This paper provides an overview of Janusz Czelakowski’s contributions to the theory of partial Boolean (𝜎-)algebras, and, more in general, to the foundation of Quantum Mechanics. Particular attention is paid to the logic of partial Boolean 𝜎-algebras, to characterizations of PBAs embeddable into Boolean (𝜎-)algebras, and their representation as self-adjoint idempotent elements of partial commutative algebras with involution. Also, applications to the theory of orthomodular posets as well as Czelakowski’s theory of partial Boolean algebras in a broader sense will be discussed. Finally, further representation theorems and their importance for quantum logic will be outlined.
On J. Czelakowski’s contributions to quantum logic and the foundation of Quantum Mechanics
Davide Fazio
2023-01-01
Abstract
This paper provides an overview of Janusz Czelakowski’s contributions to the theory of partial Boolean (𝜎-)algebras, and, more in general, to the foundation of Quantum Mechanics. Particular attention is paid to the logic of partial Boolean 𝜎-algebras, to characterizations of PBAs embeddable into Boolean (𝜎-)algebras, and their representation as self-adjoint idempotent elements of partial commutative algebras with involution. Also, applications to the theory of orthomodular posets as well as Czelakowski’s theory of partial Boolean algebras in a broader sense will be discussed. Finally, further representation theorems and their importance for quantum logic will be outlined.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
