Scattering Cross-Sections in Quantum Gravity—The Case of Matter-Matter Scattering
Author(s)
Christian Wiesendanger*
ABSTRACT
Viewing gravitational energy-momentum PGμ as equal by observation, but different in essence from inertial energy-momentum PIμ naturally leads to the gauge theory of volume-preserving diffeomorphisms of a four-dimensional inner space. To analyse scattering in this theory, the gauge field is coupled to two Dirac fields with different masses. Based on a generalized LSZ reduction formula the S-matrix element for scattering of two Dirac particles in the gravitational limit and the corresponding scattering cross-section are calculated to leading order in perturbation theory. Taking the non-relativistic limit for one of the initial particles in the rest frame of the other the Rutherford-like cross-section of a non-relativistic particle scattering off an infinitely heavy scatterer calculated quantum mechanically in Newtonian gravity is recovered. This provides a non-trivial test of the gauge field theory of volume-preserving diffeomorphisms as a quantum theory of gravity.
Viewing gravitational energy-momentum PGμ as equal by observation, but different in essence from inertial energy-momentum PIμ naturally leads to the gauge theory of volume-preserving diffeomorphisms of a four-dimensional inner space. To analyse scattering in this theory, the gauge field is coupled to two Dirac fields with different masses. Based on a generalized LSZ reduction formula the S-matrix element for scattering of two Dirac particles in the gravitational limit and the corresponding scattering cross-section are calculated to leading order in perturbation theory. Taking the non-relativistic limit for one of the initial particles in the rest frame of the other the Rutherford-like cross-section of a non-relativistic particle scattering off an infinitely heavy scatterer calculated quantum mechanically in Newtonian gravity is recovered. This provides a non-trivial test of the gauge field theory of volume-preserving diffeomorphisms as a quantum theory of gravity.
KEYWORDS
Renormalizable Quantum Gravity, Scattering Cross-Sections in Quantum Gravity, Gauge Theory of Volume-Preserving Diffeomorphisms
Renormalizable Quantum Gravity, Scattering Cross-Sections in Quantum Gravity, Gauge Theory of Volume-Preserving Diffeomorphisms
Cite this paper
Wiesendanger, C. (2015) Scattering Cross-Sections in Quantum Gravity—The Case of Matter-Matter Scattering. Journal of Modern Physics, 6, 273-282. doi: 10.4236/jmp.2015.63032.
Wiesendanger, C. (2015) Scattering Cross-Sections in Quantum Gravity—The Case of Matter-Matter Scattering. Journal of Modern Physics, 6, 273-282. doi: 10.4236/jmp.2015.63032.
References
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http://dx.doi.org/10.4236/jmp.2013.48A006 [2] Wiesendanger, C. (2013) Journal of Modern Physics, 4, 133.
http://dx.doi.org/10.4236/jmp.2013.48A013 [3] Wiesendanger, C. (2014) Journal of Modern Physics, 5, 959.
http://dx.doi.org/10.4236/jmp.2014.510099 [4] Wiesendanger, C. (2013) Classical and Quantum Gravity, 30, Article ID: 075024.
http://dx.doi.org/10.1088/0264-9381/30/7/075024 [5] Wiesendanger, C. (2014) Journal of Modern Physics, 5, 948.
http://dx.doi.org/10.4236/jmp.2014.510098 [6] O’Raifeartaigh, L. (1986) Group Structure of Gauge Theories. Cambridge University Press, Cambridge. [7] Itzykson, C. and Zuber, J.-B. (1985) Quantum Field Theory. McGraw-Hill, Singapore. [8] Bjorken, J.D. and Drell, S.D. (1964) Relativistic Quantum Mechanics. Mc Graw-Hill, New York. [9] Schiff, L.I. (1968) Quantum Mechanics. McGraw-Hill, Singapore.
[1] Wiesendanger, C. (2013) Journal of Modern Physics, 4, 37.
http://dx.doi.org/10.4236/jmp.2013.48A006 [2] Wiesendanger, C. (2013) Journal of Modern Physics, 4, 133.
http://dx.doi.org/10.4236/jmp.2013.48A013 [3] Wiesendanger, C. (2014) Journal of Modern Physics, 5, 959.
http://dx.doi.org/10.4236/jmp.2014.510099 [4] Wiesendanger, C. (2013) Classical and Quantum Gravity, 30, Article ID: 075024.
http://dx.doi.org/10.1088/0264-9381/30/7/075024 [5] Wiesendanger, C. (2014) Journal of Modern Physics, 5, 948.
http://dx.doi.org/10.4236/jmp.2014.510098 [6] O’Raifeartaigh, L. (1986) Group Structure of Gauge Theories. Cambridge University Press, Cambridge. [7] Itzykson, C. and Zuber, J.-B. (1985) Quantum Field Theory. McGraw-Hill, Singapore. [8] Bjorken, J.D. and Drell, S.D. (1964) Relativistic Quantum Mechanics. Mc Graw-Hill, New York. [9] Schiff, L.I. (1968) Quantum Mechanics. McGraw-Hill, Singapore.