Related papers: Tensorial origin of the action function, nexus bet…

A first-order action for scalar-tensor theories of gravity is proposed. The Hamiltonian analysis of the action gives the desired connection dynamical formalism, which was derived from the geometrical dynamics by canonical transformations.…

A theory of gravity with torsion is examined in which the torsion tensor is constructed from the exterior derivative of an antisymmetric rank two potential plus the dual of the gradient of a scalar field. Field equations for the theory are…

A quantum version of the action principle is formulated in terms of real parameters of a wave functional. The classical limit of the quantum action of a harmonic oscillator is obtained.

Hamilton's principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamilton's principle has a subtle pitfall that often…

Quantum theory expresses the observable relations between physical properties in terms of probabilities that depend on the specific context described by the "state" of a system. However, the laws of physics that emerge at the macroscopic…

By invoking an asymmetric metric tensor, and borrowing ideas from non-commutative geometry, string theory, and trace dynamics, we propose an action function for quantum gravity. The action is proportional to the four dimensional…

In classical mechanics, an action is defined only modulo additive terms which do not modify the equations of motion; in certain cases, these terms are topological quantities. We construct an infinite sequence of higher order topological…

I present a reconstruction of general Hamiltonian action mechanics that eliminates all foundational problems of quantum mechanics. The key advance is the completion of Hamiltonian mechanics to the universal mechanics of particles based on…

We propose a formulation of quantum mechanics in an extended Fock space in which a tensor product structure is applied to time. Subspaces of histories consistent with the dynamics of a particular theory are defined by a direct quantum…

The derivation of the recently proposed nonlinear quantum evolution of gravity from an action principle is considered in this brief note. It is shown to be possible if a set of consistency conditions are satisfied that are analogous to the…

We develop a dynamical theory, based on a system of ordinary differential equations describing the motion of particles which reproduces the results of quantum mechanics. The system generalizes the Hamilton equations of classical mechanics…

Many quantization schemes rely on analogs of classical mechanics where the connections with classical mechanics are indirect. In this work I propose a new and direct connection between classical mechanics and quantum mechanics where the…

The action principle is frequently used to derive the classical equations of motion. The action may also be used to associate group elements with curves in the space-time manifold, similar to the gauge transformations. The action principle…

Quantum mechanics is formulated as a geometric theory on a Hilbert manifold. Images of charts on the manifold are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations in this…

It is widely accepted that the fundamental geometrical law of nature should follow from an action principle. The particular subset of transformations of a system's dynamical variables that maintain the form of the action principle comprises…

We further develop a recently introduced variational principle of stationary action for problems in nonconservative classical mechanics and extend it to classical field theories. The variational calculus used is consistent with an initial…

It is well known that the action functional can be used to define classical, quantum, closed, and open dynamics in a generalization of the variational principle and in the path integral formalism in classical and quantum dynamics,…

The principle of stationary action is a cornerstone of modern physics, providing a powerful framework for investigating dynamical systems found in classical mechanics through to quantum field theory. However, computational neuroscience,…

All physical process are subject to some laws which determine with math accurately its time-space evolution. These laws are described, in the last analysis for the principle of causality. The physical space can be homogeneous or…

We give a geometrical interpretation for the principle of stationary action in classical Lagrangian particle mechanics. In a nutshell, the difference of the action along a path and its variation effectively ``counts'' the possible…