Using Non-Hermitian PT Symmetric
Hamiltonians to discern Neutrino Oscillations in Matter
PT Symmetric Quantum Mechanics allows the non-Hermitian Hamiltonians to have real Eigen values. We introduce a novel approach to extend the ordinary neutrino oscillation formalism in matter using a non-Hermitian PT Symmetric effective Hamiltonian. Since the condition of PT symmetry is less mathematical than that of hermicity and more physical, the application of this approach can lead to new results in neutrino flavor transitions similar to non-standard neutrino interactions. We derive the necessary conditions for the effective Hamiltonian to be real and relations between the fundamental and effective parameters. As a result, we find that the real spectrum of the effective Hamiltonian will depend on the new fundamental parameters introduced in the perturbation Hamiltonian. In conclusion we end up with two possibilities, either spectrum is exact and effective leptonic mixing is maximal or the spectrum is approximate and new fundamental parameters are small.
Reference: Tommy Ohlsson, Europhys. Lett. 113 (2016) 61001
Breakdown of String Perturbation Theory
in the Limit of Many External Particles
Out of the many elegant approaches to construct a successful theory of Quantum Gravity over the recent times, String Theory has stood the test of theoretical censorship and has emerged as a promising candidate for Theory of Everything(TOE). String Theory has a lot of elegance to it which is evident from its prediction of extra spatial dimensions, surprising results in case of black holes, connection of gravity with gauge theories, existence of a multiverse, etc. However, due to the extremity (~1019 GeV) of energy in which the aforementioned phenomena are supposed to occur, experimental verification of String Theory has not been possible so far. But this has not been a deterrent to theoretical physicists who are working relentlessly to develop String Theory, as many areas within it are still unexplored. One such area of interest is the extreme limits of String Theory, more precisely in this case is the String Perturbation Theory(SPT). In SPT, at each order of the perturbation expansion, there is a unique worldsheet topology (determined by the genus of the Riemann surface), and its contribution is ultraviolet(UV) finite. In SPT there is only one thing to integrate over: a g=n Riemann surface, which is less cumbersome compared to conventional QFT where one needs to sum up a myriad of Feynman diagrams for n-loops. Besides that, String Theory is believed to be more convergent than ordinary QFTs, because of its nice UV behavior. Furthermore, asymptotic analysis shows that the Superstring Scattering Amplitudes are convergent, at least for 1 and 2 loops. Nevertheless, there is no general consensus for the convergence of SPT and the hidden danger of divergence is also not precluded. In this talk, we consider a new, and relatively unexplored, regime of String Scattering Amplitudes, where the number of external particles n becomes large, even as the energy per particle remains small. Using the growth of the volume of the relevant moduli space, and by means of independent numerical evidence, it is argued that a consideration of tree-level scattering already indicates a breakdown of SPT in this limit. Remarkable implications of this breakdown of SPT for the information paradox are also discussed.
Reference: Sudip Ghosh and Suvrat Raju, Phys. Rev. Lett. 118, 131602 (2017)
For more information contact: Dr. Howard Lee, 254-710-2277