Sinha is the author of numerous scientific works[2] in scattering theory, spectral theory of Schrödinger operators, quantum stochastic calculus, noncommutative geometry, and, more broadly, in mathematical physics.

During this time he co-authored, with Werner Amrein and Josef-Maria Jauch, a well-known book[4] on scattering theory, which used mathematically rigorous methods to develop the subject.

He is currently Honorary Professor, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore.

Sinha is President of the Association for Quantum Probability and Infinite Dimensional Analysis[6] (since 2013).

[8] In 2019 Sinha was awarded the Srinivasa Ramanujan Medal of the Indian National Science Academy.