Selected Publications: • "Signatures of Noncommutative Geometry in Muon
Decay for Nonsymmetric Gravity," D. Singh,. N. Mobed, and P.-P. Ouimet, Found.
Dr. Dinesh Singh
I have a diverse range of research interests that concern the intrinsic nature of gravitation, both at the classical level as described by Einstein's theory of general relativity, and at the quantum mechanical level, which is still an unsolved problem after several decades of effort. It seems that the biggest challenge for gravitation research today is to attain reliable observational information about gravitational fields at both the quantum and classical levels of length resolution. This is a prerequisite towards a datadriven search for a satisfactory theory of quantum gravity. Therefore, my research interests focus on topics that do not appear far removed from experimental verification in one form or another within a reasonable time frame. They can be identified by the following categories.
Quantum Spin Interactions in Curved Space-Time One of my long-term interests concerns the spin properties of quantum mechanical systems as probes of space-time curvature, with the potential to attain useful observational information at the perceived boundary layer between classical and quantum aspects of gravity, which may become realized by experiments involving circular storage rings, particle interferometers, and other devices. Selected Publications:
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"Signatures of Noncommutative Geometry in Muon Decay for Nonsymmetric Gravity," D. Singh, N. Mobed, and P.-P. Ouimet, Found. Phys. 40 (2010) 1789-1799 -- 11 pages (arXiv:0901.4308 [gr-qc])
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"Breakdown of Casimir Invariance in Curved Space-Time," D. Singh and N. Mobed, Ann. Phys. 522 (2010) 555-573 -- 18 pages (arXiv:0902.0629 [hep-th])
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"Is There an Observable Limit to Lorentz Invariance at the Compton Wavelength Scale?" D. Singh and N. Mobed, Gen. Rel. Grav. 42 (2010) 1707-1718 -- 12 pages (arXiv:0903.4644 [hep-th])
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"Effects of Space-Time Curvature on Spin-1/2 Particle Zitterbewegung ," D. Singh and N. Mobed, Class. Quantum Grav. 26 (2009) 185007 -- 20 pages (arXiv:0903.1346 [gr-qc])
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"Breakdown of Lorentz Invariance for Spin-1/2 Particle Motion in Curved Space-Time with Applications to Muon Decay," D. Singh and N. Mobed, Phys. Rev. D 79 (2009) 024026 -- 20 pages (arXiv:0807.0937 [gr-qc])
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"The Implications of Noninertial Motion on Covariant Quantum Spin," D. Singh and N. Mobed, Class. Quantum Grav. 24 (2007) 2453-2463 (hep-th/0506156)
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"Helicity Precession of Spin-1/2 Particles in Weak Inertial and Gravitational Fields," D. Singh, N. Mobed, and G. Papini, J. Phys. A: Math. Gen. 37 (2004) 8329-8347 (hep-ph/0405296)
Gravitational Interactions with Neutrinos I am also very interested in the interaction of neutrinos in classical gravitational fields and whether fundamental insights can be gained about the quantum nature of space-time and/or specific properties of neutrinos as they interact with the background gravitational field. Selected Publications:
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"Can Gravity Distinguish Between Dirac and Majorana Neutrinos?" D. Singh, N. Mobed, and G. Papini, Phys. Rev. Lett. 97 (2006) 041101 -- 4 pages (gr-qc/0605153)
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"Neutrino Wave Packet Propagation in Gravitational Fields," D. Singh, N. Mobed, and G. Papini, Phys. Lett. A 351 (2006) 373-378 (gr-qc/0502098)
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"Neutrino Helicity and Chirality Transitions in Schwarzschild Space-Time," D. Singh, Phys. Rev. D 71 (2005) 105003 -- 12 pages (gr-qc/0401044)
Classical Spinning Objects in Curved Space-Time Another area of research interest is on the dynamics of classical spinning objects in the presence of strongly curved space-time backgrounds, such as neutron stars around supermassive black holes. The dynamics are governed by the Mathisson-Papapetrou-Dixon (MPD) equations of motion, in which the spinning object is driven off a geodesic trajectory by a force term proportional to the Riemann curvature tensor coupled to the object's spin tensor. Selected Publications:
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"Perturbation Approach to Classical Spinning Particles in Gravitational Fields: I. Kerr Space-Time," D. Singh, Phys. Rev. D 78 (2008) 104028 -- 21 pages (arXiv:0808.3005 [gr-qc])
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"Perturbation Approach to Classical Spinning Particles in Gravitational Fields: II. Vaidya SpaceTime," D. Singh, Phys. Rev. D 78 (2008) 104029 -- 26 pages (arXiv:0808.3006 [gr-qc])
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"An Analytic Perturbation Approach for Classical Spinning Particle Dynamics," D. Singh, Gen. Rel. and Grav. 40 (2008) 1179-1192 (arXiv:0706.0928 [gr-qc])
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"Dynamics of Extended Spinning Masses in a Gravitational Field," B. Mashhoon and D. Singh, Phys. Rev. D 74 (2006) 124006 -- 12 pages (astro-ph/0608278)
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"The Dynamics of a Classical Spinning Particle in Vaidya Space-Time," D. Singh, Phys. Rev. D 72 (2005) 084033 -- 20 pages (gr-qc/0509046)
Work in Progress:
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In collaboration with Prof. D. Bini from the University of Rome, I am also co-writing a comprehensive reference book on the MPD equations, to be published in due course.
Miscellaneous Research and Long-Term Interests Some more long-term research goals I have are to better understand the conceptual and mathematical framework of general relativity as a prelude towards attaining a quantum theory of gravity. This includes studying the mathematical structures of general relativity and quantum mechanics to search for clues
which may lead to a compatible description for both theories. I also have long-term interests in theoretical cosmology, particularly concerning the content of non-luminous or dark matter, and the formation of large-scale structures in the known Universe, such as galaxy superclusters following the Big Bang. Selected Publications:
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"Tidal Dynamics in Cosmological Spacetimes," B. Mashhoon, N. Mobed, and D. Singh, Class. Quantum Grav. 24 (2007) 5031-5046 (arXiv:0705.1312 [gr-qc])
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"Pion Induced Pion Production in Heavy-Baryon Chiral Perturbation Theory," N. Mobed, J. Zhang, and D. Singh, Phys. Rev. C 72 (2005) 045204 -- 13 pages
