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. 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 in complete analogy with the single-particle states. The z and helicity bases are presented as examples of the general procedure. These foundations permit a theoretically meaningful discussion of relativistic scattering theory and 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, which is shown to be essentially equivalent to perturbative field theory, has a number of very appealing properties. Phenomenology is discussed and dispersion-theoretic techniques of obtaining off-shell two-body scattering functions are described within this framework. Spin and angular momentum are treated in a covariant, kinematic-singularity free manner throughout these discussions. Finally, an example of the theory, which is preliminary to a more complete theory of the relativistic three-body problem, is presented. A single-particle exchange diagram is described, and an off-mass-shell three-body recoupling coefficient, which is similar to the on-shell three-body recoupling coefficent that was defined by Wick, is derived.
- Research Organization:
- Texas Univ., Austin (USA)
- OSTI ID:
- 5436596
- Country of Publication:
- United States
- Language:
- English
Similar Records
Relativity and spin in one-, two-, and three-body systems
Off-the-mass shell scattering amplitude in a two-particle potential model
Related Subjects
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
ANGULAR MOMENTUM
ANTIMATTER
ANTIPARTICLES
BANACH SPACE
CPT THEOREM
ELEMENTARY PARTICLES
ENERGY RANGE
HILBERT SPACE
INVARIANCE PRINCIPLES
LIE GROUPS
LORENTZ GROUPS
MANY-BODY PROBLEM
MATHEMATICAL SPACE
PARTICLE PROPERTIES
POINCARE GROUPS
RELATIVISTIC RANGE
SCATTERING
SCATTERING AMPLITUDES
SPACE
SPIN
SYMMETRY GROUPS
TWO-BODY PROBLEM