About the notion of eigenstates for C^*-algebras and some application in Quantum Mechanics

2023/04/05 by De Nittis, Giuseppe, Polo, Danilo · 2 citations
#47L90 #82B10 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Primary: 46L30 #Secondary: 47L80 #Soft Condensed Matter (cond-mat.soft)

paper · doi:10.48550/arxiv.2304.02685

Abstract

This work is concerned with the notion of eigenstates for C^*-algebras. After reviewing some basic and structural results, we explore the possibility of reinterpreting certain typical concepts of quantum mechanics (\eg dynamical equilibrium states, ground states, gapped states, Fermi surfaces) in terms of (algebraic) eigenstates.

Cited by

• PT-like phase transitions from square roots of supersymmetric Hamiltonians
• Eigenstates of CQ*-algebras

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