Israel A. González Medina

arXiv2019

Revisiting the Hamilton theory for second order Lagrangian

The Hamilton theories for higher orders classical Lagrange functions result on a well known Ostrogradski's instabilities. In this work, we propose a different definition for the second order canonical momentum and obtain a new set of second order's Hamilton equations. The identity transformation introduces a new set of constraints depending only on the set of velocities of all particles and removing the Ostrogradsky's instability. The evolution of the system identifies a new set of canonical variables as the poles of the constraints. The second order momentum shows to be the generator for the negative displacement of poles of such constraints. The momentum first order momentum remains as the generator for the displacement of the coordinate.

physics.class-ph↗

arXiv2018

A new proposal for a quantum theory for isolated n-particle systems with variable masses connected by a field with variable form

We propose a new quantum approach for describing a system of $n$ interacting particles with variable mass connected by an unknown field with variable form ($n$-VMVF systems). Instead of assuming any particular nature for variation of the masses and field, we propose to find them from the laws that rule the dynamic of the systems. In this context, we consider masses and field are functions depending only on the particle positions and velocities, excluding the presence of hidden variables. The quantum approach follows the modern method for constructing the quantum theory where quantum states are defined over a Hilbert space, and the operators are obtained from the canonical transformations of the corresponding classical theory. The classical theory results on two sets of second-order Hamilton constrained equations, while the Hilbert space is defined over the extension of the complex number, which is done from an unsolvable equation on the complex domain. This new approach does not contradict the existing theoretical theories in Particle Physics.

quant-ph↗