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Quaternion Octonion Reformulation of Grand Unified Theories

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Abstract

In this paper, Grand Unified theories are discussed in terms of quaternions and octonions by using the relation between quaternion basis elements with Pauli matrices and Octonions with Gell Mann λ matrices. Connection between the unitary groups of GUTs and the normed division algebra has been established to re-describe the SU(5) gauge group. We have thus described the SU(5) gauge group and its subgroup SU(3) C ×SU(2) L ×U(1) by using quaternion and octonion basis elements. As such the connection between U(1) gauge group and complex number, SU(2) gauge group and quaternions and SU(3) and octonions is established. It is concluded that the division algebra approach to the theory of unification of fundamental interactions as the case of GUTs leads to the consequences towards the new understanding of these theories which incorporate the existence of magnetic monopole and dyon.

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Acknowledgements

Two of us (P.S.B. & O.P.S.N.) are thankful to UNESCO and Third World Academy of Sciences, Trieste (Italy) for providing them UNESCO-TWAS Associateship. The hospitality and research facilities provided by Professor Yue-Liang Wu, Director ITP, in Institute of Theoretical Physics and Kavli Institute of Theoretical Physics at Chinese Academy of Sciences, Beijing (China) under the frame work of TWAS Associate Membership Scheme are also acknowledged.

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Authors and Affiliations

  1. Department of Physics, Kumaun University, S.S.J. Campus, Almora, 263601, (U.K.), India

    Pushpa, P. S. Bisht & O. P. S. Negi

  2. Institute of Theoretical Physics, Chinese Academy of Sciences, Zhong Guan Cun East Street 55, P.O. Box 2735, Beijing, 100190, P.R. China

    P. S. Bisht, Tianjun Li & O. P. S. Negi

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  1. Pushpa
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  2. P. S. Bisht
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  3. Tianjun Li
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  4. O. P. S. Negi
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Correspondence to O. P. S. Negi.

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Pushpa, Bisht, P.S., Li, T. et al. Quaternion Octonion Reformulation of Grand Unified Theories. Int J Theor Phys 51, 3228–3235 (2012). https://doi.org/10.1007/s10773-012-1204-9

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  • DOI: https://doi.org/10.1007/s10773-012-1204-9

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