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Continuity equation and local gauge invariance for the (NLO)-L-3 nuclear energy density functionals

Raimondi, F.; Carlsson, Gillis LU ; Dobaczewski, J. and Toivanen, J. (2011) In Physical Review C (Nuclear Physics) 84(6).
Abstract
Background: The next-to-next-to-next-to-leading order ((NLO)-L-3) nuclear energy density functional extends the standard Skyrme functional with new terms depending on higher-order derivatives of densities, introduced to gain better precision in the nuclear many-body calculations. A thorough study of the transformation properties of the functional with respect to different symmetries is required as a step preliminary to the adjustment of the coupling constants. Purpose: We determine to what extent the presence of higher-order derivatives in the functional can be compatible with the continuity equation. In particular, we study the relations between the validity of the continuity equation and the invariance of the functional under gauge... (More)
Background: The next-to-next-to-next-to-leading order ((NLO)-L-3) nuclear energy density functional extends the standard Skyrme functional with new terms depending on higher-order derivatives of densities, introduced to gain better precision in the nuclear many-body calculations. A thorough study of the transformation properties of the functional with respect to different symmetries is required as a step preliminary to the adjustment of the coupling constants. Purpose: We determine to what extent the presence of higher-order derivatives in the functional can be compatible with the continuity equation. In particular, we study the relations between the validity of the continuity equation and the invariance of the functional under gauge transformations. Methods: We derive conditions for the validity of the continuity equation in the framework of time-dependent density functional theory. The conditions apply separately to the four spin-isospin channels of the one-body density matrix. Results: We obtained four sets of constraints on the coupling constants of the (NLO)-L-3 energy density functional that guarantee the validity of the continuity equation in all spin-isospin channels. In particular, for the scalar-isoscalar channel, the constraints are the same as those resulting from imposing the standard U(1) local-gauge-invariance conditions. Conclusions: The validity of the continuity equation in the four spin-isospin channels is equivalent to the local-gauge invariance of the energy density functional. For vector and isovector channels, such validity requires the invariance of the functional under local rotations in the spin and isospin spaces. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Physical Review C (Nuclear Physics)
volume
84
issue
6
publisher
American Physical Society
external identifiers
  • wos:000297768100002
  • scopus:84855363215
ISSN
0556-2813
DOI
10.1103/PhysRevC.84.064303
language
English
LU publication?
yes
id
3f62d944-7a97-4a9c-b564-cc9bbbd97b2f (old id 2291571)
date added to LUP
2012-01-11 13:51:59
date last changed
2017-11-12 03:47:03
@article{3f62d944-7a97-4a9c-b564-cc9bbbd97b2f,
  abstract     = {Background: The next-to-next-to-next-to-leading order ((NLO)-L-3) nuclear energy density functional extends the standard Skyrme functional with new terms depending on higher-order derivatives of densities, introduced to gain better precision in the nuclear many-body calculations. A thorough study of the transformation properties of the functional with respect to different symmetries is required as a step preliminary to the adjustment of the coupling constants. Purpose: We determine to what extent the presence of higher-order derivatives in the functional can be compatible with the continuity equation. In particular, we study the relations between the validity of the continuity equation and the invariance of the functional under gauge transformations. Methods: We derive conditions for the validity of the continuity equation in the framework of time-dependent density functional theory. The conditions apply separately to the four spin-isospin channels of the one-body density matrix. Results: We obtained four sets of constraints on the coupling constants of the (NLO)-L-3 energy density functional that guarantee the validity of the continuity equation in all spin-isospin channels. In particular, for the scalar-isoscalar channel, the constraints are the same as those resulting from imposing the standard U(1) local-gauge-invariance conditions. Conclusions: The validity of the continuity equation in the four spin-isospin channels is equivalent to the local-gauge invariance of the energy density functional. For vector and isovector channels, such validity requires the invariance of the functional under local rotations in the spin and isospin spaces.},
  articleno    = {064303},
  author       = {Raimondi, F. and Carlsson, Gillis and Dobaczewski, J. and Toivanen, J.},
  issn         = {0556-2813},
  language     = {eng},
  number       = {6},
  publisher    = {American Physical Society},
  series       = {Physical Review C (Nuclear Physics)},
  title        = {Continuity equation and local gauge invariance for the (NLO)-L-3 nuclear energy density functionals},
  url          = {http://dx.doi.org/10.1103/PhysRevC.84.064303},
  volume       = {84},
  year         = {2011},
}