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Massless Fields on Dirac Six-Cone and De Sitter Ambient Space

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Abstract

We have proceeded to obtain manifestly conformally invariant (CI) equations for thinkable graviton fields in de Sitter (dS) space-time. The tensor fields are originally considered in 4+2 dimensional conformal space or Dirac’s six-cone and then project to dS space which is embedded in 4+1 dimensional ambient space. It will be shown that, by projecting these tensor fields there exists a correspondence between the massless fields on the cone and dS space. Also, we have shown that for rank-2 tensor field the divergenceless condition, which is necessary when we attempt to correspond the tensor field with the unitary irreducible representations (UIRs) of dS group, is not really a condition at all, it is a consequence of ambient space property. Due to the combined occurrences of corresponding fields and divergenceless property, the appropriate CI field equations have obtained in a fairly simple way and without imposing any extra condition.

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Acknowledgments

I would like to thank M.V. Takook, I learn a lot from him. I am really indebted to him. I would also like to acknowledge and thank M.R. Tanhayi for some related discussions.

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Authors and Affiliations

  1. Department of Physics, Razi University, Kermanshah, Iran

    M. Enayati & S. Khani

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  1. M. Enayati
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  2. S. Khani
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Correspondence to M. Enayati.

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Enayati, M., Khani, S. Massless Fields on Dirac Six-Cone and De Sitter Ambient Space. Int J Theor Phys 55, 4513–4520 (2016). https://doi.org/10.1007/s10773-016-3074-z

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  • DOI: https://doi.org/10.1007/s10773-016-3074-z

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