Meghraj M S

I am a BS-MS Dual Degree graduate (July 2020) from IISER-Kolkata with a major in Physical Sciences. I am currently taking a year away from Universities in order to embark on some self study. The main areas that I'm interested in learning are the mathematical foundations of theoretical physics (e.g. Differential Geometry, Operator Theory/Functional Analysis, Algebra, etc.) as well as some topics in physics (e.g. Quantum Field Theory, General Relativity, String Theory, etc.)

Room No. F-304, ICVS Hall
IISER Kolkata
Mohanpur, West Bengal, India - 741246


Master's Thesis

A New Quantum Theory of Gravity under Prof.Tejinder Pal Singh , TIFR, Mumbai with Prof.Narayan Banerjee , IISER-Kolkata as co-supervisor.

In this work, we defined a new action principle for the atom of space-time-matter (STM atom) that not only led us to the equations for a quantum theory of gravity but also gave us the Yang-Mills action along with the Einstein-Hilbert action after spontaneous localisation. For this we made use of Adler's Trace Dynamics and Connes Non-Commutative Geometry along with the Connes time parameter to incorporate gravity and Yang-Mills theory into trace dynamics.

Trace dynamics is the classical dynamics of matrices on a space-time background whose elements are complex Grassmann numbers. These elements belong to even or odd sectors of the Grassmann algebra. One then takes the trace of the polynomial P that is constructed from these matrices as P = Tr P and defines a so-called trace derivative of P with respect to a given matrix so that one can then construct a trace Lagrangian from the matrices qr and their time derivatives q̇r. This paves way for the development of classical Lagrangian and Hamiltonian dynamics from the system of matrices in the conventional way. Trace Dynamics also turns out to be an underlying theory from which quantum theory and collapse models are emergent.

The main idea behind non-commutative geometry on the other hand is that we can trade spaces for algebras. It is a geometric approach to the study of non-commutative algebras and the construction of spaces that are locally presented by non-commutative algebras of functions. For this, the notion of a spectral triple was used from which the Lagrangian(s) can be derived by the so-called heat kernel expansion of the spectral action.

We also showed the invariance of the functional form of the trace Lagrangian under a transformation that leaves the gyromagnetic ration unchanged. This transformation should be thought of as a duality between Dirac fermions and Black Holes which then explains the same gyromagnetic ratio for a charged rotating Black Hole and an electron.

The work was summarised in the paper Why does the Kerr-Newman black hole have the same gyromagnetic ratio as the electron?

Research Projects

Lecture notes for a few of the courses :

  • Computational Physics - ADG
  • Electromagnetism - ADG
  • Advanced Mathematical Methods of Physics - ADG
  • Nonlinear Dynamics - Subhasis Sinha
  • Advanced Statistical Mechanics - Bhavtosh Bansal
  • Research Methodology - Soumitro Banerjee
  • High Energy Physics - Ritesh K Singh
  • Quantum Information Processing - Chiranjib Mitra
  • Evolutionary Dynamics - Supratim Sengupta

  • My understanding so far series :

  • Newton's Laws
  • Power Spectrum of Noise