Abstract
The consequences of a generalized Dirac equation are discussed for the energy levels of the hydrogen atom. Apart from the usual generalizations of the Dirac equation by adding new interaction terms, we generalize the anticommutation rule of the Dirac matrices, which leads to spin-dependent propagation properties. Such a theory can be looked at as a model theory for testing Lorentz invariance or as an outcome of pregeometric dynamical induction schemes for space-time structure.
For special examples of generalized Dirac matrices including perturbation terms with respect to the SRT Dirac matrices, we derive the energy level of the hydrogen atom and find a hyperfine splitting due to these perturbations. A comparison of this additional splitting with Lamb shift measurements gives us upper limits for possible perturbations, which turn out to be of measurable magnitude. Spin precession experiments give much more restrictive limits. So, it turns out that the hydrogen atom is not such a sensitive indicator for the Lorentz invariance as widely believed.
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References
C. M. Will,Theory and Experiment in Gravitational Physics (Cambridge University Press, Cambridge, 1981).
A. P. Lightman and D. L. Lee,Phys. Rev. D 8, 364 (1973).
U. Bleyer and D.-E. Liebscher, “Quantum mechanical consequences of a pregeometry,” in M. A. Markov, V. M. Frolov, and V. A. Berezin, editors,Proceedings of the IVth Seminar on Quantum Gravity, Moscow 1987 (World Scientific, Singapore, 1988), p. 282.
H.-J. Treder and U. Bleyer, “Quantum gravodynamics and pregeometry,” in L. Kostro, A. Posiewnik, Jaroslaw Pykacz, and M. Zukowski, editors,Proceedings of the Conference on Fundamental Problems of Quantum Theory, Gdansk 1987 (World Scientific, Singapore, 1988), p. 832.
U. Bleyer,Dissertation B (Akademie der Wissenschaften, Berlin, 1988).
U. Bleyer,Ann. Phys. (Leipzig) 48, 489 (1991).
A. Zeilinger and H. Rauch, “Neutron interferometry: A status report,” Technical Report, Autominstitüt der Österreichischen Universitäten, Wien, 1987.
S. L. Schwebel,Int. J. Theor. Phys. 17, 931 (1978).
H. A. Bethe and E. E. Salpeter,Quantum Mechanics of One- and Two-Electron Atoms (Springer, Berlin, 1957).
B. E. Lautrup, A. Peterman, and E. de Rafael,Phys. Rep. C 3, 205 (1972).
U. Bleyer, in R. Wahsner, editor,Gravitation und Kosmos (Akademie der Wissenschaften, Berlin, 1988), Chap. 8.
P. R. Phillips and D. Woolum,Nuovo Cimento B 64, 28 (1969).
J. Audretsch, U. Bleyer, and C. Lämmerzahl,Phys. Rev. A 47, 4632 (1993).
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Bleyer, U. Energy levels of the hydrogen atom due to a generalized Dirac equation. Found Phys 23, 1025–1048 (1993). https://doi.org/10.1007/BF00736014
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DOI: https://doi.org/10.1007/BF00736014