Introduction. Operational quantum logic: An overview B. Coecke, et al. I: Algebras. Algebraic aspects of orthomodular lattices G. Bruns, J. Harding. Observables in the logico-algebraic approach P. Ptak. Test spaces and orthoalgebras A. Wilce. Representations on unigroups D.J. Foulis. Free extensions of group actions, induced representations, and the foundations of physics D.J. Foulis, A. Wilce. II: Categories. Short introduction to enriched categories F. Borceux, I. Stubbe. Operational Galois adjunctions B. Coecke, D. Moore. Operational axiomatics and compound systems F. Valckenborgh. Quantales J. Paseka, J. Rosicky. III: Languages. Quantales and observational semantics P. Resende. Quantum languages S. Gudder. Indices. Concept index. Citation index.Introduction. Operational quantum logic: An overview B. Coecke, et al. I: Algebras. Algebraic aspects of orthomodular lattices G. Bruns, J. Harding. Observables in the logico-algebraic approach P. Ptak. Test spaces and orthoalgebras A. Wilce. Representations on unigroups D.J. Foulis. Free extensions of group actions, induced representations, and the foundations of physics D.J. Foulis, A. Wilce. II: Categories. Short introduction to enriched categories F. Borceux, I. Stubbe. Operational Galois adjunctions B. Coecke, D. Moore. Operational axiomatics and compound systems F. Valckenborgh. Quantales J. Paseka, J. Rosicky. III: Languages. Quantales and observational semantics P. Resende. Quantum languages S. Gudder. Indices. Concept index. Citation index.

Kluwer Academic Publishers eBooksJan 1, 200044 citations

Short-distance expansion for products of current-like operators

S. A. Anikin, C. I. Zavialov

Springer eBooksApr 6, 20080 citations

Probing noncommutativities of phase space by using persistent charged current and its asymmetry

Kai Ma, Yajie Ren, Yahui Wang

Nontrivial algebra structures of the coordinate and momentum operators are potentially important for describing possible new physics. The persistent charged current in a metal ring is expected to be sensitive to the nontrivial dynamics due to noncommutativities of phase space. In this paper, we propose a new asymmetric observable for probing the noncommutativity of momentum operators. We also analyzed the temperature dependence of this observable, and we find that the asymmetry holds at a finite temperature. The critical temperature, above which the correction due to coordinate noncommutativity is negligible, is also derived.Nontrivial algebra structures of the coordinate and momentum operators are potentially important for describing possible new physics. The persistent charged current in a metal ring is expected to be sensitive to the nontrivial dynamics due to noncommutativities of phase space. In this paper, we propose a new asymmetric observable for probing the noncommutativity of momentum operators. We also analyzed the temperature dependence of this observable, and we find that the asymmetry holds at a finite temperature. The critical temperature, above which the correction due to coordinate noncommutativity is negligible, is also derived.

arXiv:1703.10923Physical review. D/Physical review. D.Jun 8, 201812 citations

Entanglement as a Non-Discriminant Witness: A Structural Diagnostic on Operational Algebras in Weak-Field Gravity

Danilo Tavella

This technical note addresses a narrow structural question in the current gravity debate: whether the mere presence of entanglement, within a fixed experimentally accessible domain, can function by itself as a discriminator between incompatible theoretical architectures. Working within a fixed operational algebra of accessible observables, the note shows that entanglement, considered solely as a binary witness, is not by itself sufficient for such discrimination. The result is strictly diagnostic and domain-bounded: it does not deny the relevance of entanglement in quantum gravity, nor does it claim observational equivalence in principle between classical and quantum gravity. It argues instead that discrimination requires analysis of the full observable algebra and of the scaling structure of accessible correlations, not merely the presence or absence of entanglementThis technical note addresses a narrow structural question in the current gravity debate: whether the mere presence of entanglement, within a fixed experimentally accessible domain, can function by itself as a discriminator between incompatible theoretical architectures. Working within a fixed operational algebra of accessible observables, the note shows that entanglement, considered solely as a binary witness, is not by itself sufficient for such discrimination. The result is strictly diagnostic and domain-bounded: it does not deny the relevance of entanglement in quantum gravity, nor does it claim observational equivalence in principle between classical and quantum gravity. It argues instead that discrimination requires analysis of the full observable algebra and of the scaling structure of accessible correlations, not merely the presence or absence of entanglement

Apr 3, 20260 citations

What is electric charge?: Charge as a local observable in relativistic quantum field theory

Hideyasu Yamashita

It is rather surprising that modern quantum physics does not appear to have provided any clear answer to the simple question ``what is electric charge?''. Even when the total charge operator $Q$ is well-defined, the non-locality of $Q$ implies that it is not an observable in the usual sense, which can be measured by a (local) experimental apparatus. A candidate for the ``local version'' of charge operator is the 4-current operator $j=(j^μ)_{μ=0,1,2,3}$ . However, it is known that the rigorous definition of $j$ is difficult in $(3+1)$ -dimensional Minkowski space. Although it was found that the current can be defined in $(1+1)$ -dimensions (Carey et al.), I argue that even when $j$ can be suitably defined, the interpretability of $j$ as the ``local charge operator'' is dubious. Instead I return to Araki and Wyss (1964), and propose the concept of ``scope-local charge'' $Q_ζ(P)$ for a ``scope'' $P$ , expressed by a finite-dimensional projection. I work in an abstract $C^{*}$ -algebraic setting.It is rather surprising that modern quantum physics does not appear to have provided any clear answer to the simple question ``what is electric charge?''. Even when the total charge operator $Q$ is well-defined, the non-locality of $Q$ implies that it is not an observable in the usual sense, which can be measured by a (local) experimental apparatus. A candidate for the ``local version'' of charge operator is the 4-current operator $j=(j^μ)_{μ=0,1,2,3}$. However, it is known that the rigorous definition of $j$ is difficult in $(3+1)$-dimensional Minkowski space. Although it was found that the current can be defined in $(1+1)$-dimensions (Carey et al.), I argue that even when $j$ can be suitably defined, the interpretability of $j$ as the ``local charge operator'' is dubious. Instead I return to Araki and Wyss (1964), and propose the concept of ``scope-local charge'' $Q_ζ(P)$ for a ``scope'' $P$, expressed by a finite-dimensional projection. I work in an abstract $C^{*}$-algebraic setting.

quant-pharXiv:2608.00468Aug 4, 20260 citations

It is rather surprising that modern quantum physics does not appear to have provided any clear answer to the simple question ``what is electric charge?''. Even when the total charge operator

Q

is well-defined, the non-locality of

Q

implies that it is not an observable in the usual sense, which can be measured by a (local) experimental apparatus. A candidate for the ``local version'' of charge operator is the 4-current operator

j=(j^μ)_{μ=0,1,2,3}

. However, it is known that the rigorous definition of

j

is difficult in

(3+1)

-dimensional Minkowski space. Although it was found that the current can be defined in

(1+1)

-dimensions (Carey et al.), I argue that even when

j

can be suitably defined, the interpretability of

j

as the ``local charge operator'' is dubious. Instead I return to Araki and Wyss (1964), and propose the concept of ``scope-local charge''

Q_ζ(P)

for a ``scope''

P

, expressed by a finite-dimensional projection. I work in an abstract

C^{*}

-algebraic setting.