About boundary terms in higher order theories

Lorenzo Fatibene; Mauro Francaviglia; S. Mercadante

Communications in Mathematics (2011)

  • Volume: 19, Issue: 2, page 129-136
  • ISSN: 1804-1388

Abstract

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It is shown that when in a higher order variational principle one fixes fields at the boundary leaving the field derivatives unconstrained, then the variational principle (in particular the solution space) is not invariant with respect to the addition of boundary terms to the action, as it happens instead when the correct procedure is applied. Examples are considered to show how leaving derivatives of fields unconstrained affects the physical interpretation of the model. This is justified in particular by the need of clarifying the issue for the purpose of applications to relativistic gravitational theories, where a bit of confusion still exists. On the contrary, as it is well known for variational principles of order k , if one fixes variables together with their derivatives (up to order k - 1 ) on the boundary then boundary terms leave solution space invariant.

How to cite

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Fatibene, Lorenzo, Francaviglia, Mauro, and Mercadante, S.. "About boundary terms in higher order theories." Communications in Mathematics 19.2 (2011): 129-136. <http://eudml.org/doc/246510>.

@article{Fatibene2011,
abstract = {It is shown that when in a higher order variational principle one fixes fields at the boundary leaving the field derivatives unconstrained, then the variational principle (in particular the solution space) is not invariant with respect to the addition of boundary terms to the action, as it happens instead when the correct procedure is applied. Examples are considered to show how leaving derivatives of fields unconstrained affects the physical interpretation of the model. This is justified in particular by the need of clarifying the issue for the purpose of applications to relativistic gravitational theories, where a bit of confusion still exists. On the contrary, as it is well known for variational principles of order $k$, if one fixes variables together with their derivatives (up to order $k-1$) on the boundary then boundary terms leave solution space invariant.},
author = {Fatibene, Lorenzo, Francaviglia, Mauro, Mercadante, S.},
journal = {Communications in Mathematics},
keywords = {higher order field theories; boundary terms; higher-order field theories; boundary terms; variational principle; relativistic gravitational theories},
language = {eng},
number = {2},
pages = {129-136},
publisher = {University of Ostrava},
title = {About boundary terms in higher order theories},
url = {http://eudml.org/doc/246510},
volume = {19},
year = {2011},
}

TY - JOUR
AU - Fatibene, Lorenzo
AU - Francaviglia, Mauro
AU - Mercadante, S.
TI - About boundary terms in higher order theories
JO - Communications in Mathematics
PY - 2011
PB - University of Ostrava
VL - 19
IS - 2
SP - 129
EP - 136
AB - It is shown that when in a higher order variational principle one fixes fields at the boundary leaving the field derivatives unconstrained, then the variational principle (in particular the solution space) is not invariant with respect to the addition of boundary terms to the action, as it happens instead when the correct procedure is applied. Examples are considered to show how leaving derivatives of fields unconstrained affects the physical interpretation of the model. This is justified in particular by the need of clarifying the issue for the purpose of applications to relativistic gravitational theories, where a bit of confusion still exists. On the contrary, as it is well known for variational principles of order $k$, if one fixes variables together with their derivatives (up to order $k-1$) on the boundary then boundary terms leave solution space invariant.
LA - eng
KW - higher order field theories; boundary terms; higher-order field theories; boundary terms; variational principle; relativistic gravitational theories
UR - http://eudml.org/doc/246510
ER -

References

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  8. Hinterbichler, K., Boundary Terms, Variational Principles and Higher Derivative Modified Gravity, Phys. Rev. D79 2009 024028 arXiv:0809.4033 (2009) Zbl1222.83142MR2491179
  9. Nojiri, S., Odintsov, S.D., Unified cosmic history in modified gravity: from F ( R ) theory to Lorentz non-invariant models, arXiv:1011.0544v4 [gr-qc] 
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