My new
article: G. Sardanashvily, Inequivalent Vacuum States
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
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