Anup Anand Singh
- Email: firstname.lastname@example.org
Physics and mathematics inspire each other in beautiful ways. It is this interplay between the two that draws me to mathematical physics, the broad area of my doctoral research. Together with my doctoral supervisor Dr. Vincent Caudrelier, I am trying to further our understanding of what are called classical integrable theories and devise a framework for their covariant quantisation.
An integrable model — characterised by a set of equations that can be solved exactly — is highly symmetrical and has fascinating mathematical structures. And while most integrable theories are only toy models — and not “true” theories describing physical laws — they offer great insights into the fundamental principles underlying the laws of nature.
Much of my current work is rooted in the theory of Lagrangian multiforms, a relatively new framework that captures integrability purely from a variational perspective. The theory marks an important departure from the traditional point of view on integrability that has been based on the Hamiltonian formalism. Moreover, the Lagrangian multiform approach allows for the possibility of using path integrals to quantise integrable theories in a covariant manner, overcoming the drawback of canonical quantisation which breaks the Lorentz covariance of the underlying spacetime coordinates.
Previously, as a visiting student at the Raman Research Institute, Bengaluru, I worked on causal set theory, an approach to quantum gravity that postulates that spacetime is fundamentally discrete and replaces the spacetime continuum with locally finite partially ordered sets. The result from this project, a collaboration with Dr. Abhishek Mathur and Prof. Sumati Surya, helped establish that certain classes of non-manifold-like causal sets are suppressed even though they are more typical than manifold-like causal sets.
Prior to that, I was a part of the five-year BS-MS dual degree programme at the Indian Institute of Science Education and Research (IISER) Pune. I spent my final year of the programme at the International Centre for Theoretical Sciences (ICTS-TIFR), Bengaluru, under the guidance of Prof. Spenta Wadia, learning how to think about physics. As a part of my MS thesis work done under his supervision, I tried to better understand the scrambling of information by black holes using ideas from holography, quantum information and chaotic dynamics. A novel result from the project was a derivation of the effective action of the charged version of the Sachdev-Ye-Kitaev model achieved by reducing the original theory of Majorana fermions to a theory of bilocal fields.
- Mathematical physics
- Integrable systems
- Quantum field theory
- Quantum gravity
- Master of Science