Classical and quantum-mechanical axioms with the higher time derivative formalism

6th International Workshop DICE2012 Spacetime – Matter – Quantum Mechanics: From the Planck Scale to Emergent Phenomena

物理学;力学

Kamalov, Timur^1,2

Physics Department, Moscow State Open University, P. Korchagina street 22, Moscow, 107996, Russia^1

Moscow Polytechnic Institute in Moscow, State University of Mechanical Engineering, P. Korchagina street 22, Moscow, 107996, Russia^2

关键词: Higher derivatives;    Infinite dimensions;    Infinite numbers;    Lagrange functions;    Newtonian mechanics;    Quantum mechanical;    Random initial conditions;    Temporal derivatives;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/442/1/012051/pdf
DOI  :  10.1088/1742-6596/442/1/012051

学科分类：力学，机械学

来源: IOP

【 摘 要 】

A Newtonian mechanics model is essentially the model of a point body in an inertial reference frame. How to describe extended bodies in non-inertial (vibration) reference frames with the random initial conditions? One of the most generalized ways of descriptions (known as the higher derivatives formalism) consists in taking into account the infinite number of the higher temporal derivatives of the coordinates in the Lagrange function. Such formalism describing physical objects in the infinite dimensions space does not contradict to the quantum mechanics and infinite dimensions Hilbert space.