About Lorentz Invariance and Gauge Symmetries: An Alternative Approach to Relativistic Gravitation

Author(s)
Richard Bonneville

ABSTRACT

An alternative presentation of a relativistic theory of gravitation, equivalent to general relativity, is given. It is based upon the restriction of the Lorentz invariance of special relativity from a global invariance to a local one. The resulting expressions appear rather simple as we consider the transformations of a local set of pseudo-orthonormal coordinates and not the geometry of a 4-dimension hyper-surface described by a set of curvilinear coordinates. This is the major difference with the usual presentations of general relativity but that difference is purely formal. The usual approach is most adequate for describing the universe on a large scale in astrophysics and cosmology. The approach of this paper, derived from particle physics and focused on local reference frames, underlines the formal similarity between gravitation and the other interactions inasmuch as they are associated to the restriction of gauge symmetries from a global invariance to a local one.

An alternative presentation of a relativistic theory of gravitation, equivalent to general relativity, is given. It is based upon the restriction of the Lorentz invariance of special relativity from a global invariance to a local one. The resulting expressions appear rather simple as we consider the transformations of a local set of pseudo-orthonormal coordinates and not the geometry of a 4-dimension hyper-surface described by a set of curvilinear coordinates. This is the major difference with the usual presentations of general relativity but that difference is purely formal. The usual approach is most adequate for describing the universe on a large scale in astrophysics and cosmology. The approach of this paper, derived from particle physics and focused on local reference frames, underlines the formal similarity between gravitation and the other interactions inasmuch as they are associated to the restriction of gauge symmetries from a global invariance to a local one.

Cite this paper

Bonneville, R. (2014) About Lorentz Invariance and Gauge Symmetries: An Alternative Approach to Relativistic Gravitation.*Natural Science*, **6**, 1244-1252. doi: 10.4236/ns.2014.616113.

Bonneville, R. (2014) About Lorentz Invariance and Gauge Symmetries: An Alternative Approach to Relativistic Gravitation.

References

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http://dx.doi.org/10.1103/RevModPhys.21.497

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http://dx.doi.org/10.1098/rsta.1998.0178

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http://dx.doi.org/10.1142/p781

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[1] Landau, L. and Lifshitz, E. (1966) Field Theory. Mir Editions, Moscow.

[2] Weinberg, S. (1972) Gravitation and Cosmology. John Wiley, Hoboken.

[3] Lanczos, C. (1949) Lagrangian Multiplier and Riemannian Spaces. Reviews of Modern Physics, 21, 497.

http://dx.doi.org/10.1103/RevModPhys.21.497

[4] Takeno, H. (1964) On the Spin Tensor of Lanczos. Tensor, 15, 103.

[5] Ivanenko, D. and Sardanashvili, G. (1983) The Gauge Treatment of Gravity. Physics Report, 94, 1-45.

[6] Lasenby, A., Doran, C. and Gull, S. (1998) Gauge Theories and Geometric Algebra. Philosophical Transactions of the Royal Society, A356, 487-582.

http://dx.doi.org/10.1098/rsta.1998.0178

[7] Blagojevic, M. and Hehl, F.W. (2013) Gauge Theories of Gravitation: A Reader with Commentaries. World Scientific, Singapore.

http://dx.doi.org/10.1142/p781

[8] Becchi, C. (1997) Introduction to Gauge Theories. arXiv:hep-ph/9705211v1

[9] Mann, R. (2010) An Introduction to Particle Physics and the Standard Model. CRC Press, Boca Raton.

[10] Roll, P.G., Krotkov, R. and Dicke, R.H. (1964) The Equivalence of Inertial and Passive Gravitational Mass. Annals of Physics, 26, 442-517.