Related papers: Scope of the action principle
We study fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives, generalized fractional integrals and derivatives. We obtain necessary optimality conditions for the…
A lattice gauge theory with an action polynomial in independent field variables is considered. The link variables are described by unconstrained complex matrices instead of unitary ones. A mechanism which permits to switch off in the…
Field theory and gauge theory on noncommutative spaces have been established as their own areas of research in recent years. The hope prevails that a noncommutative gauge theory will deliver testable experimental predictions and will thus…
Time boundary terms usually added to action principles are systematically handled in the framework of Dirac's canonical analysis. The procedure begins with the introduction of the boundary term into the integral Hamiltonian action and then…
In this paper we discuss how the gauge principle can be applied to classical-mechanics models with finite degrees of freedom. The local invariance of a model is understood as its invariance under the action of a matrix Lie group of…
Newton's second law has limited scope of application when transient phenomena are present. We consider a modification of Newton's second law in order to take into account a sudden change (surge) of angular momentum or linear momentum. We…
The two-thirds power law is a link between angular speed $\omega$ and curvature $\kappa$ observed in voluntary human movements: $\omega$ is proportional to $\kappa^{2/3}$. Squared jerk is known to be a Lagrangian leading to the latter law.…
We consider topological contributions to the action integral in a gauge theory formulation of gravity. Two topological invariants are found and are shown to arise from the scalar and pseudoscalar parts of a single integral. Neither of these…
We describe how to construct the dynamics of relativistic particles following, either timelike or null curves, by means of an auxiliary variables method instead of the standard theory of deformations for curves. There are interesting…
Standard and non-standard Lagrangians that give the same equation of motion are significantly different in their forms, as the latter do not have terms that clearly discernable energy-like expressions. A special family of these Lagrangians…
In this paper we examine an alternative formulation of the gauge principle in which the emphasis is shifted from the symmetry transformations to their generators. We show that the gauge principle can be entirely reformulated in terms of…
The Ostrogradsky theorem implies that higher-derivative terms of a single mechanical variable are either trivial or lead to additional, ghost-like degrees of freedom. In this letter we systematically investigate how the introduction of…
We introduce action-driven flows for causal variational principles, being a class of non-convex variational problems emanating from applications in fundamental physics. In the compact setting, H\"older continuous curves of measures are…
In the extended Lagrange formalism of classical point dynamics, the system's dynamics is parametrized along a system evolution parameter $s$, and the physical time $t$ is treated as a \emph{dependent} variable $t(s)$ on equal footing with…
The construction of a gauge field theory for elementary particles usually starts by promoting global invariance of the matter action to a local one, this in turn implying the introduction of gauge fields. We present here a procedure that…
The equations for the critical points of the action functional defined by a Lagrangian depending on higher-order derivatives of admissible curves on a Lie algebroid are found. The relation with Euler-Poincar\'e and Lagrange Poincar\'e type…
The restriction of hydrodynamics to non-viscous, potential (gradient, irrotational) flows is a theory both simple and elegant; a favorite topic of introductory textbooks. It is known that this theory can be formulated as an action principle…
At first, we consider the path integral method for the covariant symmetry breaking in gravity. We replace the scalar fields, instead of the degrees of freedom which have been removed by gauge fixing constraints. Finally the specific ghost…
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…
Variational principles are important in the investigation of large classes of physical systems. They can be used both as analytical methods as well as starting points for the formulation of powerful computational techniques such as…