Dimensional expansion for the Ising limit of quantum field theory

Bender, Carl M.; Boettcher, Stefan

doi:10.1103/PhysRevD.48.4919

Dimensional expansion for the Ising limit of quantum field theory

Nov 15, 1993

10 pages

Published in:

Phys.Rev.D 48 (1993) 4919-4923

e-Print:

hep-th/9311060 [hep-th]

DOI:

10.1103/PhysRevD.48.4919

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Abstract:

A recently-proposed technique, called the dimensional expansion, uses the space-time dimension

D

as an expansion parameter to extract nonperturbative results in quantum field theory. Here we apply dimensional-expansion methods to examine the Ising limit of a self-interacting scalar field theory. We compute the first few coefficients in the dimensional expansion for

\gamma_{2n}

, the renormalized

2n

-point Green's function at zero momentum, for

n\!=\!2

, 3, 4, and 5. Because the exact results for

\gamma_{2n}

are known at

D\!=\!1

we can compare the predictions of the dimensional expansion at this value of

D

. We find typical errors of less than

5\%

. The radius of convergence of the dimensional expansion for

\gamma_{2n}

appears to be

{{2n}\over {n-1}}

. As a function of the space-time dimension

D

,

\gamma_{2n}

appears to rise monotonically with increasing

D

and we conjecture that it becomes infinite at

D\!=\!{{2n}\over {n-1}}

. We presume that for values of

D

greater than this critical value,

\gamma_{2n}

vanishes identically because the corresponding

\phi~{2n}

scalar quantum field theory is free for

D\!>\!{{2n}\over{n-1}}

.

expansion: dimensional
field theory: scalar
n-point function
Ising model
expansion: strong coupling
strong coupling: expansion

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Figures(0)

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