My new
article: G. Sardanashvily, Inequivalent Vacuum States in
Algebraic Quantum Theory, arXiv: 1508.03286
Abstract
The GNS
representation construction is considered in a general case of topological
involutive algebras of quantum systems, including quantum fields, and
inequivalent state spaces of these systems are characterized. We aim to show
that, from the physical viewpoint, they can be treated as classical fields by
analogy with a Higgs vacuum field.
Contents
- Introduction
- GNS construction.
Bounded operators
- Inequivalent
vacua
- Example.
Infinite qubit systems
- Example.
Locally compact groups
- GNS construction.
Unbounded operators
- Example.
Commutative nuclear groups
- Infinite
canonical commutation relations
- Free
quantum fields
- Euclidean
QFT
- Higgs
vacuum
- Automorphisms
of quantum systems
- Spontaneous
symmetry breaking
- Appendixes:
Topological vector spaces; Hilbert, countably Hilbert and nuclear spaces; Measures
on locally compact spaces; Haar measures; Measures on infinite-dimensional
vector spaces
