Rigorous Construction of Planar Diagram Field Theories in Four-dimensional Euclidean Space

't Hooft, Gerard

doi:10.1007/BF01206876

Rigorous Construction of Planar Diagram Field Theories in Four-dimensional Euclidean Space

Gerard 't Hooft
(
- Utrecht U.
)

Oct, 1982

52 pages

Published in:

Commun.Math.Phys. 88 (1983) 1

DOI:

10.1007/BF01206876

Report number:

Print-82-0776 (UTRECHT)

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Abstract: (Springer)

Asymptotically free quantum field theories with planar Feynman diagrams [such as SU(∞) gauge theory] are considered in 4 dimensional Euclidean space. It is shown that if all particles involved have non-vanishing masses and if the coupling constant(s) γ (org2) are small enough (λ≦λcrit), then an absolutely convergent procedure exists to obtain Green functions that uniquely solve the Dyson-Schwinger equations.

field theory: Euclidean
asymptotic freedom
Dyson-Schwinger equation
asymptotic expansion
Feynman graph: planar
perturbation theory
n-point function
renormalization group
short-distance behavior

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