Hamiltonian formulation of two-dimensional gauge theories on the light cone

Journal Article · Wed May 15 00:00:00 EDT 1991 · Annals of Physics (New York); (United States)

DOI:https://doi.org/10.1016/0003-4916(91)90342-6· OSTI ID:6972661

Lenz, F; Thies, M ^[1]; Levit, S ^[2]; Yazaki, K ^[3]

---

1. Univ. of Erlangen-Nuernberg, Erlangen (Germany)
2. Weizmann Inst. of Science, Rehovot (Israel)
3. Univ. of Erlangen-Nuernberg (Germany) Univ. of Tokyo (Japan)

Two-dimensional quantum electrodynamics (QED{sub 2}) and quantum chromodynamics (QCD{sub 2}) are studied in the framework of canonical quantization on the light cone. The crucial feature of the present approach is the formulation on a finite interval. This allows resolution of the severe infrared ambiguities of two-dimensional gauge theories and clarification of the relationship between light-cone and equal-time quantization. In particular, the naive light-cone approach emerges as an effective theory with well-defined limitations. For QED{sub 2}, it is demonstrated that the known non-perturbative phenomena can be obtained on the light-cone. For QCD{sub 2}, using the light-cone Coulomb gauge, the role of the gauge degrees of freedom for regularizing the infrared singularity of the gluon propagator is exhibited. The structure of the Hilbert space, the properties of the vacuum and of the elementary excitations are addressed. In the chiral limit (vanishing quark mass), analytical result for both SU(N) and U(N) QCD{sub 2} are presented. Relativistic many-body techniques are employed to solve the theory in the large N limit, and the quark condensate is evaluated on the light-cone. It is pointed out that the finite interval techniques allow taking advantage of the technical simplification usually attributed to light-cone quantization, even when using ordinary coordinates. This surprising result is intimately connected to Lorentz invariance.

• OSTI ID: 6972661
• Journal Information: Annals of Physics (New York); (United States), Vol. 208:1; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
LIGHT CONE
QUANTIZATION
QUANTUM CHROMODYNAMICS
HAMILTONIANS
QUANTUM ELECTRODYNAMICS
DIMENSIONS
HILBERT SPACE
INFRARED DIVERGENCES
LORENTZ INVARIANCE
MANY-BODY PROBLEM
PERTURBATION THEORY
PROPAGATOR
RELATIVITY THEORY
VACUUM STATES
BANACH SPACE
ELECTRODYNAMICS
FIELD THEORIES
GENERAL RELATIVITY THEORY
INVARIANCE PRINCIPLES
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
QUANTUM FIELD THEORY
QUANTUM OPERATORS
SPACE
SPACE-TIME
662220* - Quantum Electrodynamics- (1992-)
662230 - Quantum Chromodynamics- (1992-)