Related papers: Nonstandard Null Lagrangians and Gauge Functions a…
The equations of motion for electromechanical systems are traced back to the fundamental Lagrangian of particles and electromagnetic fields, via the Darwin Lagrangian. When dissipative forces can be neglected the systems are conservative…
Gauge-invariance is a mathematical concept that has profound implications in Physics---as it provides the justification of the fundamental interactions. It was recently adapted to the Cellular Automaton (CA) framework, in a restricted case.…
I consider Lagrangians which depend nonlocally in time but in such a way that there is no mixing between times differing by more than some finite value $\Delta t$. By considering these systems as the limits of ever higher derivative…
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…
The role of viscous forces coupled with Brownian forces in momentum conserving computer simulations is studied here in the context of their contribution to the total average pressure of a simple fluid as derived from the virial theorem, in…
Given a model for self-dual non-linear electrodynamics in four spacetime dimensions, any deformation of this theory which is constructed from the duality-invariant energy-momentum tensor preserves duality invariance. In this work we present…
The aim of this paper is to show that the Lagrange-d'Alembert and its equivalent the Gauss and Appel principle are not the only way to deduce the equations of motion of the nonholonomic systems. Instead of them, here we consider the…
Lagrangians linear in velocities were analyzed using the fractional calculus and the Euler-Lagrange equations were derived. Two examples were investigated in details, the explicit solutions of Euler-Lagrange equations were obtained and the…
The use of statistical methods to model gravitational systems is crucial to physics practice, but the extent to which thermodynamics and statistical mechanics genuinely apply to these systems is a contentious issue. This paper provides new…
In previous papers we have introduced a natural nonequilibrium free energy by considering the functional describing the large fluctuations of stationary nonequilibrium states. While in equilibrium this functional is always convex, in…
It is proved that in order to keep both the Lagrangian and the motion equation of non-Abelian gauge fields unchanged under the gauge transformation simultaneously, a certain restriction conditions should be established between the gauge…
A least action principle for damping motion has been previously proposed with a Hamiltonian and a Lagrangian containing the energy dissipated by friction. Due to the space-time nonlocality of the Lagrangian, mathematical uncertainties…
We study the non-linear corrections to the matter and velocity power spectra in the synchronous gauge (SG). We consider the perturbations up to third order in a zero-pressure fluid in flat cosmological background, which is relevant for the…
In this short note we show that any action for $N$ interacting particles can be made invariant under gauged Galilean transformations. While resulting Lagrangian is generally very complicated its Hamiltonian has simple form with first class…
Special relativity beyond its basic treatment can be inaccessible, in particular because introductory physics courses typically view special relativity as decontextualized from the rest of physics. We seek to place special relativity back…
The aim of the present text is twofold: to provide a compendium of Lagrangian and Hamiltonian geometries and to introduce and investigate new analytical Mechanics: Finslerian, Lagrangian and Hamiltonian. The fundamental equations (or…
The lower invariance under a given arbitrary group of diffeomorphisms extends the notion of quasiconvexity. The non-commutativity of the group operation (the function composition) modifies the classical equivalence between lower…
It is shown that any singular Lagrangian theory: 1) can be formulated without the use of constraints by introducing a Clairaut-type version of the Hamiltonian formalism; 2) leads to a special kind of nonabelian gauge theory which is similar…
We present a phenomenological Lagrangian and Poisson brackets for obtaining nondissipative hydrodynamic theory of supersolids. A Lagrangian is constructed on the basis of unification of the principles of non-equilibrium thermodynamics and…
We investigate gauge invariance against phase space shifting in nonequilibrium systems, as represented by time-dependent many-body Hamiltonians that drive an initial ensemble out of thermal equilibrium. The theory gives rise to gauge…