Foldy-Wouthuysen transformation and a new form of relativistic quantum mechanics
Seminars
Seminar of department “Theory of Fundamental Interactions”
Date and Time: Thursday, 14 December 2017, at 4:00 PM
Venue: Blokhintsev Hall (4th floor), Bogoliubov Laboratory of Theoretical Physics
Seminar topic: «Foldy-Wouthuysen transformation and a new form of relativistic quantum mechanics»
Speaker: Alexander J. Silenko (BLTP JINR)
Abstract:
The Foldy-Wouthuysen (FW) transformation restoring the Schrödinger form of relativistic wave equations is one of basic methods of contemporary quantum mechanics (QM). An importance of this transformation for physics has been significantly increased nowadays due to the great progress of the art of analytic computer calculations. We demonstrate that the use of the FW representation has some important advantages. The relativistic FW Hamiltonian can be derived for particles with any spin in strong external fields and can be expressed as a series in powers of the Planck constant. In this case, terms proportional to the zero and first powers are determined exactly. A consideration of energy expectation values of a particle in nonstationary fields shows the basic role of the FW representation in relativistic QM. We analyze general properties of the FW transformation and discuss specific forms of this transformation for particles with spins 0, 1/2, and 1. Examples of the exact FW transformation are presented. The exact form of the exponential FW transformation operator for an arbitrary-spin particle is found. The analysis demonstrates that the use of the FW transformation allows one to obtain the new (Schrödinger) form of relativistic QM.