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An asymptotic loop extension for the effective potential in the p(ø)₂ quantum field theory Slade, Gordon Douglas
Abstract
The effective potential V(n,a) for the Euclidean p(ø)₂ quantum field theory is defined to be the Fenchel transform (convex conjugate) of the pressure in an external field, and is shown to be finite. The parameter h is Planck’s constant divided by 2π. The classical limit (h↓0) of the effective potential is shown to be the convex hull of the classical potential P(a) + 1/2m²a². For values of a for which the classical potential is equal to its convex hull and has a nonvanishing second derivative, the usual one-particle irreducible loop expansion for the effective potential is shown to be asymptotic as (h↓0), using a uniformly convergent (as h↓0) high temperature cluster expansion and irreducibility properties of the Legendre transform. For the same values of a, V is shown to be analytic in a for sufficiently small h. Finally an example is given for a double well classical potential where the one-particle irreducible loop expansion fails to be asymptotic, and the true asymptotics are obtained.
Item Metadata
Title |
An asymptotic loop extension for the effective potential in the p(ø)₂ quantum field theory
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1984
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Description |
The effective potential V(n,a) for the Euclidean p(ø)₂ quantum field theory is defined to be the Fenchel transform (convex conjugate) of the pressure in an external field, and is shown to be finite. The parameter h is Planck’s constant divided by 2π. The classical limit (h↓0) of the effective potential is shown to be the convex hull of the classical potential P(a) + 1/2m²a². For values of a for which the classical potential is equal to its convex hull and has a nonvanishing second derivative, the usual one-particle irreducible loop expansion for the effective potential is shown to be asymptotic as (h↓0), using a uniformly convergent (as h↓0) high temperature cluster expansion and irreducibility properties of the Legendre transform. For the same values of a, V is shown to be analytic in a for sufficiently small h.
Finally an example is given for a double well classical potential where the one-particle irreducible loop expansion fails to be asymptotic, and the true asymptotics are obtained.
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Genre | |
Type | |
Language |
eng
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Date Available |
2010-06-13
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0080304
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.