Renormalization in the complete Mellin representation of Feynman amplitudes

C. de Calan; F. David; V. Rivasseau

doi:10.1007/bf02046763

Renormalization in the complete Mellin representation of Feynman amplitudes

Communications in Mathematical Physics ◽

10.1007/bf02046763 ◽

1981 ◽

Vol 78 (4) ◽

pp. 531-544 ◽

Cited By ~ 18

Author(s):

C. de Calan ◽

F. David ◽

V. Rivasseau

Keyword(s):

Feynman Amplitudes ◽

Mellin Representation

Download Full-text

EXISTENCE OF ASYMPTOTIC EXPANSIONS IN NONCOMMUTATIVE QUANTUM FIELD THEORIES

Reviews in Mathematical Physics ◽

10.1142/s0129055x0800347x ◽

2008 ◽

Vol 20 (08) ◽

pp. 933-949

Author(s):

C. A. LINHARES ◽

A. P. C. MALBOUISSON ◽

I. RODITI

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Field Theories ◽

Quantum Field Theories ◽

Quantum Field ◽

Asymptotic Behaviors ◽

Scalar Quantum ◽

Feynman Amplitudes ◽

Mellin Representation ◽

Noncommutative Quantum

Starting from the complete Mellin representation of Feynman amplitudes for noncommutative vulcanized scalar quantum field theory, introduced in a previous publication, we generalize to this theory the study of asymptotic behaviors under scaling of arbitrary subsets of external invariants of any Feynman amplitude. This is accomplished in both convergent and renormalized amplitudes.

Download Full-text

ASYMPTOTIC EXPANSIONS OF FEYNMAN AMPLITUDES IN A GENERIC COVARIANT GAUGE

International Journal of Modern Physics A ◽

10.1142/s0217751x08039402 ◽

2008 ◽

Vol 23 (07) ◽

pp. 1089-1103

Author(s):

C. A. LINHARES ◽

A. P. C. MALBOUISSON ◽

I. RODITI

Keyword(s):

Scalar Field ◽

Asymptotic Expansions ◽

Gauge Theories ◽

Present Situation ◽

Parametric Representation ◽

Field Theories ◽

Covariant Gauge ◽

Feynman Amplitudes ◽

Mellin Representation

We show in this paper how to construct Symanzik polynomials and the Schwinger parametric representation of Feynman amplitudes for gauge theories in a generic covariant gauge. The complete Mellin representation of such amplitudes is then established in terms of invariants (squared sums of external momenta and squared masses). From the scaling of the invariants by a parameter we extend for the present situation a theorem on asymptotic expansions, previously proven for the case of scalar field theories, valid for both ultraviolet or infrared behaviors of Feynman amplitudes.

Download Full-text