Mukunda's higher education began at Delhi University where he was granted a B.Sc. (Hon) degree in 1953. For his Ph.D. he studied at University of Rochester with E. C. G. Sudarshan and graduated in 1964. Mukunda’s thesis dealt with Hamiltonian mechanics, symmetry groups and elementary particles. He also studied group theory at Princeton University with Valentine Bargmann, including topological groups and Lie theory.
He was a post-doctoral fellow at Syracuse University before he returned to India. In 1967 he became a Fellow at Tata Institute of Fundamental Research. In 1969 he transferred to IISc, Bangalore. From 1972 to 2001 he served a professor at the Center for Theoretical Studies. Using the notes from Bargmann's lectures, Mukunda contributed chapters on Lie groups to Classical Dynamics: a modern perspective that he authored with Sudarshan in 1974. The expression of symmetries on physics rests largely on Lie groups, and his later works exploit these classical groups for physical theory. Mukunda was particularly impressed by W. R. Hamilton's "theory of turns" (versors), and worked to extend the use of turns in Sp(2), SU(1,1) and the Lorentz group. In 1989 Mukunda, Rajiah Simon and Sudarshan published "Hamilton’s theory of turns and a new geometrical representation for polarization optics" which developed the coset space SU(2)/U(1) = S3/S1 as an alternative to the Poincaré sphere in the description of light polarization.
Mukunda is an honorary professor at IISER Mohali and IISER Thiruvananthapuram. He is also the Distinguished associate of Ramakrishna Mission Vivekananda Educational and Research Institute.
He was awarded the Shanti Swarup Bhatnagar Award for work in Nonlinear and Quantum Optics in 1980 In 2016 Mukunda gave the Fifteenth Memorial V.G. Kulkarni Lecture: "The Nature of Scientific Knowledge: some reflections".
According to Mathematical Reviews, Mukunda contributed to 143 scholarly publications, including
- 1974: (with George Sudarshan) Classical Dynamics: a modern perspective, John Wiley & Sons MR0434047
- 1987: "The mathematical style of modern physics", pages 1 to 20 in Recent Developments in Theoretical Physics, World Scientific MR935612
- 1989: (with Rajiah Simon and Sudarshan) "Hamilton's theory of turns generalized to Sp(2,R)", Physical Review Letters 62(12): 1331–4 MR0986460
- 1989: (with R. Simon and George Sudarshan) "The theory of screws: a new geometric representation for the group SU(1,1"), Journal of Mathematical Physics 30(5): 1000–1006 doi:10.1063/1.528365 MR0992568
- 1989: (with R. Simon and George Sudarshan) "Hamilton's turns and a new geometrical representation for polarization optics", Pramana 32(6): 769–92.
- 1989: Mukunda and collaborators initiated the "Quantum theory of charged-particle beam optics" by working out the focusing action of a magnetic quadrupole using the Dirac Equation.
- 1992: (with R. Simon) "Hamilton's turns and geometric phase for two-level systems", Journal of Physics A 25(22): 6135–44 MR1193846
- 1993: Twisted Gaussian Schell-model beams. I & II. Symmetry structure and normal-mode spectrum via Indian Academy of Sciences
- 1996: "Planetary Motions and the Birth of Classical Mechanics", Current Science 71(7): 527–32 MR1412435
- 1997: "Geometry, Fields, and Cosmology", Fundamental Theories of Physics 88, Kluwer MR1601142 (from First Inter-University Graduate School on Gravitation and Cosmology held in Pune, 1989)
- 1999: "Mathematics and the Physicist's Conception of Nature", Current Science 76(5): 634–9 MR1678395
- 2006: (with R. Simon, S. Chaturvedi, and V. Srinivasan) "Hamiltion's Turns for the Lorentz Group", International Journal of Theoretical Physics 45(11): 2051–2070 MR2275839
- 2010: (with Sunil Mukhi) Lectures on Advanced Mathematical Methods for Physicists, World Scientific, ISBN 981-4299-73-1 MR2777931 (Mukunda wrote part 2: Group Theory and Structure and Representations of Compact, Simple Lie Groups and Algebras.)
- 2017: (with Arvind and Chaturvedi) "Global aspects of polarization optics and coset space geometry", Physics Letters A 381(35): 3005–9 doi:10.1016/j.physleta.2017.06.053 MR3688582
- "Brief Resume - Prof. N. Mukunda" (PDF). ICAST. Retrieved 19 May 2019.
- Narasimhaigar Mukunda (1964) Studies in Hamiltonian theories of relativistic interacting particles, and in the application of symmetry groups to elementary particle physics, Seventh supplement to Checklist of Doctors’ Theses from University of Rochester
- Faculty at Ramakrishna Mission
- Handbook of Shanti Swarup Bhatnagar Prize Winners (1958 - 1998) (PDF). Council of Scientific & Industrial Research, New Delhi. 1999. Archived from the original (PDF) on 4 March 2016. Retrieved 11 April 2012.
- VGK Memorial Lecture Series from Tata Institute of Fundamental Research
- Jagannathan, R.; Simon, R.; Sudarshan, E. C. G.; Mukunda, N. (1989). "Quantum theory of magnetic electron lenses based on the Dirac equation" (PDF). Physics Letters A. 134 (8–9): 457. Bibcode:1989PhLA..134..457J. doi:10.1016/0375-9601(89)90685-3.