Email: phyksi@nus.edu.sg
Office: S15-03-02
Tel: +65 6516 6756
Current Research
- My current research focus is primarily in area of mathematical physics. I have keen interest in examining some of the foundational issues connected with theories of gravity, both from the general relativistic as well the gauge-theoretic perspectives. Of particular interest, is the Teleparallel-Equivalent to General Relativity (TEGR) theory and the central role it plays in connecting the Riemannian structures on a manifold with the gauge structures associated with the translation group. In addition, I am also interested in deformed algebras and their relevance to quantum gravity.
The Teleparallel Equivalent to General Relativity (TEGR) has been widely regarded as an alternative description of gravity. One of the principal advantages of TEGR over General Relativity (GR) is the claim that it is a gauge theory (of the translation group). The difference between the two formulations is that in GR, gravitational effects arise from the curvature of spacetime while that in TEGR, it is associated with torsion. The connection in GR being torsionless, while that in TEGR being flat (curvature = 0).
More interestingly the mathematical structures that underlie these formulations are markedly different. Indeed, the structure of TEGR, when approached as a special case of the Einstein-Cartan spacetime (employing the Weitzenbork connection) does not bear any semblance to a gauge theory. Its identification as a gauge theory becomes apparent when the translation group is gauged and the corresponding field strength is identified as the torsion (that appears in the Einstein-Cartan theory).
This identification and the concomitant status of TEGR as a gauge theory has, however, been questioned. The work here seeks to examine the structural issues and the problems from a bundle-theoretic approach. The goal is to see how TEGR or its equivalent can be recovered from a gauge-theoretic framework.
Selected Publications
- M. Johansson, M. Ericsson, K. Singh, E. Sjoqvist, and M.S. Williamson, “Topological phases and multiqubit entanglement” Phys. Rev. A 85 032112 (2012).
- C.L. Ching, R.R Parwani, and K. Singh, “Constraints and spectra of a deformed quantum mechanics”, Phys. Rev. D 86 084053, (2012).
- M. Johansson, E. Sjoqvist, L.M. Andersson, M. Ericsson, B. Hessmo, K. Singh and D.M. Tong, “Robustness of nonadiabatic holonomic gates”, Phys. Rev. A 86 062322, (2012).
- K. Singh, D.M. Tong, K. Basu, J.L. Chen and J.F. Du, “Geometric phases for nondegenerate and degenerate mixed states”, Phys. Rev. A 67 032106, (2003).
- C.H. Oh, K. Singh, “Real forms of the oscillator quantum algebra and its representations”, Lett. Math. Phys. 36 77, (1996).
- C.H. Oh and K. Singh, “Realizations of the q-Heisenberg and q-Virasoro Algebras ”, J. Phys. A: Math. Gen. 27 3439, (1994).
- C.H Oh, and K. Singh, “Generalized q-Oscillators and their Hopf Structures”, J. Phys. A: Math.Gen. 27 5907, (1994).
- C.H. Oh and K. Singh, “Conformal Properties of Primary Fields in a q-Deformed Theory”, J. Phys. A: Math.Gen. 25 L149, (1992).
- C.H. Oh and K. Singh, “Some Comments on Torsion in the Kaluza-Klein Scheme”, Class. Quant. Grav. 6 1053 (1989).
- C.H. Oh, K. Singh and C.H. Lai, “Some Global Properties and Invariance of Bundle Metrics in the Kaluza-Klein Scheme”, J. Math. Phys. 29, 2641 (1988).
Affiliations & Links
- Admin Director, Centre for Quantum Technologies
- Master, King Edward VII Hall