Narasimhaiengar Mukunda (born 25 January 1939,

New Delhi New Delhi (, , ''Naī Dillī'') is the capital of India and a part of the National Capital Territory of Delhi (NCT). New Delhi is the seat of all three branches of the government of India, hosting the Rashtrapati Bhavan, Parliament House ...

India India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the so ...

) is an Indian theoretical physicist. Mukunda's higher education began at

Delhi University Delhi University (DU), formally the University of Delhi, is a collegiate university, collegiate Central university (India), central university located in New Delhi, India. It was founded in 1922 by an Act of the Central Legislative Assembly and ...

, where he was granted a B.Sc. (Hon) degree in 1953. For his Ph.D. he studied at

University of Rochester The University of Rochester (U of R, UR, or U of Rochester) is a private research university in Rochester, New York. The university grants undergraduate and graduate degrees, including doctoral and professional degrees. The University of Roc ...

with E. C. G. Sudarshan and graduated in 1964. Mukunda’s thesis dealt with

Hamiltonian mechanics Hamiltonian mechanics emerged in 1833 as a reformulation of Lagrangian mechanics. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities \dot q^i used in Lagrangian mechanics with (generalized) ''momenta ...

symmetry group In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Such a transformation is an invertible mapping of the ambient ...

s and

elementary particle In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include electrons, the fundamental fermions ( quarks, leptons, an ...

s. He also studied

group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

with

Valentine Bargmann Valentine "Valya" Bargmann (April 6, 1908 – July 20, 1989) was a German-American mathematician and theoretical physicist. Biography Born in Berlin, Germany, to a German Jewish family, Bargmann studied there from 1925 to 1933. After the National ...

, including

topological group In mathematics, topological groups are logically the combination of groups and topological spaces, i.e. they are groups and topological spaces at the same time, such that the continuity condition for the group operations connects these two str ...

s and

Lie theory In mathematics, the mathematician Sophus Lie ( ) initiated lines of study involving integration of differential equations, transformation groups, and contact of spheres that have come to be called Lie theory. For instance, the latter subject is L ...

. He was a post-doctoral fellow at

Syracuse University Syracuse University (informally 'Cuse or SU) is a Private university, private research university in Syracuse, New York. Established in 1870 with roots in the Methodist Episcopal Church, the university has been nonsectarian since 1920. Locate ...

before he returned to India. In 1967, he became a Fellow at

Tata Institute of Fundamental Research Tata Institute of Fundamental Research (TIFR) is a public deemed research university located in Mumbai, India that is dedicated to basic research in mathematics and the sciences. It is a Deemed University and works under the umbrella of the D ...

. In 1969 he transferred to

IISc The Indian Institute of Science (IISc) is a public, deemed, research university for higher education and research in science, engineering, design, and management. It is located in Bengaluru, in the Indian state of Karnataka. The institute wa ...

, Bangalore. From 1972 to 2001 he served as professor at the Center for Theoretical Studies. Using the notes from Bargmann's lectures, Mukunda contributed chapters on

Lie group In mathematics, a Lie group (pronounced ) is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the additio ...

s 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 group In mathematics, the classical groups are defined as the special linear groups over the reals , the complex numbers and the quaternions together with special automorphism groups of symmetric or skew-symmetric bilinear forms and Hermitian or ske ...

s for physical theory. Mukunda was particularly impressed by

W. R. Hamilton Sir William Rowan Hamilton LL.D, DCL, MRIA, FRAS (3/4 August 1805 – 2 September 1865) was an Irish mathematician, astronomer, and physicist. He was the Andrews Professor of Astronomy at Trinity College Dublin, and Royal Astronomer of Ireland ...

's "theory of turns" (

versor In mathematics, a versor is a quaternion of norm one (a ''unit quaternion''). The word is derived from Latin ''versare'' = "to turn" with the suffix ''-or'' forming a noun from the verb (i.e. ''versor'' = "the turner"). It was introduced by Willi ...

s), and worked to extend the use of turns in Sp(2),

SU(1,1) In mathematics, the special unitary group of degree , denoted , is the Lie group of unitary matrices with determinant 1. The more general unitary matrices may have complex determinants with absolute value 1, rather than real 1 in the special ...

and the

Lorentz group In physics and mathematics, the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical and quantum setting for all (non-gravitational) physical phenomena. The Lorentz group is named for the Dutch physicis ...

. In 1989 Mukunda,

Rajiah Simon Rajiah Simon, is a Professor of Physics at the Institute of Mathematical Sciences, Chennai, India. Rajiah Simon received the Shanti Swarup Bhatnagar Prize for Science and Technology in 1993 for pioneering work in Quantum optics. Simon and collab ...

and Sudarshan published "Hamilton’s theory of turns and a new geometrical representation for polarization optics" which developed the

coset space In mathematics, particularly in the theories of Lie groups, algebraic groups and topological groups, a homogeneous space for a group ''G'' is a non-empty manifold or topological space ''X'' on which ''G'' acts transitively. The elements of ''G' ...

SU(2)/U(1) = S³/S¹ as an alternative to the

Poincaré sphere Poincaré sphere may refer to: * Poincaré sphere (optics), a graphical tool for visualizing different types of polarized light ** Bloch sphere, a related tool for representing states of a two-level quantum mechanical system * Poincaré homology s ...

in the description of

light polarization Polarization ( also polarisation) is a property applying to transverse waves that specifies the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of t ...

