Part A: a convergent iteration scheme for soliton dynamics. Part B: quantum fields in a Lorentz basis

Thesis/Dissertation · Fri Jan 01 04:00:00 EST 1982

OSTI ID:7000306

Weidemann, A W

Part A: A (1 + 1)-dimensional model with two different sine-Gordon fields coupled by a perturbing term is considered. Besides the usual sine-Gordon solitons, which also occur in the absence of coupling, the existence of a 'diagonal' solution is established using the implicit function theorem for Banach spaces after projecting out the 'translation mode' (Lyapunov-Schmidt method). The implicit function theorem leads to an iteration scheme for the construction of this solution. For a typical interaction the lowest-order perturbation and energy shift are calculated analytically. The techniques developed here are applicable to a broad class of soliton problems beyond the model considered. Part B: A basis in the representation space of the irreducible unitary representations of the homogeneous Lorentz group (''Lorentz basis'') and its relation to the commonly used representation of the inhomogeneous Lorentz group are explained. Quantum fields of any spin are expanded in terms of the (spinor) coefficients relating these two bases; their transformation properties under Lorentz transformations, T, C, and P are given. The correct spin-statistics relation is found from (anti-) commutators of the field components. The relation between co- and contravariant field components yields a Dirac equation for any spin.

• Research Organization: Maryland Univ., College Park (USA)
• OSTI ID: 7000306
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COMMUTATION RELATIONS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
EQUATIONS
FIELD THEORIES
IRREDUCIBLE REPRESENTATIONS
ITERATIVE METHODS
LIE GROUPS
LORENTZ GROUPS
LORENTZ TRANSFORMATIONS
PARTIAL DIFFERENTIAL EQUATIONS
POINCARE GROUPS
QUANTUM FIELD THEORY
QUASI PARTICLES
SOLITONS
SPINORS
SYMMETRY GROUPS
TRANSFORMATIONS
WAVE EQUATIONS