Back
 JMP  Vol.5 No.10 , June 2014
A Renormalizable Theory of Quantum Gravity: Renormalization Proof of the Gauge Theory of Volume Preserving Diffeomorphisms
Christian Wiesendanger*
Show more
Abstract: Inertial and gravitational mass or energy momentum need not be the same for virtual quantum states. Separating their roles naturally leads to the gauge theory of volume-preserving diffeomorphisms of an inner four-dimensional space. The gauge-fixed action and the path integral measure occurring in the generating functional for the quantum Green functions of the theory are shown to obey a BRST-type symmetry. The related Zinn-Justin-type equation restricting the corresponding quantum effective action is established. This equation limits the infinite parts of the quantum effective action to have the same form as the gauge-fixed Lagrangian of the theory proving its spacetime renormalizability. The inner space integrals occurring in the quantum effective action which are divergent due to the gauge group’s infinite volume are shown to be regularizable in a way consistent with the symmetries of the theory demonstrating as a byproduct that viable quantum gauge field theories are not limited to finite-dimensional compact gauge groups as is commonly assumed.
Keywords: Renormalization Proof of Gauge Field Theory of Volume-Preserving Diffeomorphisms
Cite this paper: Wiesendanger, C. (2014) A Renormalizable Theory of Quantum Gravity: Renormalization Proof of the Gauge Theory of Volume Preserving Diffeomorphisms. Journal of Modern Physics, 5, 959-983. doi: 10.4236/jmp.2014.510099.
References

[1]   Rovelli, C. (2004) Quantum Gravity. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/CBO9780511755804

[2]   Kiefer, C. (2007) Quantum Gravity. Oxford University Press, Oxford.
http://dx.doi.org/10.1093/acprof:oso/9780199212521.001.0001

[3]   Weinberg, S. (1995) The Quantum Theory of Fields I. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/CBO9781139644167

[4]   Weinberg, S. (1996) The Quantum Theory of Fields II. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/CBO9781139644174

[5]   Itzykson, C. and Zuber, J.-B. (1985) Quantum Field Theory. McGraw-Hill, Singapore.

[6]   O’Raifeartaigh, L. (1986) Group Structure of Gauge Theories. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/CBO9780511564031

[7]   Pokorski, S. (1987) Gauge Field Theories. Cambridge University Press, Cambridge.

[8]   Cheng, T.-P. and Li, L.-F. (1984) Gauge Theory of Elementary Particle Physics. Oxford University Press, Oxford.

[9]   Weinberg, S. (1972) Gravitation and Cosmology. John Wiley & Sons, New York.

[10]   Landau, L.D. and Lifschitz, E.M. (1981) Lehrbuch der Theoretischen Physik II: Klassische Feldtheorie. Akademie-Verlag, Berlin.

[11]   Will, C.M. (1993) Theory and Experiment in Gravitational Physics. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/CBO9780511564246

[12]   Wiesendanger, C. (2013) Journal of Modern Physics, 4, 37. arXiv:1102.5486 [math-ph]
http://dx.doi.org/10.4236/jmp.2013.48A006

[13]   Wiesendanger, C. (2013) Journal of Modern Physics, 4, 133. arXiv:1103.1012 [math-ph]

[14]   Wiesendanger, C. (2013) Classical and Quantum Gravity, 30, 075024. arXiv:1203.0715 [math-ph]
http://dx.doi.org/10.1088/0264-9381/30/7/075024

[15]   Zinn-Justin, J. (1993) Quantum Field Theory and Critical Phenomena. Oxford University Press, Oxford.

[16]   Wiesendanger, C. (2013) General Relativity as the Classical Limit of the Renormalizable Gauge Theory of Volume Preserving Dieomorphisms. arXiv:1308.2385 [math-ph]

[17]   Weinberg, S. (2008) Cosmology. Oxford University Press, Oxford.

 
 
Top