Documents

I have prepared a couple of notes from the lectures I have attended either during my coursework or some school/conference/seminar, etc. The notes are uploaded in Google Drive and can be accessed through the following links :

📒 Notes based on ''String Theory I (Bosonic String Theory)'' course by Ashoke Sen. The notes will be updated occasionally.

📒 Notes based on ''String Theory II (Fermionic String Theory)'' course by Ashoke Sen. The notes will be updated occasionally.

Before my comprehensive exam for PhD at ICTS, I have done three projects in the timeline between January 2024 and January 2025 as a part of the Ph.D. coursework and credit requirements. All the project reports are uploaded in Google Drive and can be accessed from the links below :

📗  "All order electromagnetic (and gravitational) wave tails":

In the Fall semester 2024 (Aug - Dec), I did a semester project in collaboration with Babli Khatun under the supervision of prof. Ashoke Sen at ICTS. This project provided me with the knowledge of soft photon and soft graviton theorem.  In this project, we have considered a scattering event involving multiple particles (charged and massive) coming from the asymptotic past, going through some interaction process and then moving to the asymptotic future. Such an event emits radiation (which could be electromagnetic and/or gravitational). We have studied the late time behaviour of the emitted radiation and found that it solely depends on the charge (in presence of long range electromagnetic force only) and momenta of the particles involved in the scattering process at any arbitrary order in retarded time. 

📘  "Cosmological correlators in de Sitter using in-out formalism":

During the summer of 2024 (May–July), I undertook a research project in collaboration with my colleague and friend, Babli Khatun, under the supervision of Professor Suvrat Raju. The project provided me with an introduction to quantum field theory in curved spacetime and cosmological correlators. As part of this work, we computed several tree-level and loop-level Witten diagrams using both the Schwinger-Keldysh formalism and the in-out formalism in the Poincaré patch of de Sitter space. Our findings align with the claims made by Enrico Pajer et al. in arXiv: 2402.05999 . 

📙  "Photon emission in temperature gradient":

During the Spring 2024 semester (January - May), I undertook a project under the supervision of Professor Loganayagam R. The project primarily  focused on exploring finite temperature field theory and techniques for calculating quantum mechanical observables, such as cross-sections and decay rates. Specifically, I analyzed a system comprising two qubits located at different temperatures within a thermal bath filled with photons. The qubits interacted with the photon bath through processes of photon absorption and emission, accompanied by spin flips. My findings demonstrated that the emissivity and absorptivity of one qubit are influenced by the temperature of the other qubit, and that the spectra of the system are sensitive to the temperature of the photon bath.

During the period from Aug 2021 to Aug 2022, I worked on the entanglement entropy and related topics. I have done my M.Sc. thesis under the supervision of  Dr. Debajyoti Sarkar. I have studied the change between the modular Hamiltonian of the vacuum state and the excited state (prepared by acting an unitary operator on the vacuum) perturbatively in a 2 dimensional conformal field theory. The change picks up a contribution what is known as 'endpoint contribution' in literature. In my thesis, I attempted to find the change at an arbitrary order of perturbation and write it in a closed simple form. For more details, please check the thesis below :

📚 "Entanglement in field theory and gravity"