. Mukunda is an honorary professor at

IISER Bhopal Indian Institute of Science Education and Research, Bhopal (IISER-B or IISER – Bhopal) is an autonomous institute. ] in Bhauri, Bhopal district, Madhya Pradesh, India. It was established by the Ministry of Human Resource Development, Gov ...

IISER Mohali Indian Institute of Science Education and Research, Mohali (IISER Mohali) is an autonomous public university established in 2006 at Mohali, Punjab, India. It is one of the seven Indian Institutes of Science Education and Research (IISERs), estab ...

and

IISER Thiruvananthapuram Indian Institute of Science Education and Research, Thiruvananthapuram (abbreviated as IISER Thiruvananthapuram or IISER-TVM) is an autonomous public university located in Thiruvananthapuram, India. The institute is one of the seven IISERs esta ...

. He is also the Distinguished associate of

Ramakrishna Mission Vivekananda Educational and Research Institute Ramakrishna Mission Vivekananda Educational and Research Institute, formerly Ramakrishna Mission Vivekananda University or simply Vivekananda University, is a education institute deemed-to-be-university headquartered at Belur, West Bengal, wi ...

. 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".

Selected publications

According to

Mathematical Reviews ''Mathematical Reviews'' is a journal published by the American Mathematical Society (AMS) that contains brief synopses, and in some cases evaluations, of many articles in mathematics, statistics, and theoretical computer science. The AMS also pu ...

, Mukunda contributed to 143 scholarly publications, including * 1974: (with

George Sudarshan Ennackal Chandy George Sudarshan (also known as E. C. G. Sudarshan; 16 September 1931 – 13 May 2018) was an Indian American theoretical physicist and a professor at the University of Texas. Sudarshan has been credited with numerous contrib ...

) ''Classical Dynamics: a modern perspective'',

John Wiley & Sons John Wiley & Sons, Inc., commonly known as Wiley (), is an American multinational publishing company founded in 1807 that focuses on academic publishing and instructional materials. The company produces books, journals, and encyclopedias, in p ...

* 1987: "The mathematical style of modern physics", pages 1 to 20 in ''Recent Developments in Theoretical Physics'',

World Scientific World Scientific Publishing is an academic publisher of scientific, technical, and medical books and journals headquartered in Singapore. The company was founded in 1981. It publishes about 600 books annually, along with 135 journals in various f ...

* 1989: (with

and Sudarshan) "Hamilton's theory of turns generalized to Sp(2,R)",

Physical Review Letters ''Physical Review Letters'' (''PRL''), established in 1958, is a peer-reviewed, scientific journal that is published 52 times per year by the American Physical Society. As also confirmed by various measurement standards, which include the ''Journa ...

62(12): 1331–4 * 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 The ''Journal of Mathematical Physics'' is a peer-reviewed journal published monthly by the American Institute of Physics devoted to the publication of papers in mathematical physics. The journal was first published bimonthly beginning in Januar ...

30(5): 1000–1006 * 1989: (with R. Simon and George Sudarshan) "Hamilton's turns and a new geometrical representation for polarization optics",

Pramana ''Pramana'' (Sanskrit: प्रमाण, ) literally means " proof" and "means of knowledge".beam optics" by working out the focusing action of a magnetic quadrupole using the

Dirac Equation In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin- massive particles, called "Dirac part ...

. * 1992: (with R. Simon) "Hamilton's turns and geometric phase for two-level systems",

Journal of Physics A The ''Journal of Physics A: Mathematical and Theoretical'' is a peer-reviewed scientific journal published by IOP Publishing. It is part of the ''Journal of Physics'' series and covers theoretical physics focusing on sophisticated mathematical and ...

25(22): 6135–44 * 1993
Twisted Gaussian Schell-model beams. I & II. Symmetry structure and normal-mode spectrum
via

Indian Academy of Sciences The Indian Academy of Sciences, Bangalore was founded by Indian Physicist and Nobel Laureate C. V. Raman, and was registered as a society on 24 April 1934. Inaugurated on 31 July 1934, it began with 65 founding fellows. The first general meet ...

* 1996: "Planetary Motions and the Birth of Classical Mechanics",

Current Science ''Current Science'' is an English-language peer-reviewed multidisciplinary scientific journal. It was established in 1932 and is published by the Current Science Association along with the Indian Academy of Sciences. According to the ''Journal C ...

71(7): 527–32 * 1997: "Geometry, Fields, and Cosmology", ''Fundamental Theories of Physics'' 88,

Kluwer Wolters Kluwer N.V. () is a Dutch information services company. The company is headquartered in Alphen aan den Rijn, Netherlands (Global) and Philadelphia, United States (corporate). Wolters Kluwer in its current form was founded in 1987 with a m ...

(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 * 2006: (with R. Simon, S. Chaturvedi, and V. Srinivasan) "Hamiltion's Turns for the Lorentz Group",

International Journal of Theoretical Physics The ''International Journal of Theoretical Physics'' is a peer-reviewed scientific journal of physics published by Springer Science+Business Media since 1968. According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 1 ...

45(11): 2051–2070 * 2010: (with Sunil Mukhi) ''Lectures on Advanced Mathematical Methods for Physicists'',

, (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 ''Physics Letters'' was a scientific journal published from 1962 to 1966, when it split in two series now published by Elsevier: *''Physics Letters A'': condensed matter physics, theoretical physics, nonlinear science, statistical physics, mathema ...

A 381(35): 3005–9

References

{{DEFAULTSORT:Mukunda, N. 20th-century Indian physicists Living people Indian theoretical physicists University of Rochester alumni Indian Institute of Science faculty 1939 births Ramakrishna Mission Vivekananda Educational and Research Institute faculty