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Revisiting the local potential approximation of the exact renormalization group equation

C. Bervillier
(
- Tours U., CNRS
)

Jul 13, 2013

18 pages

Published in:

Nucl.Phys.B 876 (2013) 587-604

Published: Nov 11, 2013

e-Print:

1307.3679 [hep-th]

DOI:

10.1016/j.nuclphysb.2013.08.008

View in:

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Abstract: (Elsevier)

The conventional absence of field renormalization in the local potential approximation (LPA) — implying a zero value of the critical exponent η — is shown to be incompatible with the logic of the derivative expansion of the exact renormalization group (RG) equation. We present a LPA with η≠0 that strictly does not make reference to any momentum dependence. Emphasis is made on the perfect breaking of the reparametrization invariance in that pure LPA (absence of any vestige of invariance) which is compatible with the observation of a progressive smooth restoration of that invariance on implementing the two first orders of the derivative expansion whereas the conventional requirement ( η=0 in the LPA) precluded that observation.

Note:

Final version, some misprints corrected

Anomalous dimension
Reparametrization invariance
Exact renormalization group equation
Derivative expansion
Local potential approximation
potential: approximation
expansion: derivative
potential: local
invariance: reparametrization
renormalization group

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