Hamiltonian formulation of non-Abelian gauge fields and nonrelativistic bound states

Journal Article · Mon May 15 04:00:00 EDT 1978 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.17.2659· OSTI ID:6778325

Feinberg, F L

For fermions minimally coupled to non-Abelian gauge fields, first-order quantization in the radiation gauge is presented in which the validity of naive Ward identities simplifies the renormalization procedure. Then, successive Foldy-Wouthuysen transformations are used to determine the nonrelativistic Hamiltonian operator as well as its first relativistic correction. This operator expansion is verified to all orders of perturbation theory by an extension of the Appelquist-Carazzone decoupling theorem. Next, the Hamiltonian, which provides a systematic starting point for any nonrelativistic calculation, is used to cast the fermion-antifermion nonrelativistic bound-state kernel into a simple and compact form which is spin independent and serves as the basis of a perturbative analysis. Through two loops, calculation of the kernel reveals that a mass-independent static potential exists in the nonrelativistic limit only for singlet states of the gauge group. Higher-loop corrections, three-fermion bound states, and nonperturbative methods are also discussed.

• Research Organization: Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
• OSTI ID: 6778325
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 17:10; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645201* -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- General & Scattering Theory
645400 -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOUND STATE
CANONICAL TRANSFORMATIONS
COMPOSITE MODELS
COULOMB FIELD
COUPLING CONSTANTS
ELECTRIC FIELDS
FERMIONS
FIELD THEORIES
FOLDY-WOUTHUYSEN TRANSFORM
GAUGE INVARIANCE
HAMILTONIANS
INVARIANCE PRINCIPLES
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
PARTICLE MODELS
PERTURBATION THEORY
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
QUARK MODEL
RENORMALIZATION
WARD IDENTITY