Classical Mechanics and the Electromagnetic Field

George Adolphus Schott

Aubrey Truman, Huaizhong Zhao

In this paper we consider the ℏ→0 asymptotics for the solutions to stochastic Schrödinger equations for quantum mechanical particles in random electromagnetic fields in Rn. We obtain semi-classical expansions for their solutions up to any order in L2(Rn) a.s. by using a stochastic Hamilton Jacobi equation and a stochastic continuity equation. We conclude that as ℏ→0 the stochastic quantum mechanics with random electromagnetic fields tends to stochastic classical mechanics.

Pierre Meystre, Murray Sargent

Franco Battaglia, Thomas F. George

Introduction Classical physics: Newtonian mechanics Lagrangian mechanics Hamiltonian mechanics Canonical description of fields Electromagnetic field Quantum physics: Mathematical formalism Physical interpretation One-dimensional systems Angular momentum Many-body systems Electromagnetic field Appendix: Special relativity.

A. A. Beilinson

The article describes a relation between the fundamental solutions of Dirac's equations for free electron and electron in given electromagnetic field viewed as functionals on bump functions. We explain how classical relativistic mechanics of a charged particle in given electromagnetic field arises from quantum mechanics of Dirac's electron in that field.

Pierre Meystre, Murray Sargent