The paper emphasizes the significance of density of an elementary massive quantum particle. In quantum field theory, a quantum function of an elementary particle takes the form of Ψ(r,t). This kind of function is used for putting the inner product of the corresponding Hilbert space in the form of an appropriate integral, and the inner product of a function with itself depends on the particle’s density. Density also affects the multi-particle Fock space, because this space relies on single-particle Hilbert space. This work shows a new reason where a coherent theoretical expression for the density of an elementary particle is required: A theoretical description of experiments that measure the transition of unstable states and the decay of an elementary quantum particle. This new aspect of density strengthens its meaning in quantum theories. The usefulness of this outcome is shown in its application to the decay of the muon and the electroweak’s W±,Z particles. It turns out that the Dirac theory provides a consistent description of the muon decay. In contrast, the electroweak theory fails to explain the decay of the W±,Z particles.
References
[1]
Schweber, S.S. (1964) An Introduction to Relativistic Quantum Field Theory. Harper & Row, New York.
[2]
Itzykson, C. and Zuber, J.B. (1980) Quantum Field Theory. McGraw-Hill, New York.
[3]
Sterman, G. (1993) An Introduction to Quantum Field Theory. Cambridge University Press, Cambridge, 518. https://doi.org/10.1017/CBO9780511622618
[4]
Landau, L.D. and Lifshitz, E.M. (2005) The Classical Theory of Fields. Elsevier, Amsterdam.
[5]
Rohrlich, F. (2007) Classical Charged Particles. 3rd Edition, World Scientific, New Jersey. https://doi.org/10.1142/6220
[6]
Dirac, P.A.M. (1958) The Principles of Quantum Mechanics. Oxford University Press, London.
[7]
Schiff, L.I. (1955) Quantum Mechanics. McGraw-Hill, New York.
[8]
Weinberg, S. (1995) The Quantum Theory of Fields. Vol. I, Cambridge University Press, Cambridge.
[9]
Halzen, F. and Martin, A.D. (1984) Quarks and Leptons, An Introductory Course in Modern Particle Physics. John Wiley, New York.
[10]
Bjorken, J.D. and Drell, S.D. (1965) Relativistic Quantum Fields. McGraw-Hill, New York.
[11]
Peskin, M.E. and Schroeder, D.V. (1995) An Introduction to Quantum Field Theory. Addison-Wesley, Reading Mass.
[12]
Bjorken, J.D. and Drell, S.D. (1964) Relativistic Quantum Mechanics. McGraw-Hill, New York.
[13]
Messiah, A. (1967) Quantum Mechanics. Vol. 1, North Holland, Amsterdam.
[14]
Particle Data Group (2020) Review of Particle Physics. Progress of Theoretical and Experimental Physics, 2020, Article ID: 083C01.
https://doi.org/10.1093/ptep/ptaa104
[15]
Weinberg, S. (1996) The Quantum Theory of Fields. Vol. II, Cambridge University Press, Cambridge.
[16]
Hagiwara, K., Peccei, R.D., Zeppenfeld, D. and Hikaso, K. (1987) Probing the Weak Boson Sector in ee-→WW-. Nuclear Physics B, 282, 253-307.
[17]
Hagiwara, K., Woodside, J. and Zeppenfeld, D. (1990) Measuring the WWZ Coupling at the Fermilab Tevatron. Physical Review D, 41, 2113-2119.
[18]
D0 Collaboration (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
[19]
ATLAS Collaboration (2012) Measurement of the WW Cross Section in sqrt(s) =7 TeV 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
[20]
Dirac, P.A.M. (1928) The Quantum Theory of the Electron. Proceedings of the Royal Society A, 117, 610-324. https://doi.org/10.1098/rspa.1928.0023
[21]
Goldstein, H., Poole, C. and Safko, J. (2002) Classical Mechanics. 3rd Edition, Addison Wesley, San Francisco.