scholarly journals A general expression for symmetry factors of Feynman diagrams

2002 ◽  
Vol 80 (8) ◽  
pp. 847-854 ◽  
Author(s):  
C D Palmer ◽  
M E Carrington
Keyword(s):  
General Expression ◽  
Feynman Diagram ◽  
Simple Formula ◽  
Feynman Diagrams ◽  
Scalar Theory ◽  
Symmetry Factor

The calculation of the symmetry factor corresponding to a given Feynman diagram is well known to be a tedious problem. We have derived a simple formula for these symmetry factors. Our formula works for any diagram in scalar theory (ϕ3 and ϕ4 interactions), spinor QED, scalar QED, or QCD. PACS Nos.: 11.10-z, 11.15-q, 11.15Bt

scholarly journals Symmetry factors of Feynman diagrams and the homological perturbation lemma

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Christian Saemann ◽  
Emmanouil Sfinarolakis
Keyword(s):  
Scalar Field ◽  
Scattering Amplitudes ◽  
General Formula ◽  
Feynman Diagram ◽  
Direct Proof ◽  
Feynman Diagrams ◽  
Field Theories ◽  
Polynomial Potential ◽  
Symmetry Factor ◽  
Homological Perturbation

Abstract We discuss the symmetry factors of Feynman diagrams of scalar field theories with polynomial potential. After giving a concise general formula for them, we present an elementary and direct proof that when computing scattering amplitudes using the homological perturbation lemma, each contributing Feynman diagram is indeed included with the correct symmetry factor.

scholarly journals Feynman diagrams and rooted maps

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 149-167 ◽  
Author(s):  
Andrea Prunotto ◽  
Wanda Maria Alberico ◽  
Piotr Czerski
Keyword(s):  
Single Particle ◽  
Feynman Diagram ◽  
Feynman Diagrams ◽  
Topological Properties ◽  
Many Body ◽  
Perturbative Order ◽  
Original Definition ◽  
Many Body Systems ◽  
Definition Of ◽  
Particle Propagator

Abstract The rooted maps theory, a branch of the theory of homology, is shown to be a powerful tool for investigating the topological properties of Feynman diagrams, related to the single particle propagator in the quantum many-body systems. The numerical correspondence between the number of this class of Feynman diagrams as a function of perturbative order and the number of rooted maps as a function of the number of edges is studied. A graphical procedure to associate Feynman diagrams and rooted maps is then stated. Finally, starting from rooted maps principles, an original definition of the genus of a Feynman diagram, which totally differs from the usual one, is given.

A PROOF OF THE MELVIN–MORTON CONJECTURE AND FEYNMAN DIAGRAMS

1998 ◽  
Vol 07 (01) ◽  
pp. 23-40 ◽  
Author(s):  
S. CHMUTOV
Keyword(s):  
Hopf Algebra ◽  
Feynman Diagram ◽  
Invariant Function ◽  
Feynman Diagrams ◽  
Chord Diagrams ◽  
Knot Invariant ◽  
Difficult Part

The Melvin–Morton conjecture says how the Alexander–Conway knot invariant function can be read from the coloured Jones function. It has been proved by D. Bar-Natan and S. Garoufalidis. They reduced the conjecture to a statement about weight systems. The proof of the latter is the most difficult part of their paper. We give a new proof of the statement based on the Feynman diagram description of the primitive space of the Hopf algebra [Formula: see text] of chord diagrams.

scholarly journals Finite calculation of divergent self-energy diagrams

2003 ◽  
Vol 81 (12) ◽  
pp. 1433-1445 ◽  
Author(s):  
A Aste ◽  
D Trautmann
Keyword(s):  
Perturbation Theory ◽  
Dispersion Relation ◽  
Imaginary Part ◽  
Feynman Diagram ◽  
Feynman Diagrams ◽  
Energy Diagram ◽  
The Real ◽  
Self Energy ◽  
Single Integral ◽  
Analytic Expression

Using dispersive techniques, it is possible to avoid ultraviolet divergences in the calculation of Feynman diagrams, making subsequent regularization of divergent diagrams unnecessary. We give a simple introduction to the most important features of such dispersive techniques in the framework of the so-called finite causal perturbation theory. The method is also applied to the "divergent" general massive two-loop sunrise self-energy diagram, where it leads directly to an analytic expression for the imaginary part of the diagram in accordance with the literature, whereas the real part can be obtained by a single integral dispersion relation. It is pointed out that dispersive methods have been known for decades and have been applied to several nontrivial Feynman diagram calculations.PACS Nos.: 11.10.–z, 11.15.Bt, 12.20.Ds, 12.38.Bx

scholarly journals Generalized planar Feynman diagrams: collections

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Francisco Borges ◽  
Freddy Cachazo
Keyword(s):  
Compatibility Condition ◽  
Natural Generalization ◽  
Feynman Diagrams ◽  
Tree Level ◽  
Scalar Theory ◽  
Metric Tree

