Hamiltonian formulation of non-Abelian gauge fields and nonrelativistic bound states
- 15 May 1978
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 17 (10), 2659-2686
- https://doi.org/10.1103/physrevd.17.2659
Abstract
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.Keywords
This publication has 23 references indexed in Scilit:
- Static limit of quantum chromodynamicsPhysical Review D, 1978
- Calculations of the infrared behavior of quantum chromodynamics: The color-singlet quark form factor in the near-mass-shell regimePhysical Review D, 1977
- Quark-antiquark potential in QCDNuclear Physics B, 1977
- Non-Abelian Gauge Fields and Nonrelativistic Bound StatesPhysical Review Letters, 1977
- The static potential in quantum chromodynamicsPhysics Letters B, 1977
- Quantum Mechanics of One- and Two-Electron AtomsPublished by Springer Nature ,1957
- Reduction of Relativistic Two-Particle Wave Equations to Approximate Forms. IIIPhysical Review B, 1955
- Reduction of Relativistic Two-Particle Wave Equations to Approximate Forms. IIPhysical Review B, 1953
- Reduction of Relativistic Two-Particle Wave Equations to Approximate Forms. IPhysical Review B, 1953
- On the Dirac Theory of Spin 1/2 Particles and Its Non-Relativistic LimitPhysical Review B, 1950