Abstract.
We study spontaneous symmetry breaking for field algebras on Minkowski space in the presence of a condition of geometric modular action (CGMA) proposed earlier as a selection criterion for vacuum states on general space-times. We show that any internal symmetry group must commute with the representation of the Poincaré group (whose existence is assured by the CGMA) and each translation-invariant vector is also Poincaré invariant. The subspace of these vectors can be centrally decomposed into pure invariant states and the CGMA holds in the resulting sectors. As positivity of the energy is not assumed, similar results may be expected to hold for other space-times.
Communicated by Klaus Fredenhagen
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to the memory of Siegfried Schlieder
submitted 25/05/04, accepted 29/10/04
Rights and permissions
About this article
Cite this article
Buchholz, D., Summers, S.J. Geometric Modular Action and Spontaneous Symmetry Breaking. Ann. Henri Poincaré 6, 607–624 (2005). https://doi.org/10.1007/s00023-005-0217-9
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00023-005-0217-9