Number and weights of Feynman diagrams

Cvitanović, Predrag; Lautrup, B.; Pearson, Robert B.

doi:10.1103/physrevd.18.1939

Cited by 57 publications

(130 citation statements)

References 8 publications

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“…Another example which generates a neater result is this, invoking the modified Bessel functions. The conciseness of its form is entirely due to the familiarity of the functions involved, though, and in fact it is almost identical in construction to the previous one: The first of these occurs in QED as the number of Feynman diagrams with exact propagators [5] and is #A005411 in the OEIS, though the expression as an integral is, again, apparently new. We are not sure if the second expression, which is not in the OEIS at the time of writing, has an application in the same field.…”

Section: Introductionmentioning

confidence: 99%

“…. ), which is obtained by v n = (n − 1)(u n + 2nu n−1 ), n ≥ 2, is thereby solved too, and in QED is the number of graphs with 'proper vertices' [5].…”

Section: Miscellaneousmentioning

confidence: 99%

“…A sequence that bears intriguing similarity to that one is S(2, −2, 1) n = ∞ 0 2x n−1 e x/2 G 2 ( 1 2 x) 2 + π 2 G 3 ( 1 2 x) 2 dx, where and is the number of Feynman diagrams with proper self-energies arising in QED [5]; the integral representation is apparently new. Another example which generates a neater result is this, invoking the modified Bessel functions.…”

Section: Introductionmentioning

confidence: 99%

“…There are more known cases in this category, in fact, and here is another result from combinatorics: and is the number of nonisomorphic connected Feynman diagrams of order 2(n+1) arising in a simplified model of quantum electrodynamics (QED) [5]. On multiplication term-by-term by 2n − 1 the following sequence (#A005416) is generated, (1, 6, 50, 518, 6354, 89782, .…”

Section: Introductionmentioning

confidence: 99%

“…This sequence and a related one described later are encountered in a number of applications including the moments of the area function of a Brownian excursion [10,11], quantum field theory [5] (quite a fertile ground for these: more of this shortly) and combinatorics [8]. For reference this sequence is #A062980 in the Online Encyclopedia of Integer Sequences (OEIS) [19], and begins S(6, −8, 1) = (1, 5, 60, 1105, 27120, 828250, .…”

Section: Introductionmentioning

confidence: 99%

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An exactly solvable self-convolutive recurrence

Martin

Kearney

2010

Aequat. Math.

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Abstract. We consider a self-convolutive recurrence whose solution is the sequence of coefficients in the asymptotic expansion of the logarithmic derivative of the confluent hypergeometic function U (a, b, z). By application of the Hilbert transform we convert this expression into an explicit, non-recursive solution in which the nth coefficient is expressed as the (n − 1)th moment of a measure, and also as the trace of the (n − 1)th iterate of a linear operator. Applications of these sequences, and hence of the explicit solution provided, are found in quantum field theory as the number of Feynman diagrams of a certain type and order, in Brownian motion theory, and in combinatorics.

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Section: Introductionmentioning

confidence: 99%

“…. ), which is obtained by v n = (n − 1)(u n + 2nu n−1 ), n ≥ 2, is thereby solved too, and in QED is the number of graphs with 'proper vertices' [5].…”

Section: Miscellaneousmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An exactly solvable self-convolutive recurrence

Martin

Kearney

2010

Aequat. Math.

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Table of Feynman diagrams of the interacting Fermion Green's function

Mathar

2007

Int J of Quantum Chemistry

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The Feynman diagrams of the Green's function expansion of fermions interacting with a nonrelativistic 2-body interaction are displayed in first, second and third order of the interaction as 2, 10 and 74 diagrams, respectively. A name convention for the diagrams is proposed and then used to tabulate the 706 diagrams of fourth order. The Hartree-Fock approximation summons up 2, 8, 40 and 224 of them, respectively.

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Quantum Field Theory on a Discrete Space and Noncommutative Geometry

Haeussling

2002

Annals of Physics

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We analyse in detail the quantization of a simple noncommutative model of spontaneous symmetry breaking in zero dimensions taking into account the noncommutative setting seriously. The connection to the counting argument of Feynman diagrams of the corresponding theory in four dimensions is worked out explicitly. Special emphasis is put on the motivation as well as the presentation of some well-known basic notions of quantum field theory which in the zero-dimensional theory can be studied without being spoiled by technical complications due to the absence of divergencies.

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Number and weights of Feynman diagrams

Cited by 57 publications

References 8 publications

An exactly solvable self-convolutive recurrence

An exactly solvable self-convolutive recurrence

Table of Feynman diagrams of the interacting Fermion Green's function

Quantum Field Theory on a Discrete Space and Noncommutative Geometry

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