### Abstract

We present and discuss two different possibilities to construct position space version for Magueijo-Smolin (MS) doubly special relativity proposal. The first possibility is to start from ordinary special relativity and then to define conserved momentum in special way. It generates MS invariant as well as nonlinear MS transformations on the momentum space, leading to consistent picture for one-particle sector of the theory. The second possibility is based on the following observation. Besides the nonlinear MS transformations, the MS energy-momentum relation is invariant also under some inhomogeneous linear transformations. The latter are induced starting from linearly realized Lorentz group in five-dimensional position space. Particle dynamics and kinematics are formulated starting from the corresponding five-dimensional interval. There is no problem of total momentum in the theory. The formulation admits two observer independent scales, the speed of light, c, and k with dimension of velocity. We speculate on different possibilities to relate k with fundamental constants. In particular, expression of k in terms of vacuum energy suggests emergence of (minimum) quantum of mass.

Original language | English |
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Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 71 |

Issue number | 12 |

DOIs | |

Publication status | Published - 15 Jun 2005 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Nuclear and High Energy Physics
- Mathematical Physics

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*71*(12). https://doi.org/10.1103/PhysRevD.71.123515

**Position space versions of the Magueijo-Smolin doubly special relativity proposal and the problem of total momentum.** / Deriglazov, A. A.; Rizzuti, B. F.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 71, no. 12. https://doi.org/10.1103/PhysRevD.71.123515

}

TY - JOUR

T1 - Position space versions of the Magueijo-Smolin doubly special relativity proposal and the problem of total momentum

AU - Deriglazov, A. A.

AU - Rizzuti, B. F.

PY - 2005/6/15

Y1 - 2005/6/15

N2 - We present and discuss two different possibilities to construct position space version for Magueijo-Smolin (MS) doubly special relativity proposal. The first possibility is to start from ordinary special relativity and then to define conserved momentum in special way. It generates MS invariant as well as nonlinear MS transformations on the momentum space, leading to consistent picture for one-particle sector of the theory. The second possibility is based on the following observation. Besides the nonlinear MS transformations, the MS energy-momentum relation is invariant also under some inhomogeneous linear transformations. The latter are induced starting from linearly realized Lorentz group in five-dimensional position space. Particle dynamics and kinematics are formulated starting from the corresponding five-dimensional interval. There is no problem of total momentum in the theory. The formulation admits two observer independent scales, the speed of light, c, and k with dimension of velocity. We speculate on different possibilities to relate k with fundamental constants. In particular, expression of k in terms of vacuum energy suggests emergence of (minimum) quantum of mass.

AB - We present and discuss two different possibilities to construct position space version for Magueijo-Smolin (MS) doubly special relativity proposal. The first possibility is to start from ordinary special relativity and then to define conserved momentum in special way. It generates MS invariant as well as nonlinear MS transformations on the momentum space, leading to consistent picture for one-particle sector of the theory. The second possibility is based on the following observation. Besides the nonlinear MS transformations, the MS energy-momentum relation is invariant also under some inhomogeneous linear transformations. The latter are induced starting from linearly realized Lorentz group in five-dimensional position space. Particle dynamics and kinematics are formulated starting from the corresponding five-dimensional interval. There is no problem of total momentum in the theory. The formulation admits two observer independent scales, the speed of light, c, and k with dimension of velocity. We speculate on different possibilities to relate k with fundamental constants. In particular, expression of k in terms of vacuum energy suggests emergence of (minimum) quantum of mass.

UR - http://www.scopus.com/inward/record.url?scp=33644506188&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevD.71.123515

DO - 10.1103/PhysRevD.71.123515

M3 - Article

AN - SCOPUS:33644506188

VL - 71

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 12

ER -