Bose-Einstein condensate and spontaneous breaking of conformal symmetry on Killing horizons II
- Dipartimento di Matematica dell'Universita di Trento and Istituto Nazionale di Alta Matematica 'F. Severi', Unita Locale di Trento (Italy)
In the paper cited in the title [J. Math. Phys. 46, 062303 (2005)] local scalar QFT (in Weyl algebraic approach) has been constructed on degenerate semi-Riemannian manifolds S{sup 1}x{sigma} corresponding to the extension of Killing horizons by adding points at infinity to the null geodesic forming the horizon. It has been proved that the theory admits a natural representation of PSL(2,R) in terms of *-automorphisms and this representation is unitarily implementable if referring to a certain invariant state {lambda}. Among other results it has been proved that the theory admits a class of inequivalent algebraic (coherent) states {l_brace}{lambda}{sub {zeta}}{r_brace}, with {zeta} set-membership sign L{sup 2}({sigma}), which break part of the symmetry, in the sense that each of them is not invariant under the full group PSL(2,R) and so there is no unitary representation of whole group PSL(2,R) which leaves fixed the cyclic GNS vector. These states, if restricted to suitable portions of M are invariant and extremal KMS states with respect to a surviving one-parameter group symmetry. In this paper we clarify the nature of symmetry breakdown. We show that, in fact, spontaneous symmetry breaking occurs in the natural sense of algebraic quantum field theory: if {zeta}{ne}0, there is no unitary representation of whole group PSL(2,R) which implements the *-automorphism representation of PSL(2,R) itself in the GNS representation of {lambda}{sub {zeta}} (leaving fixed or not the state)
- OSTI ID:
- 20768737
- Journal Information:
- Journal of Mathematical Physics, Vol. 47, Issue 3; Other Information: DOI: 10.1063/1.2173174; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
Similar Records
Implication of compensator field and local scale invariance in the standard model
A symmetry reduction scheme of the Dirac algebra without dimensional defects