Cancellation of divergences and gauge invariance in the massive Yang--Mills field theory

Journal Article · Sat Sep 01 04:00:00 EDT 1973 · Yadern. Fiz., v. 18, no. 3, pp. 630-648

OSTI ID:4416964

Ivanov, A N; Shekhter, V M

Neutrino-neutrino scattering is considered in the massive YangMills vector field theory. All the diagrams of one-loop approximation are calculated in the unitary gauge. The results are presented as sums of these graphs computed in the Feymnan gauge and additional terms of three types. The terms of the first type coincide with the contributions from ghosts'' that are well-known to be necessary to introduce when working in a non-unitary gauge. The terms of the second type contribute only to the renormalization constants or are cancelled by courter-terms in order to satisfy the Ward identities. The integrals of the third type diverge quadratically and are shown to cancel themselves when all diagrams are summed up. Therefore, gauge invariance of the amplitude is confirmed by direct computation in spite of non-invariance of Green functions. The cancellation of additional quadratic divergences occurs only in presence of symmetry when all the coupling constants obey the Yang-Mills relations. The results are generalized to the cases of (i) an electron with non-zero mass, (ii) presence of the Higgs scalar particle, and (iii) inclusion of the electromagnetic field (Weinberg model). (auth)

• Research Organization: Leningrad Inst. of Nuclear Physics
• NSA Number: NSA-29-003513
• OSTI ID: 4416964
• Journal Information: Yadern. Fiz., v. 18, no. 3, pp. 630-648, Journal Name: Yadern. Fiz., v. 18, no. 3, pp. 630-648; ISSN YAFIA
• Country of Publication: Country unknown/Code not available
• Language: Russian

Related Subjects

*NEUTRINO-NEUTRINO INTERACTIONS-- YANG-MILLS THEORY
*YANG-MILLS THEORY-- GAUGE INVARIANCE
ELECTRONS
N64230* --Physics (High Energy)--Particle Interactions & Properties (Theoretical)--Weak
RENORMALIZATION
SCATTERING AMPLITUDES
WEINBERG LEPTON MODEL