scholarly journals Mellin representation of the graviton bulk-to-bulk propagator in AdS space

2011 ◽  
Vol 83 (8) ◽  
Author(s):  
Ian Balitsky
Keyword(s):  
Mellin Representation

scholarly journals EXISTENCE OF ASYMPTOTIC EXPANSIONS IN NONCOMMUTATIVE QUANTUM FIELD THEORIES

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.

scholarly journals ASYMPTOTIC EXPANSIONS OF FEYNMAN AMPLITUDES IN A GENERIC COVARIANT GAUGE

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.

scholarly journals Conformal correlators as simplex integrals in momentum space

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Adam Bzowski ◽  
Paul McFadden ◽  
Kostas Skenderis
Keyword(s):  
Momentum Space ◽  
Point Contact ◽  
Circuit Theory ◽  
Momentum Conservation ◽  
Electrical Circuit ◽  
Recursive Method ◽  
Recursive Structure ◽  
Conformal Field ◽  
General Dimension ◽  
Mellin Representation

Abstract We find the general solution of the conformal Ward identities for scalar n-point functions in momentum space and in general dimension. The solution is given in terms of integrals over (n − 1)-simplices in momentum space. The n operators are inserted at the n vertices of the simplex, and the momenta running between any two vertices of the simplex are the integration variables. The integrand involves an arbitrary function of momentum-space cross ratios constructed from the integration variables, while the external momenta enter only via momentum conservation at each vertex. Correlators where the function of cross ratios is a monomial exhibit a remarkable recursive structure where n-point functions are built in terms of (n − 1)-point functions. To illustrate our discussion, we derive the simplex representation of n-point contact Witten diagrams in a holographic conformal field theory. This can be achieved through both a recursive method, as well as an approach based on the star-mesh transformation of electrical circuit theory. The resulting expression for the function of cross ratios involves (n − 2) integrations, which is an improvement (when n > 4) relative to the Mellin representation that involves n(n − 3)/2 integrations.

scholarly journals Renormalization in the complete Mellin representation of Feynman amplitudes

1981 ◽  
Vol 78 (4) ◽  
pp. 531-544 ◽  
Author(s):  
C. de Calan ◽  
F. David ◽  
V. Rivasseau
Keyword(s):  
Feynman Amplitudes ◽  
Mellin Representation

scholarly journals Non-Commutative Complete Mellin Representation for Feynman Amplitudes

2007 ◽  
Vol 81 (2) ◽  
pp. 161-175 ◽  
Author(s):  
Razvan Gurau ◽  
Adolfo Malbouisson ◽  
Vincent Rivasseau ◽  
Adrian Tanasă
Keyword(s):  
Feynman Amplitudes ◽  
Mellin Representation
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