# Geometric modular action and spontaneous symmetry breaking

May 25, 2004

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 Poincare group (whose existence is assured by the CGMA) and each
translation-invariant vector is also Poincare 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.

Keywords:

geometric modular action, spontaneous symmetry breaking