Related papers: Augmented Variational Principles and Relative Cons…
The variational formalism for classical field theories is extended to the setting of Lie algebroids. Given a Lagrangian function we study the problem of finding critical points of the action functional when we restrict the fields to be…
A Lagrangian formulation is constructed for particle interpretations of quantum mechanics, a well-known example of such an interpretation being the Bohm model. The advantages of such a description are that the equations for particle motion,…
It is generally believed that physical laws, reflecting an inherent order in the universe, are ordained by nature. However, in modern physics the observer plays a central role raising questions about how an observer-centric physics can…
We consider the higher-order gravity theory derived from the quadratic lagrangian $R+\epsilon R^2$ in vacuum as a first-order (ADM-type) system with constraints, and build time developments of solutions of an initial value formulation of…
We calculate the relative conserved currents, superpotentials and conserved quantities between two homogeneous and isotropic universes. In particular we prove that their relative "energy" (defined as the conserved quantity associated to…
We speculate on the role of relativistic versions of delayed differential equations in fundamental physics. Relativistic invariance implies that we must consider both advanced and retarded terms in the equations, so we refer to them as…
We develop a Liouville perturbation theory for weakly driven and weakly open quantum systems in situations when the unperturbed system has a number of conservations laws. If the perturbation violates the conservation laws, it drives the…
We show that classical particle mechanics (Hamiltonian and Lagrangian consistent with relativistic electromagnetism) can be derived from three fundamental assumptions: infinite reducibility, deterministic and reversible evolution, and…
We reexamine the problem of having nonconservative equations of motion arise from the use of a variational principle. In particular, a formalism is developed that allows the inclusion of fractional derivatives. This is done within the…
A variational principle is suggested within Riemannnian geometry, in which an auxiliary metric and the Levi Civita connection are varied independently. The auxiliary metric plays the role of a Lagrange multiplier and introduces non-minimal…
In the work it has been shown that there are two types of the conservation laws. 1. The conservation laws that can be called exact ones. They point to an avalability of some conservative quantities or objects. Such objects are the physical…
This paper describes general relativity at the gravito-electromagnetic precision level as a constrained field theory. In this novel formulation, the gravity field comprises two auxiliary fields, a static matter field and a moving matter…
We explore the connections between the constraints on the precision of quantum logical operations that arise from a conservation law, and those arising from quantum field fluctuations. We show that the conservation-law based constraints…
In the Lagrangian framework for symmetries and conservation laws of field theories, we investigate globality properties of conserved currents associated with non-global Lagrangians admitting global Euler--Lagrange morphisms. Our approach is…
We show that the naive application of the maximum entropy principle can yield answers which depend on the level of description, i.e. the result is not invariant under coarse-graining. We demonstrate that the correct approach, even for…
The structure of classical electrodynamics based on the variational principle together with causality and space-time homogeneity is analyzed. It is proved that in this case the 4-potentials are defined uniquely. On the other hand, the…
The treatment of exact conservation laws in Lagrangian gauge theories constitutes the main axis of the first part of the thesis. The formalism is developed as a self-consistent theory but is inspired by earlier works, mainly by…
A transition of focus from state space to frames of reference and their transformations is argued as being the appropriate setup for ensuring the covariance of physical laws. Such an approach can not only simplify and clarify aspects of…
For difference variational problems on lattice, this paper presents a relation between divergence variational symmetries and conservation laws for the associated Euler-Lagrange system provided by Noether's theorem. This hence inspires us to…
Action-dependent field theories are systems where the Lagrangian or Hamiltonian depends on new variables that encode the action. They model a larger class of field theories, including non-conservative behavior, while maintaining a…