The time evolution of the Higgs, the Faddeev-Popov ghost fields, and the gauge phase functions of the standard model are analyzed using the ghost Lagrangian density from Chapter 11 of Taylor’s “Gauge Theories of Weak Interactions”. The results assume that the amplitudes of the vector bosons are negligible for homogeneous solutions. With a broken SU(2) × U(1) symmetry, 3 of the 4 Higgs fields have no physical significance independent of the 3 vector bosons W1, W2 and Z. However, with a literal interpretation of the ghost Lagrangian density, the Higgs ghost fields are found to have independent physical significance. It is found that the Higgs, ghosts, and gauge functions are both the occupants and the generators of gratings which can be interpreted as the “potential wells” of mass matrices of an anomaly-free quantum field theory. This implies that the charged and uncharged ghosts of the minimal Higgs sector can be interpreted as preons. One set of consequences of this standard-model-based analysis is that neutrinos are found to have mass and also mass oscillations.
References
[1]
Taylor, J.C. (1976) Gauge Theories of Weak Interactions. Cambridge University Press.
[2]
Weinberg, S. (1967) A Model of Leptons. PhysicalReviewLetters, 19, 1264-1266. https://doi.org/10.1103/physrevlett.19.1264
[3]
Weinberg, S. (1996) The Quantum Theory of Fields. Cambridge University Press. https://doi.org/10.1017/cbo9781139644174
[4]
Peskin, M. and Schroeder, D. (1995) Introduction to Quantum Field Theory. Perseus. https://doi.org/10.1201/9780429503559
[5]
Yang, C.N. and Mills, R. (1954) Conservation of Isotopic Spin and Isotopic Gauge Invariance. Physical Review, 96, 191-195. https://doi.org/10.1103/PhysRev.96.191
[6]
Faddeev, L.D. and Popov, V.N. (1967) Feynman Diagrams for the Yang-Mills Field. PhysicsLettersB, 25, 29-30. https://doi.org/10.1016/0370-2693(67)90067-6
[7]
Feynman, R.P. (1963) Quantum Theory of Gravitation. ActaPhysicaPolonica, 24, 697-722.
[8]
‘tHooft, G. (1971) Renormalization of Massless Yang-Mills Fields. NuclearPhysicsB, 33, 173-199. https://doi.org/10.1016/0550-3213(71)90395-6
[9]
Hooft, G. (1971) Renormalizable Lagrangians for Massive Yang-Mills Fields. NuclearPhysicsB, 35, 167-188. https://doi.org/10.1016/0550-3213(71)90139-8
[10]
Hooft, G. and Veltman, M. (1972) Combinatorics of Gauge Fields. NuclearPhysicsB, 50, 318-353. https://doi.org/10.1016/s0550-3213(72)80021-x
[11]
Lee, B.W. and Zinn-Justin, J. (1972) Spontaneously Broken Gauge Symmetries. I. Preliminaries. PhysicalReviewD, 5, 3121-3137. https://doi.org/10.1103/physrevd.5.3121
[12]
Lee, B.W. and Zinn-Justin, J. (1972) Spontaneously Broken Gauge Symmetries. II. Perturbation Theory and Renormalization. PhysicalReviewD, 5, 3137-3155. https://doi.org/10.1103/physrevd.5.3137
[13]
Lee, B.W. and Zinn-Justin, J. (1972) Spontaneously Broken Gauge Symmetries. III. Equivalence. PhysicalReviewD, 5, 3155-3160. https://doi.org/10.1103/physrevd.5.3155
[14]
Lee, B.W. and Zinn-Justin, J. (1973) Spontaneously Broken Gauge Symmetries. IV. General Gauge Formulation. PhysicalReviewD, 7, 1049-1056. https://doi.org/10.1103/physrevd.7.1049
Kallosh, R.E. and Tyutin, I.V. (1973) The Equivalence Theorem and Gauge Invariance in Renormalizable Theories. Soviet Journal of Nuclear Physics, 17, 98-106.
[17]
Ross, D.A. and Taylor, J.C. (1973) Renormalization of a Unified Theory of Weak and Electromagnetic Interactions. Nuclear Physics B, 51, 125-144. https://doi.org/10.1016/0550-3213(73)90505-1
[18]
Becchi, C., Rouet, A. and Stora, R. (1976) Renormalization of Gauge Theories. AnnalsofPhysics, 98, 287-321. https://doi.org/10.1016/0003-4916(76)90156-1
[19]
Thomson, M. (2013) Modern Particle Physics. Cambridge University Press. https://doi.org/10.1017/cbo9781139525367
[20]
Kane, G. (1993) Modern Elementary Particle Physics. Updated Edition, Perseus, 111-112.
