• Corpus ID: 119124072

Interaction from Geometry, Classical and Quantum

@article{Laudato2017InteractionFG,
  title={Interaction from Geometry, Classical and Quantum},
  author={Marco Laudato},
  journal={arXiv: Mathematical Physics},
  year={2017}
}
  • M. Laudato
  • Published 18 March 2017
  • Physics
  • arXiv: Mathematical Physics
In this work, we have studied classical and quantum systems in interaction by means of geometric reduction procedure. The main target is the description in these terms of fundamental interactions. We have shown that, to describe in a canonical way (i.e., in terms of Poisson/Dirac Brackets) even a simple system like the relativistic free particle, one has to deal with non-commutative positions. We have explored some consequences of this result in the framework of Non-Commutative Geometry and in… 

Figures from this paper

References

SHOWING 1-10 OF 36 REFERENCES

REDUCTION PROCEDURES IN CLASSICAL AND QUANTUM MECHANICS

This work presents, in a pedagogical style, many instances of reduction procedures appearing in a variety of physical situations, both classical and quantum, elucidating the analogies and the differences between the classical and the quantum situations.

Unified geometrical approach to relativistic particle dynamics

Models for systems of relativistic particle dynamics are reviewed in terms of a geometrical setting for constraint dynamics. They are derived from the same grand abstract space by means of a common

Relativistic particle dynamics: Lagrangian proof of the no-interaction theorem

An economical proof is given, in the Lagrangian framework, of the no-interaction theorem of relativistic particle mechanics. It is based on the assumption that there is a Lagrangian, which if

Separability in relativistic Hamiltonian particle dynamics

The problem of separability in recent models of classical relativistic interacting particles is examined. This physical requirement is shown to be more subtle than naive separability of all the

Constraint Dynamics of Particle World Lines

The Dirac generator fomulations for relativistic Hamiltonian dynamics is extended by explicitly separating the question of dynamical evolution in an inertial frame from that of changes of frame. We

Form of relativistic dynamics with world lines

In any Hamiltonian relativistic theory there are ten generators of the Poincare group which are realized canonically. The dynamical evolution is described by a Hamiltonian which is one of the ten

Generalized Hamiltonian dynamics

  • P. Dirac
  • Physics
    Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
  • 1958
The author’s procedure for passing from the Lagrangian to the Hamiltonian when the momenta are not independent functions of the velocities is put into a simpler and more practical form, the main

Generalized Reduction Procedure: Symplectic and Poisson Formalism

We present a generalized reduction procedure which encompasses the one based on the momentum map and the projection method. By using the duality between manifolds and ring of functions defined on

Gauge Symmetries and Fibre Bundles: Applications To Particle Dynamics

Meaning of gauge invariance.- Nonrelativistic particles with spin.- Magnetic monopoles.- Relativistic spinning particles.- Yang-mills particles.- Kaluza-Klein theory.- The canonical formalism and