Quantization of the Yang-Mills field and Mandelstam's theory in gauge-independent path-dependent formalism. [Commutation relations, Peierls method, Green functions, Feyman rules]

Journal Article · Tue Dec 14 23:00:00 EST 1976 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.14.3584· OSTI ID:7327774

Naito, S

We derive commutation relations (CR's) between gauge-invariant quantities in the Yang-Mills field theory by applying the Peierls method. The CR's obtained are different from those given by Mandelstam in his gauge-independent, path-dependent formalism. However, our CR's are shown to give a consistently quantized field theory, while his CR's do not. In fact, there exist systematic errors in Mandelstam's treatment of the covariant Green's functions. On the other hand, if we correctly treat covariant Green's functions guided by his procedure, our CR's are shown to lead to the same Feynman rules for the Yang-Mills field as prescribed by Feynman, DeWitt, Faddeev and Popov, and Mandelstam. (AIP)

• Research Organization: Department of Physics, Osaka City University, Sumiyoshiku, Osaka, Japan
• OSTI ID: 7327774
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 14:12; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COMMUTATION RELATIONS
DIAGRAMS
FEYNMAN DIAGRAM
FIELD THEORIES
FUNCTIONS
GAUGE INVARIANCE
GREEN FUNCTION
INVARIANCE PRINCIPLES
LAGRANGIAN FUNCTION
MANDELSTAM REPRESENTATION
PEIERLS METHOD
QUANTUM FIELD THEORY
YANG-MILLS THEORY