Spin precession in a homogeneous gravitational field

Thesis/Dissertation · Tue Jan 01 04:00:00 EST 1980

OSTI ID:5225673

Klein, G K

First a geometrical approach for the homogeneous gravitational field is given, emphasizing its main physical features, and in accordance with relativity in which this field is interpreted as the field apparently experienced by a uniformly accelerated observer (Born-Motion). A stationary beam of particles is then studied in both the particle and the wave pictures. In the particle picture, we first study the beam in the non-relativistic approximation, and then the relativistic beam. The velocity fields, and orbit equations, as well as the connection of the relativistic beam to the non-relativistic beam, as c..-->.. infinity, are given. Our main result is then established by calculating the so-called Quasi-Thomas precession of the spin of the particle in a homogeneous gravitational field. The differences with the regular Thomas precession are discussed and illustrated with space-time diagrams. Some numerical estimates are given. The beam is then studied in the wave picture for Dirac particles. First the Dirac equation is established in the homogeneous gravitational field by the appropriate coordinate, and Lorentz transformation, on the Dirac 4-component spinor wave function in the freely falling frame. Then working to first order in the coupling constant g, an approximate plane wave function is given as a solution for the stationary beam. The precession of the spin is then obtained, and it agrees with the result given by the particle picture. The translationary motion is also discussed briefly. The similar problem of a homogeneous electric field is discussed, via the principle of equivalence, and some formal analogies are found. Finally, a brief discussion of future research, in connection with recently available experiments to test the principle of equilavence at the quantum level, and in the context of this thesis, is given.

• Research Organization: New York Univ., NY (USA)
• OSTI ID: 5225673
• Country of Publication: United States
• Language: English

Related Subjects

657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANGULAR MOMENTUM
BASIC INTERACTIONS
BEAMS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
ELECTRIC FIELDS
EQUATIONS
FIELD THEORIES
FUNCTIONS
GENERAL RELATIVITY THEORY
GRAVITATIONAL FIELDS
GRAVITATIONAL INTERACTIONS
INTERACTIONS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE BEAMS
PARTICLE PROPERTIES
PRECESSION
SPIN
WAVE EQUATIONS
WAVE FUNCTIONS