nLab
quasi-state

Context

AQFT

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)

Introduction

Concepts

field theory: classical, pre-quantum, quantum, perturbative quantum

Lagrangian field theory

quantization

quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization

renormalization

Theorems

States and observables

Operator algebra

Local QFT

Perturbative QFT

Contents

Idea

In quantum mechanics, a quasi-state on an algebra of observables AA is a function ρ:A\rho : A \to \mathbb{C} that is required to satisfy the axioms of a genuine state (linearity and positivity) only on the poset of commutative subalgebras of AA.

While therefore the condition on quasi-states is much weaker than that for states, Gleason's theorem asserts that if A=B(H)A = B(H) for dimH>2dim H \gt 2, then all quasi-states are in fact already genuine quantum states.

Notice that a quasi-state is naturally regarded as an actual state, but internal to the ringed topos over the poset of commutative subalgebras of AA – the “Bohr topos”. Therefore Gleason's theorem is one of the motivations for regarding this ringed topos as the quantum phase space (“Bohrification”.) The other is the Kochen-Specker theorem.

Last revised on October 3, 2013 at 00:33:36. See the history of this page for a list of all contributions to it.