The optical equivalence theorem is examined for the particular class of the electromagnetic fields. It is shown that the distribution function can be taken as a non-negative function, if the density operator describing the states of the electromagnetic field is diagonal in the occupation number representation. Hence the equivalence is not only formal but also essential for this class of the electromagnetic fields, so long as the description of the optical coherence theory is concerned. As a typical example the “diagonal” representation of the density operator for blackbody radiation is studied.The optical equivalence theorem is examined for the particular class of the electromagnetic fields. It is shown that the distribution function can be taken as a non-negative function, if the density operator describing the states of the electromagnetic field is diagonal in the occupation number representation. Hence the equivalence is not only formal but also essential for this class of the electromagnetic fields, so long as the description of the optical coherence theory is concerned. As a typical example the “diagonal” representation of the density operator for blackbody radiation is studied.

Journal of the Physical Society of JapanFeb 1, 19740 citations

2025-10-20_RFT_Relational_Coherence_Density_in_Relational_Field_Theory_RFT_Technical_Note_0.3

Svancara, Clinton

This paper forms part of the Relational Field Theory Technical Note Series (0.1–0.3), mapping the continuum from ontological boundary to measurable coherence density. This work extends Notes 0.1–0.2, completing the ontological-to-measurable mapping of Relational Field Theory (RFT). It introduces a relational coherence density metric, ρc = Rc(local) Rc(univ) , bridging micro-coherence (quantum behavior) and macro-coherence (gravitational/cosmological structure). Singularities at ρc → 0 (undefined variation, see Note 0.1) and ρc → ∞ (divergent stability, see Note 0.2) frame this metric, unifying emergent phenomena—quantum decoherence to cosmic acceleration—within a testable ontology for physical transitions Provenance: Originally published on Zenodo (Oct 2025). 10.5281/zenodo.17400900This paper forms part of the Relational Field Theory Technical Note Series (0.1–0.3), mapping the continuum from ontological boundary to measurable coherence density. This work extends Notes 0.1–0.2, completing the ontological-to-measurable mapping of Relational Field Theory (RFT). It introduces a relational coherence density metric, ρc = Rc(local) Rc(univ) , bridging micro-coherence (quantum behavior) and macro-coherence (gravitational/cosmological structure). Singularities at ρc → 0 (undefined variation, see Note 0.1) and ρc → ∞ (divergent stability, see Note 0.2) frame this metric, unifying emergent phenomena—quantum decoherence to cosmic acceleration—within a testable ontology for physical transitions Provenance: Originally published on Zenodo (Oct 2025). 10.5281/zenodo.17400900

Jan 1, 20250 citations

Dynamic equations for density operators in external fields

M. A. Galakhov, P.B. Gusiatnikov

Soviet physics. DokladySep 1, 19780 citations

A density calculus for quantum field theory

Tanay Kibe, Pratik Roy

These notes provide an introduction to Haagerup noncommutative $L^p$ spaces for quantum field theorists. The aim is to explain how the familiar calculus of density matrices, fractional powers, and Schatten norms extends to local observable algebras of type~III, where an intrinsic trace is unavailable. We develop the construction first for a matrix algebra, making the crossed product, its trace, and the dual action explicit, before passing to general von Neumann algebras. Particular attention is paid to the representation of normal states by Haagerup densities and to the distinction between the crossed-product trace and the canonical Haagerup functional used to compute expectation values. As a concrete application, we calculate the sandwiched Rényi divergence for a coherent excitation of a chiral current, verifying monotonicity under restriction and the Rényi quantum null energy condition at every real order $α>1$ . The presentation assumes familiarity with quantum mechanics and elementary quantum field theory, while introducing the operator-algebraic concepts needed for the construction and calculation.These notes provide an introduction to Haagerup noncommutative $L^p$ spaces for quantum field theorists. The aim is to explain how the familiar calculus of density matrices, fractional powers, and Schatten norms extends to local observable algebras of type~III, where an intrinsic trace is unavailable. We develop the construction first for a matrix algebra, making the crossed product, its trace, and the dual action explicit, before passing to general von Neumann algebras. Particular attention is paid to the representation of normal states by Haagerup densities and to the distinction between the crossed-product trace and the canonical Haagerup functional used to compute expectation values. As a concrete application, we calculate the sandwiched Rényi divergence for a coherent excitation of a chiral current, verifying monotonicity under restriction and the Rényi quantum null energy condition at every real order $α>1$. The presentation assumes familiarity with quantum mechanics and elementary quantum field theory, while introducing the operator-algebraic concepts needed for the construction and calculation.

hep-thCross-listedarXiv:2610.40174Oct 30, 2026

New light fields based on integration theory within the Weyl ordering product of operators

Ke Zhang, Lanlan Li, Da-wei Guo +1 more

The development of quantum optics theory based on the method of integration within an ordered product of operators (IWOP) has greatly stimulated the study of quantum states in the light field, especially non-Gaussian states with various non-classical properties. In this paper, the two-mode squeezing operator is derived with integral theory within the Weyl ordering product of operators using a combinatorial field in which one mode is a chaotic field and the other mode is a vacuum field. The density operator of the new light field, its entanglement property and photon number distribution are analyzed. We also note that tracing a three-mode pure state can yield this new light field. These methods represent a theoretical approach to investigating new density operators of light fields.The development of quantum optics theory based on the method of integration within an ordered product of operators (IWOP) has greatly stimulated the study of quantum states in the light field, especially non-Gaussian states with various non-classical properties. In this paper, the two-mode squeezing operator is derived with integral theory within the Weyl ordering product of operators using a combinatorial field in which one mode is a chaotic field and the other mode is a vacuum field. The density operator of the new light field, its entanglement property and photon number distribution are analyzed. We also note that tracing a three-mode pure state can yield this new light field. These methods represent a theoretical approach to investigating new density operators of light fields.

Chinese Physics BJul 5, 20224 citations

These notes provide an introduction to Haagerup noncommutative

L^p

spaces for quantum field theorists. The aim is to explain how the familiar calculus of density matrices, fractional powers, and Schatten norms extends to local observable algebras of type~III, where an intrinsic trace is unavailable. We develop the construction first for a matrix algebra, making the crossed product, its trace, and the dual action explicit, before passing to general von Neumann algebras. Particular attention is paid to the representation of normal states by Haagerup densities and to the distinction between the crossed-product trace and the canonical Haagerup functional used to compute expectation values. As a concrete application, we calculate the sandwiched Rényi divergence for a coherent excitation of a chiral current, verifying monotonicity under restriction and the Rényi quantum null energy condition at every real order

α>1

. The presentation assumes familiarity with quantum mechanics and elementary quantum field theory, while introducing the operator-algebraic concepts needed for the construction and calculation.