Relativistic off-mass-shell and off-energy-shell scattering theories: an application of the rotation and Lorentz groups
A relativistic, phenomenological scattering theory for particles with arbitrary spin is presented, and the relation between off-mass-shell and off-energy-shell theories is discussed. The theory is formulated from the Hilbert-space representation of particles with spin in relativistic quantum mechanics. This topic is reviewed in a basis-independent manner by appealing to the properties of the rotation and Lorentz groups and their representations. Spin is discussed and a set of basis state vectors for the single-particle Hilbert space is derived from this perspective. Two- and three-particle Hilbert-space bases are then constructed, and angular momentum is discussed. The z-circumflex and helicity bases are presented as examples of the general procedure. These foundations allow the on-shell scattering amplitude to be defined. The space-inversion and time-reversal properties of this amplitude suggest that a new scattering function be defined such that a continuation of that function to negative energies can be considered. Antiparticle scattering events are associated with the continued function, and the CPT theorem arises as a natural consequence of this association. Moreover, these considerations lead to the definition of an off-mass-shell scattering function. The resulting off-mass-shell scattering theory has a number of very appealing properties. The off-energy-shell theory is dependent on fewer variables than the off-mass-shell theory, and is more susceptible to a phenomenological treatment.
- Research Organization:
- Los Alamos Scientific Lab., NM (USA)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 7092887
- Report Number(s):
- LA-8548-T
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
653003 -- Nuclear Theory-- Nuclear Reactions & Scattering
658000 -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
AMPLITUDES
ANALYTIC FUNCTIONS
ANGULAR MOMENTUM
BANACH SPACE
ENERGY RANGE
FUNCTIONS
HILBERT SPACE
LIE GROUPS
LORENTZ GROUPS
MATHEMATICAL MODELS
MATHEMATICAL SPACE
PARTICLE PROPERTIES
POINCARE GROUPS
RELATIVISTIC RANGE
SCATTERING
SCATTERING AMPLITUDES
SPACE
SPIN
SYMMETRY GROUPS