zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Planar diagrams. (English) Zbl 0997.81548
The authors describe their method for counting planar Feynman diagrams of quantum field theory. Mathematicians who are not familiar with the current jargon of quantum field theory are likely to find this paper rather difficult to follow. In order to demonstrate the usefulness of their method, the authors calculate the ground state energy of a system of coupled anharmonic oscillators with a φ 4 interaction in the planar approximation. They obtain the value 0·58993g 1/3 in the limit of large g, where g is the coupling constant. By comparing this with the value 0·66799g 1/3 which is described as exact, the authors conclude that the planar approximation is at most 12% wrong!

MSC:
81T18Feynman diagrams
81T99Quantum field theory
References:
[1]’t Hooft, G.: Nucl. Phys. B72, 461–473 (1974) · doi:10.1016/0550-3213(74)90154-0
[2]’t Hooft, G.: Nucl. Phys. B75, 461–470 (1974) · doi:10.1016/0550-3213(74)90154-0
[3]Tutte, W. T.: Can. J. Math.14, 21–38 (1962) · Zbl 0103.39603 · doi:10.4153/CJM-1962-002-9
[4]Koplik, J., Neveu, A., Nussinov, S.: Nucl. Phys. B123, 109–131 (1977) · doi:10.1016/0550-3213(77)90344-3
[5]Mehta, M. L.: Random matrices. New-York and London: Academic Press 1967
[6]Hioe, F. T., Montroll, E. W.: J. Math. Phys.16, 1945–1955 (1975) · doi:10.1063/1.522747
[7]’t Hooft, G.: Private communication