreducible representations of the $SU(N)$ Lie group, the Poincare group, Little Group, discrete…
We consider the Lagrangian formulation with duplicated variables of dissipative mechanical systems. The application of Noether theorem leads to physical observable quantities which are not conserved, like energy and angular momentum, and…
We perform the BFV quantization of the 2+1 projectable and the 3+1 nonprojectable versions of the Horava theory. This is a Hamiltonian formalism, and noncanonical gauges can be used with it. In the projectable case, we show that the…
An effective field approximation, similar to the atomic Thomas-Fermi approach, is proposed for studying non-Abelian gauge theories which includes finite-volume effects. As applications of the formalism the equation of state for an SU(2)…
We study well-posedness, local and global, existence of solutions for a general class of physically meaningful nonlinear Schr\"odinger systems with magnetic field involving local and nonlocal nonlinearities.
It is shown that an arbitrary singular Lagrangian theory (with first and second class constraints up to $N$-th stage in the Hamiltonian formulation) can be reformulated as a theory with at most third-stage constraints. The corresponding…
In the framework of the generalized Hamiltonian formalism by Dirac, the local symmetries of dynamical systems with first- and second-class constraints are investigated in the general case without restrictions on the algebra of constraints.…
Some of the key cohomological features of the two $(1+1)$-dimensional (2D) free Abelian- and self-interacting non-Abelian gauge theories (having no interaction with matter fields) are briefly discussed first in the language of symmetry…
We prove Noether-type theorems for fractional isoperimetric variational problems with Riemann-Liouville derivatives. Both Lagrangian and Hamiltonian formulations are obtained. Illustrative examples, in the fractional context of the calculus…
In recent years, many new developments in theoretical physics, and in practical applications rely on different techniques of noncommutative algebras. In this review, we introduce the basic concepts and techniques of noncommutative physics…
Invariance theorems in analytical mechanics, such as Noether's theorem, can be adapted to continuum mechanics. For this purpose, it is useful to give a functional representation of the motion and to interpret the groups of invariance with…
This paper is devoted to studying symmetries of k-symplectic Hamiltonian and Lagrangian first-order classical field theories. In particular, we define symmetries and Cartan symmetries and study the problem of associating conservation laws…
The standard Hamiltonian machinery, being applied to field theory, leads to infinite-dimensional phase spaces. It is not covariant. In this article, we present covariant finite-dimensional multimomentum Hamiltonian formalism for field…
We discuss some of the key topological aspects of a two $(1+1)$-dimensional (2D) self-interacting non-Abelian gauge theory (having no interaction with matter fields) in the framework of {\it chiral} superfield formalism. We provide the…
This paper focuses on extending our previous discussion of an Abelian U(1) gauge theory involving infinite derivatives to a non-Abelian SU(N) case. The renormalization group equation (RGEs) of the SU(N) gauge coupling is calculated and…
We suggest an extension of the Yang-Mills theory which includes non-Abelian tensor gauge fields. The invariant Lagrangian is quadratic in the field strength tensors and describes interaction of charged tensor gauge bosons of arbitrary large…
In this survey, we present a geometric description of Lagrangian and Hamiltonian Mechanics on Lie algebroids. The flexibility of the Lie algebroid formalism allows us to analyze systems subject to nonholonomic constraints, mechanical…
Classical and quantum mechanical descriptions of physical world are seamlessly abridged within the framework of Lagrangian formalism which, besides revealing the essence of nonlocally correlated dynamic evolution, helps understanding abrupt…
We consider the second variational derivative of a given gauge-natural invariant Lagrangian taken with respect to (prolongations of) vertical parts of gauge-natural lifts of infinitesimal principal automorphisms. By requiring such a second…