The concept of density in quantum theories of an elementary particle is discussed. Density is, at least implicitly, recognized in contemporary textbooks on quantum field theories, where the Noether theorem is utilized for a derivation of a conserved 4-current j,μμ=0 and a conserved energy-momentum tensor T,νμν=0. Here the component j0 is the particle’s density and the components Tμ0 are the energy-momentum density. The novelty of this work is the analysis of the particle’s density and the energy-momentum density of these expressions and their application to several specific quantum theories. As of today, these tasks have not been adequately accomplished in contemporary textbooks. The results show that the first-order Dirac theory of an elementary massive spin-1/2 particle yields consistent results. In contrast, second- order quantum theories, such as the Klein-Gordon theory, the electroweak theory of W±, Z the particles, and the Higgs boson theory are inherently wrong.
ATLAS Collaboration (2012) Determination of the Strange Quark Density of the Proton from ATLAS Measurements of the W→lν and Z→ll Cross Sections. Physical Review Letters, 109, Article ID: 012001. https://arxiv.org/abs/1203.4051
Halzen, F., Martin, A.D. and Mitra, N. (1984) Quarks and Leptons: An Introductory Course in Modern Particle Physics. American Journal of Physics, 53, Article No. 287.
https://doi.org/10.1119/1.14146
Comay, E. (2021) Broken Physics: The Theoretical Errors and Experimental Failures of the Standard Model of Particle Physics. Booksmango Incorporated, Tel Aviv.
Dirac, P.A.M. (1928) The Quantum Theory of the Electron. Proceedings of the Royal Society of London. Series A, 117, 610-624. https://doi.org/10.1098/rspa.1928.0023
Darwin, C.G. (1928) The Wave Equations of the Electron. Proceedings of the Royal Society of London. Series A, 118, 654-680. https://doi.org/10.1098/rspa.1928.0076
ATLAS Collaboration, et al. (2012) Measurement of the WW Cross Section in √s=7TeV pp Collisions with the ATLAS Detector and Limits on Anomalous Gauge Couplings. Physics Letters B, 712, 289-308.
https://doi.org/10.1016/j.physletb.2012.05.003
Abazov, V.M., et al. (2012) Limits on Anomalous Trilinear Gauge Boson Couplings from WW, WZ and Wγ Production in pp Collisions at √s=1.96TeV. Physics Letters B, 718, 451-459. https://doi.org/10.1016/j.physletb.2012.10.062