Abstract Tree-level Feynman diagrams in a cubic scalar theory can be given a metric such that each edge has a length. The space of metric trees is made out of orthants joined where a tree degenerates. Here we restrict to planar trees since each degeneration of a tree leads to a single planar neighbor. Amplitudes are computed as an integral over the space of metrics where edge lengths are Schwinger parameters. In this work we propose that a natural generalization of Feynman diagrams is provided by what are known as metric tree arrangements. These are collections of metric trees subject to a compatibility condition on the metrics. We introduce the notion of planar col lections of Feynman diagrams and argue that using planarity one can generate all planar collections starting from any one. Moreover, we identify a canonical initial collection for all n. Generalized k = 3 biadjoint amplitudes, introduced by Early, Guevara, Mizera, and one of the authors, are easily computed as an integral over the space of metrics of planar collections of Feynman diagrams.

scholarly journals Feynman diagrams and $Ω$-deformed M-theory

2021 ◽  
Vol 10 (2) ◽  
Author(s):  
Jihwan Oh ◽  
Yehao Zhou
Keyword(s):  
Feynman Diagram ◽  
Operator Algebras ◽  
Feynman Diagrams ◽  
Commutation Relations ◽  
Set Up ◽  
M Theory

We derive the simplest commutation relations of operator algebras associated to M2 branes and an M5 brane in the \OmegaΩ-deformed M-theory, which is a natural set-up for Twisted holography. Feynman diagram 1-loop computations in the twisted-holographic dual side reproduce the same algebraic relations.

scholarly journals Note on the Labelled tree graphs

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Bo Feng ◽  
Yaobo Zhang
Keyword(s):  
Feynman Diagrams ◽  
Tree Level ◽  
Scalar Theory ◽  
Tree Graphs ◽  
Pole Structure ◽  
Interesting Generalization

Abstract In the CHY-frame for the tree-level amplitudes, the bi-adjoint scalar theory has played a fundamental role because it gives the on-shell Feynman diagrams for all other theories. Recently, an interesting generalization of the bi-adjoint scalar theory has been given in [1] by the “Labelled tree graphs”, which carries a lot of similarity comparing to the bi-adjoint scalar theory. In this note, we have investigated the Labelled tree graphs from two different angels. In the first part of the note, we have shown that we can organize all cubic Feynman diagrams produces by the Labelled tree graphs to the “effective Feynman diagrams”. In the new picture, the pole structure of the whole theory is more manifest. In the second part, we have generalized the action of “picking pole” in the bi-adjoint scalar theory to general CHY-integrands which produce only simple poles.

scholarly journals SYSTEMATIC IMPLEMENTATION OF IMPLICIT REGULARIZATION FOR MULTILOOP FEYNMAN DIAGRAMS

2011 ◽  
Vol 26 (15) ◽  
pp. 2591-2635 ◽  
Author(s):  
A. L. CHERCHIGLIA ◽  
MARCOS SAMPAIO ◽  
M. C. NEMES
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Feynman Diagram ◽  
Lorentz Invariance ◽  
Recursion Formula ◽  
Feynman Diagrams ◽  
Quantum Field ◽  
Loop Momentum ◽  
Loop Order ◽  
Fundamental Symmetry

Implicit Regularization (IReg) is a candidate to become an invariant framework in momentum space to perform Feynman diagram calculations to arbitrary loop order. In this work we present a systematic implementation of our method that automatically displays the terms to be subtracted by Bogoliubov's recursion formula. Therefore, we achieve a twofold objective: we show that the IReg program respects unitarity, locality and Lorentz invariance and we show that our method is consistent since we are able to display the divergent content of a multiloop amplitude in a well-defined set of basic divergent integrals in one-loop momentum only which is the essence of IReg. Moreover, we conjecture that momentum routing invariance in the loops, which has been shown to be connected with gauge symmetry, is a fundamental symmetry of any Feynman diagram in a renormalizable quantum field theory.

scholarly journals Asymptotic analysis of Feynman diagrams and their maximal cuts

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
B. Ananthanarayan ◽  
Abhijit B. Das ◽  
Ratan Sarkar
Keyword(s):  
Asymptotic Analysis ◽  
Feynman Diagram ◽  
Feynman Diagrams ◽  
Newton Polytope ◽  
Feynman Integrals ◽  
Power Geometry

AbstractThe ASPIRE program, which is based on the Landau singularities and the method of Power geometry to unveil the regions required for the evaluation of a given Feynman diagram asymptotically in a given limit, also allows for the evaluation of scaling coming from the top facets. In this work, we relate the scaling having equal components of the top facets of the Newton polytope to the maximal cut of given Feynman integrals. We have therefore connected two independent approaches to the analysis of Feynman diagrams.

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