scholarly journals Strings from Feynman graph counting: Without largeN

2012 ◽  
Vol 85 (2) ◽  
Author(s):  
Robert de Mello Koch ◽  
Sanjaye Ramgoolam
Keyword(s):  
Feynman Graph

scholarly journals Feynman graph generation and calculations in the Hopf algebra of Feynman graphs

2014 ◽  
Vol 185 (12) ◽  
pp. 3317-3330 ◽  
Author(s):  
Michael Borinsky
Keyword(s):  
Hopf Algebra ◽  
Feynman Graph ◽  
Feynman Graphs ◽  
Graph Generation

scholarly journals The diagrammatic coaction beyond one loop

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Samuel Abreu ◽  
Ruth Britto ◽  
Claude Duhr ◽  
Einan Gardi ◽  
James Matthew
Keyword(s):  
Differential Equations ◽  
Hypergeometric Functions ◽  
Differential Forms ◽  
Feynman Graph ◽  
Loop Order ◽  
Feynman Integrals ◽  
Mathematical Properties ◽  
Multiple Polylogarithms ◽  
Complete Set ◽  
General Tool

Abstract The diagrammatic coaction maps any given Feynman graph into pairs of graphs and cut graphs such that, conjecturally, when these graphs are replaced by the corresponding Feynman integrals one obtains a coaction on the respective functions. The coaction on the functions is constructed by pairing a basis of differential forms, corresponding to master integrals, with a basis of integration contours, corresponding to independent cut integrals. At one loop, a general diagrammatic coaction was established using dimensional regularisation, which may be realised in terms of a global coaction on hypergeometric functions, or equivalently, order by order in the ϵ expansion, via a local coaction on multiple polylogarithms. The present paper takes the first steps in generalising the diagrammatic coaction beyond one loop. We first establish general properties that govern the diagrammatic coaction at any loop order. We then focus on examples of two-loop topologies for which all integrals expand into polylogarithms. In each case we determine bases of master integrals and cuts in terms of hypergeometric functions, and then use the global coaction to establish the diagrammatic coaction of all master integrals in the topology. The diagrammatic coaction encodes the complete set of discontinuities of Feynman integrals, as well as the differential equations they satisfy, providing a general tool to understand their physical and mathematical properties.

PERFECT STOCHASTIC SUMMATION IN HIGH ORDER FEYNMAN GRAPH EXPANSIONS

2006 ◽  
Vol 17 (11) ◽  
pp. 1527-1549 ◽  
Author(s):  
J. N. CORCORAN ◽  
U. SCHNEIDER ◽  
H.-B. SCHÜTTLER
Keyword(s):  
Monte Carlo ◽  
Feynman Graph ◽  
Sampling Technique ◽  
Small Samples ◽  
Brute Force ◽  
Perfect Sampling ◽  
Self Energy ◽  
Graph Expansions ◽  
Low Dimensional ◽  
True Values

We describe a new application of an existing perfect sampling technique of Corcoran and Tweedie to estimate the self energy of an interacting Fermion model via Monte Carlo summation. Simulations suggest that the algorithm in this context converges extremely rapidly and results compare favorably to true values obtained by brute force computations for low dimensional toy problems. A variant of the perfect sampling scheme which improves the accuracy of the Monte Carlo sum for small samples is also given.

Feynman-Graph Expansion for the Equation of State near the Critical Point (Ising-like Case)

1972 ◽  
Vol 29 (9) ◽  
pp. 591-594 ◽  
Author(s):  
E. Brézin ◽  
D. J. Wallace ◽  
Kenneth G. Wilson
Keyword(s):  
Equation Of State ◽  
Critical Point ◽  
Feynman Graph ◽  
Graph Expansion

scholarly journals Schouten identities for Feynman graph amplitudes; The Master Integrals for the two-loop massive sunrise graph

2014 ◽  
Vol 880 ◽  
pp. 343-377 ◽  
Author(s):  
Ettore Remiddi ◽  
Lorenzo Tancredi
Keyword(s):  
Feynman Graph

scholarly journals Algebraic reduction of one-loop Feynman graph amplitudes

2000 ◽  
Vol 566 (1-2) ◽  
pp. 423-440 ◽  
Author(s):  
J. Fleischer ◽  
F. Jegerlehner ◽  
O.V. Tarasov
Keyword(s):  
Feynman Graph ◽  
Algebraic Reduction

Feynman graph derivation of the Einstein quadrupole formula

1982 ◽  
Vol 15 (2) ◽  
pp. 473-492 ◽  
Author(s):  
N D Hari Dass ◽  
V Soni
Keyword(s):  
Feynman Graph

QUANTUM SUPERCONDUCTING FLUCTUATIONS AND DISSIPATION IN VORTEX STATES

1996 ◽  
Vol 10 (06) ◽  
pp. 601-634 ◽  
Author(s):  
RYUSUKE IKEDA
Keyword(s):  
Phase Diagram ◽  
Vortex Flow ◽  
Mean Field ◽  
Feynman Graph ◽  
Transition Line ◽  
Single Vortex ◽  
Ginzburg Landau ◽  
Vortex States ◽  
Resistance Curves ◽  
Superconducting Fluctuations

Quantum effects on renormalized superconducting fluctuations are studied in the context of vortex states. It is argued by taking account of existing resistivity data that inclusion of dissipative (metallic) dynamics is indispensable at any nonzero temperature. Analysis is largely based on simple extensions of the usual time-dependent Ginzburg–Landau (TDGL) dynamics to quantum regime. First, phase diagram and dc conductivities resulting from a quantum GL action with purely dissipative dynamics are investigated, and it is noticed that, on (or, in the vicinity of) the transition line between the vortex lattice and the resulting quantum vortex liquid regime, the inverse of vortex flow conductance becomes a nearly universal value of the order of R q = 6.45 ( k Ω) and independent of material parameters. On the other hands, based on the usual Feynman graph analysis of Kubo formula, the superconducing (i.e. fluctuation) contribution to dc diagonal conductance decreases upon cooling in the disordered phase affected by quantum fluctuations, and becomes zero in T = 0 liquid regime [and above Hc2 (0)] irrespective of the details of dynamics. Reflecting these theoretical results, calculated resistance curves show the behavior quite similar to those observed in homogeneously disordered thin films, even though the presence of a field-tuned insulator–superconductor transition at T = 0 is neglected and the dynamics is purely dissipative. Phenomena in systems with quantum fluctuation of moderate strength are also considered. Analysis is also extended to the cases with other dynamical terms. It is pointed out that the usual (mean field) vortex flow Hall conductivity is never found in any nondissipative T = 0 liquid regime, and argued that, in general, the superconducting Hall effect itself is absent there at low enough fields irrespective of the presence of particle–hole assymmetry. Therefore, in contrast to the thermal vortex states with no pinning disorder, the dc transport phenomena at T = 0 are quite sensitive to the corresponding phase diagram, and hence, discussions based on the single vortex dynamics are even qualitatively invalid in the liquid regime at extremely low temperatures.

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