arXiv subjects

Daniel W. Piasecki

Publications and source records attributed to Daniel W. Piasecki.

3 recordsLinked to original sources

arXiv2026

Origin of the Covariant Wigner Operator as a Quantum Amplitude in QCD

The Wigner function plays a central role in QCD as a phase space object encoding correlations among quarks, antiquarks, and gluons, yet its interpretation remains subtle due to its quasiprobabilistic nature and possible negativity. Recent work based on the Koopman-von Neumann-Sudarshan (KvNS) Hilbert space formulation of classical mechanics suggests the Wigner function arises as a quantum probability amplitude projected onto classical phase space, rather than a quasiprobability density (Bondar et al., 2013; McCaul et al., 2023). In the classical limit, this amplitude reduces to the classical Koopman wavefunction. In this work, we extend this perspective to relativistic QCD by constructing a Koopman description of the quark Wigner operator. We show that the Wigner operator is naturally isomorphic to a phase space spinor, providing a unified framework in which both classical and quantum dynamics are expressed. Within this formulation, the Wigner function retains its interpretation as an amplitude even in the relativistic regime. This viewpoint clarifies the origin of negativity and other nonclassical features, and provides a more transparent foundation for parton distribution functions in QCD. Remarkably, the relativistic Koopman framework reproduces the classical limit of QCD.

hep-ph↗

arXiv2024

Dirac-von Neumann Type Axiomatic Structure for Classical Electromagnetism

We demonstrate the existence of a complex Hilbert Space with Hermitian operators for calculations in \textit{classical} electromagnetism that parallels the Hilbert Space of quantum mechanics. The axioms of this classical theory are the so-called Dirac-von Neumann axioms, however, with classical potentials in place of the wavefunction and the indeterministic collapse postulate removed. This approach lets us derive a variety of fundamental expressions for electromagnetism using minimal mathematics and a calculation sequence well-known for traditional quantum mechanics. We also demonstrate the existence of the wave commutation relationship $[\hat{x},\hat{k}]=i$, which is a unique classical analogue to the canonical commutator $[\hat{x},\hat{p}]=i\hbar$. The difference between classical and quantum mechanics lies in the presence of $\hbar$. The noncommutativity of observables for a classical theory simply reflects its wavenature. A classical analogue of the Heisenberg Uncertainty Principle is developed for electromagnetic waves, and its implications discussed. Further comparisons between electromagnetism, Koopman-von Neumann-Sudarshan (KvNS) classical mechanics (for point particles), and quantum mechanics are made. Finally, supplementing the analysis presented, we additionally demonstrate an elegant, completely relativistic version of Feynman's proof of Maxwell's equations \citep{Dyson}. Unlike what \citet{Dyson} indicated, there is no need for Galilean relativity for the proof to work. This fits parsimoniously with our usage of classical Lie commutators for electromagnetism.

physics.class-ph↗

arXiv2018

Using UHE Cosmic Rays to Probe the CBR and Test Standard Model Particle Physics

Tipler has shown that if we assume that the particle physics Standard Model and DeWitt-Wheeler quantum gravity (equivalent to Feynman-Weinberg quantum gravity) are a Theory of Everything, then in the very early universe, the Cosmic Background Radiation (CBR) could not have coupled to right handed electrons and quarks. Tipler further showed that if this property of CBR has continued, the Sunyaev-Zel'dovich (SZ) effect would be observed to be too low by a factor of two. WMAP and PLANCK observed this. Tipler showed that this CBR property would also mean the Ultra High Energy Cosmic Rays (UHECR) would propagate a factor of ten further than standard theory predicts, since most of the cross section for pion production when a UHECR hits a CBR photon is due to a quark spin flip, and such a flip cannot occur if a CBR particle cannot couple to right-handed quarks. We show that taking this additional propagation distance into account allows us to identify the sources of 86\% of the UHECR seen by the Pierre Auger Collaboration. We can also identify the sources of 9 of the 11 UHECR seen by the AGASA observatory, and the source of the 320 EeV UHECR seen by the Fly's Eye instrument. We propose observations to test the theory underlying the UHECR identifications, beginning with measuring the redshifts of five galaxies whose apparent visual magnitude we estimate to be about 15, and whose positions we give to within one arcsecond. The particle physics Standard Model identifies the Dark Energy and Dark Matter.

astro-ph.HE↗