Diophantine Quantization: Application of the Methods of Algebraic Number Theory to the Theory of Elementary Particles

Robert L. Pease

doi:10.1103/PhysRevD.2.1069

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Diophantine Quantization: Application of the Methods of Algebraic Number Theory to the Theory of Elementary Particles

Robert L. Pease

Department of Physics, State University College, New Paltz, New York 12561

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Phys. Rev. D 2, 1069 – Published 15 September, 1970

DOI: https://doi.org/10.1103/PhysRevD.2.1069

Abstract

The Gell-Mann—Okubo broken- $SU (3)$ meson mass formula is treated as a quadratic Diophantine equation and solved in integers. The relative masses of $π$ , $η$ , $K$ , many known $K^{*}$ , and the probable lowest $L$ may be predicted unambiguously. The requirement of least-integer solutions mandates a unit mass of 70 MeV ( $137 m_{e} c^{2}$ ). Connections between rest masses and angular momenta can be made, and there is evidence of a general linear group.

References (6)

S. Okubo, Progr. Theoret. Phys. (Kyoto) 27, 949 (1962) M. Gell-Mann, California Institute of Technology Report No. CTSL-20, 1961 [unpublished but reprinted (as is Okubo's paper) in M. Gell-Mann and Y. Ne'eman, The Eightfold Way (Benjamin, New York, 1964)]
R. D. Carmichael, Diophantine Analysis (Wiley, New York, 1915; reprinted by Dover, New York, 1959) G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 4th ed. (Oxford U. P., Oxford, England, 1960)
A. Barbaro-Galtieri et al., Rev. Mod. Phys. 42, 87 (1970)
Y. Nambu, Progr. Theoret. Phys. (Kyoto) 7, 595 (1952)
S. Coleman and S. L. Glashow, Phys. Rev. Letters 6, 423 (1961)
W. Heisenberg, Z. Physik 32, 20 (1938)

[c1] S. Okubo, Progr. Theoret. Phys. (Kyoto) 27, 949 (1962) M. Gell-Mann, California Institute of Technology Report No. CTSL-20, 1961 [unpublished but reprinted (as is Okubo's paper) in M. Gell-Mann and Y. Ne'eman, The Eightfold Way (Benjamin, New York, 1964)]

[c2] R. D. Carmichael, Diophantine Analysis (Wiley, New York, 1915; reprinted by Dover, New York, 1959) G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 4th ed. (Oxford U. P., Oxford, England, 1960)

[c3] A. Barbaro-Galtieri et al., Rev. Mod. Phys. 42, 87 (1970)

[c4] Y. Nambu, Progr. Theoret. Phys. (Kyoto) 7, 595 (1952)

[c5] S. Coleman and S. L. Glashow, Phys. Rev. Letters 6, 423 (1961)

[c6] W. Heisenberg, Z. Physik 32, 20 (1938)

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Diophantine Quantization: Application of the Methods of Algebraic Number Theory to the Theory of Elementary Particles

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