The God has created a man in order that he creates that the God fails to do

Friday, 14 August 2015

My new article: Inequivalent Vacuum States in Algebraic Quantum Theory

My new article: G. Sardanashvily, Inequivalent Vacuum States in Algebraic Quantum Theory, arXiv: 1508.03286


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.


  • 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

No comments:

Post a Comment