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##

Constraints for the scalar-isoscalar channel

For the standard CE in the scalar-isoscalar channel,
Eq. (27), the constraints that we found from
Eq. (48) are exactly the same as those defining the
gauge-invariant functional up to NLO [Carlsson et al.(2008)Carlsson,
Dobaczewski, and Kortelainen]. This
constitutes an explicit verification of the general result presented
in Sec. 2.2.1. As in Ref. [Carlsson et al.(2008)Carlsson,
Dobaczewski, and Kortelainen], we obtained
two sets of independent constraints, one for the isoscalar coupling
constants
and one for the isovector coupling
constants
. Within each isospin channel, the
linear conditions for the scalar coupling constants,
, are disconnected
from the linear conditions for the vector coupling constants,
.

Jacek Dobaczewski
2011-11-11