JMP  Vol.4 No.8 A , August 2013
Conservation of Gravitational Energy Momentum and Renormalizable Quantum Theory of Gravitation
ABSTRACT

Viewing gravitational energy-momentum as equal by observation, but different in essence from inertial energymomentum naturally leads to the gauge theory of volume-preserving diffeomorphisms of an inner Minkowski space which can describe gravitation at the classical level. This theory is quantized in the path integral formalism starting with a non-covariant Hamiltonian formulation with unconstrained canonical field variables and a manifestly positive Hamiltonian. The relevant path integral measure and weight are then brought into a Lorentz- and gauge-covariant form allowing to express correlation functions—applying the De Witt-Faddeev-Popov approach—in any meaningful gauge. Next the Feynman rules are developed and the quantum effective action at one loop in a background field approach is renormalized which results in an asymptotically free theory without presence of other fields and in a theory without asymptotic freedom including the Standard Model (SM) fields. Finally the BRST apparatus is developed as preparation for the renormalizability proof to all orders and a sketch of this proof is given.


Cite this paper
C. Wiesendanger, "Conservation of Gravitational Energy Momentum and Renormalizable Quantum Theory of Gravitation," Journal of Modern Physics, Vol. 4 No. 8, 2013, pp. 133-152. doi: 10.4236/jmp.2013.48A013.
References
[1]   C. Wiesendanger, “I—Conservation of Gravitational Energy Momentum and Inner Diffeomorphism Group Gauge Invariance,” arXiv:1102.5486 [math-ph].

[2]   C. Wiesendanger, Physical Review D, Vol. 80, 2009, Article ID: 025018. doi:10.1103/PhysRevD.80.025018

[3]   C. Wiesendanger, Physical Review D, Vol. 80, 2009, Article ID: 025019. doi:10.1103/PhysRevD.80.025019

[4]   C. Wiesendanger, “II—Conservation of Gravitational Energy Momentum and Poincaré-Covariant Classical Theory of Gravitation,” arXiv:1103.0349 [math-ph].

[5]   S. Weinberg, “The Quantum Theory of Fields I,” Cambridge University Press, Cambridge, 1995. doi:10.1017/CBO9781139644167

[6]   S. Weinberg, “The Quantum Theory of Fields II,” Cambridge University Press, Cambridge, 1996. doi:10.1017/CBO9781139644174

[7]   C. Wiesendanger, Classical and Quantum Gravity, Vol. 30, 2013, Article ID: 075024. doi:10.1088/0264-9381/30/7/075024

[8]   J. Zinn-Justin, “Quantum Field Theory and Critical Phenomena,” Oxford University Press, Oxford, 1993.

[9]   C. Rovelli, “Quantum Gravity,” Cambridge University Press, Cambridge, 2004.

[10]   C. Kiefer, “Quantum Gravity,” Oxford University Press, Oxford, 2007. doi:10.1093/acprof:oso/9780199212521.001.0001

[11]   C. Itzykson and J.-B. Zuber, “Quantum Field Theory,” McGraw-Hill, Singapore City, 1985.

[12]   L. O’Raifeartaigh, “Group Structure of Gauge Theories,” Cambridge University Press, Cambridge, 1986.

[13]   S. Pokorski, “Gauge Field Theories,” Cambridge University Press, Cambridge, 1987.

[14]   T.-P. Cheng and L.-F. Li, “Gauge Theory of Elementary Particle Physics,” Oxford University Press, Oxford, 1984.

 
 
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