[21]
Rugh, S.E. and Zinkernagel, H. (2002) The Quantum Vacuum and the Cosmological Constant Problem. StudiesinHistoryandPhilosophyofSciencePartB: StudiesinHistoryandPhilosophyofModernPhysics, 33, 663-705. https://doi.org/10.1016/s1355-2198(02)00033-3
[22]
Holmes, R.B. (2025) Derivation and Fits of Fermion Masses from the Higgs Sector. JournalofModernPhysics, 16, 613-626. https://doi.org/10.4236/jmp.2025.164033
[23]
Holmes, R. (2021) A Quantum Field Theory with Permutational Symmetry. 2nd Edition, Lambert Academic Press. https://doi.org/10.5281/zenodo.5047237
[24]
Harari, H. (1979) A Schematic Model of Quarks and Leptons. PhysicsLettersB, 86, 83-86. https://doi.org/10.1016/0370-2693(79)90626-9
[25]
Harari, H. and Seiberg, N. (1982) The Rishon Model. NuclearPhysicsB, 204, 141-167. https://doi.org/10.1016/0550-3213(82)90426-6
[26]
Shupe, M.A. (1979) A Composite Model of Leptons and Quarks. PhysicsLettersB, 86, 87-92. https://doi.org/10.1016/0370-2693(79)90627-0
[27]
D’Souza, I.A. and Kalman, C.S. (1992) Preons: Models of Leptons, Quarks, and Gauge Bosons as Composite Objects. World Scientific. https://doi.org/10.1142/1700
[28]
Finkelstein, R.J. (2015) The SLq(2) Extension of the Standard Model. InternationalJournalofModernPhysicsA, 30, Article ID: 1530037. https://doi.org/10.1142/s0217751x15300379
[29]
Robson, B.A. (2024) The Generation Model of Particle Physics. European Journal of Applied Sciences, 12, 1-17. https://doi.org/10.14738/aivp.123.16922
[30]
Raitio, R. (2018) Supersymmetric Preons and the Standard Model. NuclearPhysicsB, 931, 283-290. https://doi.org/10.1016/j.nuclphysb.2018.04.021
[31]
Fan, X., Myers, T.G., Sukra, B.A.D. and Gabrielse, G. (2023) Measurement of the Electron Magnetic Moment. PhysicalReviewLetters, 130, Article ID: 071801. https://doi.org/10.1103/physrevlett.130.071801
[32]
Shen, Y.R. and Bloembergen, N. (1965) Theory of Stimulated Brillouin and Raman Scattering. PhysicalReview, 137, A1787-A1805. https://doi.org/10.1103/physrev.137.a1787
[33]
Holmes, R. and Flusberg, A. (1988) Rotationally Invariant Theory of Stimulated Raman Scattering. PhysicalReviewA, 37, 1588-1596. https://doi.org/10.1103/physreva.37.1588
[34]
Workman, R.L., Burkert, V.D., Crede, V., Klempt, E., Thoma, U., Tiator, L., et al. (2022) Review of Particle Physics. “Electroweak Model and Constraints on New Physics”. Progress of Theoretical and Experimental Physics, 2022, 083C01. https://doi.org/10.1093/ptep/ptac097
[35]
Workman, R.L., Burkert, V.D., Crede, V., Klempt, E., Thoma, U., Tiator, L., et al. (2022) Review of Particle Physics. “Gauge and Higgs Bosons”. Progress of Theoretical and Experimental Physics, 2022, 083C01. https://doi.org/10.1093/ptep/ptac097
[36]
Sirunyan, A.M., Tumasyan, A., Adam, W., Asilar, E., Bergauer, T., et al. (2017) Search for Light Vector Resonances Decaying to a Quark Pair Produced in Association with a Jet in Proton-Proton Collisions at √s = 13 TeV. CMS PAS EXO-17-001, Figure 7. https://doi.org/10.48550/arXiv.1710.00159
[37]
Leutwyler, H. (1997) Phonons as Goldstone Bosons. Helvetica Physica Acta, 70, 275-286. https://doi.org/10.48550/arXiv.hep-ph/9609466
[38]
Workman, R.L., Burkert, V.D., Crede, V., Klempt, E., Thoma, U., Tiator, L., et al. (2022) Review of Particle Physics. “Neutrino Mixing”. Progress of Theoretical and Experimental Physics, 2022, 083C01. https://doi.org/10.1093/ptep/ptac097
[39]
Holmes, R.B. (2024) Method for Fitting and Deriving the CKM and PMNS Matrices from Underlying Wavefunctions. JournalofModernPhysics, 15, 2407-2421. https://doi.org/10.4236/jmp.2024.1513099
[40]
Van der Houwen, P.J. and Sommeijer, B.P. (1989) Diagonally Implicit Runge-Kutta-Nyström Methods for Oscillatory Problems. SIAMJournalonNumericalAnalysis, 26, 414-429. https://doi.org/10.1137/0726023
