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Conservation of Gravitational Energy-Momentum and Inner Diffeomorphism Group Gauge Invariance

DOI: 10.4236/jmp.2013.48A006, PP. 37-47

Keywords: Gauge Field Theory, Volume-Preserving Diffeomorphism Group, Inner Minkowski Space

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Abstract:

Viewing gravitational energy momentum \"\" as equal by observation, but different in essence from inertial energy-momentum \"\" requires two different symmetries to account for their independent conservations—spacetime and inner translation invariance. Gauging the latter a generalization of non-Abelian gauge theories of compact Lie groups is developed resulting in the gauge theory of the non-compact group of volume-preserving diffeomorphisms of an inner Minkowski space M4. As usual the gauging requires the introduction of a covariant derivative, a gauge field and a field strength operator. An invariant and minimal gauge field Lagrangian is derived. The classical field dynamics and the conservation laws for the new gauge theory are developed. Finally, the theorys Hamiltonian in the axial gauge is expressed by two times six unconstrained independent canonical variables obeying the usual Poisson brackets and the positivity of the Hamiltonian is related to a condition on the support of the gauge fields.

References

[1]  L. O’Raifeartaigh, “Group Structure of Gauge Theories,” Cambridge University Press, Cambridge, 1986.
[2]  S. Weinberg, “The Quantum Theory of Fields I,” Cambridge University Press, Cambridge, 1995. doi:10.1017/CBO9781139644167
[3]  S. Weinberg, “The Quantum Theory of Fields II,” Cambridge University Press, Cambridge, 1996. doi:10.1017/CBO9781139644174
[4]  C. Wiesendanger, Classical and Quantum Gravity, Vol. 12, 1995, p. 585; C. Wiesendanger, Classical and Quantum Gravity, Vol. 13, 1996, p. 681 and references therein. doi:10.1088/0264-9381/13/4/008
[5]  C. Rovelli, “Quantum Gravity,” Cambridge University Press, Cambridge, 2004.
[6]  C. Kiefer, “Quantum Gravity,” Oxford University Press, Oxford, 2007. doi:10.1093/acprof:oso/9780199212521.001.0001
[7]  C. Wiesendanger, Physical Review D, Vol. 80, 2009, Article ID: 025018. doi:10.1103/PhysRevD.80.025018
[8]  C. Wiesendanger, Physical Review D, Vol. 80, 2009, Article ID: 025019. doi:10.1103/PhysRevD.80.025019
[9]  C. Wiesendanger, “II—Conservation of Gravitational Energy Momentum and Poincaré-Covariant Classical Theory of Gravitation,” arXiv:1103.0349 [math-ph].
[10]  C. Wiesendanger, “III—Conservation of Gravitational Energy Momentum and Renormalizable Quantum Theory of Gravitation,” arXiv:1103.1012 [math-ph].

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