Table of Contents

# A Short Biography

Ennackal Chandy George (ECG) was born into a Syrian Christian family on 16 September 1931 in Pallam, Kottayam, Kerala. His mother, Achamma was a school teacher, and his father E. I. Chandy was a revenue inspector in the old Travancore state.

He was the second of three boys, between Joseph and Thomas Alexander. After high school, he completed the two-year Intermediate at the Church Missionary Society (CMS) College in Kottayam in 1948.

Sudarshan attended the Madras Christian College (MCC) in Madras (now Chennai) for his B.Sc (Honours) in Physics from 1948 to 1951, after which he stayed on for a year as a demonstrator in physics. In 1952, he received his MA degree from the University of Madras.

Sudarshan joined the Tata Institute of Fundamental Research (TIFR) in Bombay (now Mumbai) in the spring of 1952 as a research student. He then moved to the University of Rochester in New York to work under Robert Marshak as a graduate student in 1955.

In 1958, he received his Ph.D. degree from the University of Rochester. After submitting his Ph.D. thesis, Sudarshan spent two years from 1957 to 1959 as Research Fellow with Schwinger at Harvard University. In 1959, ECG returned to Rochester and joined the physics faculty as Assistant Professor, and two years later, he became Associate Professor.

Sudarshan took sabbatical leave in 1963–64, spending the first half at the University of Bern and the second at Brandeis University. He also visited the Institute of Mathematical Sciences (IMSc) in Madras in India. In 1964, Sudarshan moved from Rochester to Syracuse University as Professor.

In 1969, Sudarshan moved from Syracuse to the University of Texas at Austin as a Professor and Co-Director (with Yuval Neeman) of the Centre for Particle Theory. He taught at the Tata Institute of Fundamental Research (TIFR), University of Rochester, Syracuse University, and Harvard University. He was a senior professor at the Indian Institute of Science.

He worked as the director of the Institute of Mathematical Sciences (IMSc), Chennai, India, for five years during the 1980s, dividing his time between India and USA. He died on 13 May 2018, aged 86.

**References**

- Mukunda, N. (2019). The Life and Work of E. C. George Sudarshan.
*Resonance – Journal of Science Education. Indian Academy of Sciences. 24*(2), pp 129-167.

# What are his Scientific Contributions?

# Glauber-Sudarshan P-Representation

The Sudarshan-Glauber P-Representation is a suggested way of writing down a quantum system’s phase space distribution in the quantum mechanics’ phase space formulation. The P representation is the quasiprobability distribution in which observables are expressed in normal order.

In quantum optics, this representation, formally equivalent to several other representations, is sometimes championed over alternative representations to describe light in optical phase space because typical optical observables, such as the particle number operator, are naturally expressed in normal order. It is named after George Sudarshan and Roy J. Glauber, who worked on the topic in 1963.

**References**

- L. Cohen. (1966). Generalized phase-space distribution functions. J. Math. Phys. 7 (5), 781–786. Bibcode:1966JMP…..7..781C. doi:10.1063/1.1931206.
- L. Cohen. (1976). Quantization problem and variational principle in the phase space formulation of quantum mechanics. J. Math. Phys. 17 (10),1863-1866. Bibcode:1976JMP….17.1863C. doi:10.1063/1.522807.
- Sudarshan, E. C. G. (1963). Equivalence of semi-classical and quantum mechanical descriptions of statistical light beams. Phys. Rev. Lett. 10 (7): 277–279. Bibcode:1963PhRvL..10..277S. doi:10.1103/PhysRevLett.10.277.
- Glauber, R. J. (1963). Coherent and incoherent states of the radiation field. Phys. Rev. 131 (6): 2766–2788. Bibcode:1963PhRv..131.2766G. doi:10.1103/PhysRev.131.2766.

# Gorini–Kossakowski–Sudarshan–Lindblad equation

The Gorini–Kossakowski–Sudarshan–Lindblad equation (GKSL equation, named after Vittorio Gorini, Andrzej Kossakowski, George Sudarshan, and Göran Lindblad), is the most general type of Markovian and time-homogeneous master equation describing (in general non-unitary) evolution of the density matrix *ρ* that preserves the laws of quantum mechanics (i.e., is trace-preserving and completely positive for any initial condition).

The Schrödinger equation is a particular case of the more general Lindblad equation, which has led to some speculation that quantum mechanics may be productively extended and expanded through further application and analysis of the Lindblad equation.

The Schrödinger equation deals with state vectors, which can only describe pure quantum states and are thus less general than density matrices, which can also represent mixed states.

**References**

- Breuer, Heinz-Peter., Petruccione, F. (2002). The Theory of Open Quantum Systems. Oxford University Press. ISBN 978-0-1985-2063-4.
- Weinberg, Steven (2014). Quantum Mechanics Without State Vectors. Phys. Rev. A. 90: 042102. arXiv:1405.3483. doi:10.1103/PhysRevA.90.042102.

# V-A Theory

Gravity, Electromagnetism, and Strong Force conserve the law of symmetry. In the mid-1950s, Chen-Ning Yang and Tsung-Dao Lee suggested that weak interaction might violate the law of symmetry. Chien Shiung Wu and collaborators in 1957 discovered that the weak interaction violates parity, earning Yang and Lee the 1957 Nobel Prize in Physics.

Although Fermi’s theory once described weak interaction, the discovery of parity violation and renormalization theory suggested that a new approach was needed. In 1957, Robert Marshak and George Sudarshan and, somewhat later, Richard Feynman and Murray Gell-Mann proposed a V−A (vector minus axial vector or left-handed) Lagrangian for weak interactions.

In this theory, the weak interaction acts only on left-handed particles (and right-handed antiparticles). Since the mirror reflection of a left-handed particle is right-handed, this explains the maximal parity violation. The V−A theory was developed before the discovery of the Z boson, so it did not include the right-handed fields that enter the neutral current interaction.

**References**

- Carey, Charles W. (2006). Lee, Tsung-Dao. American scientists. Facts on File Inc. p. 225. ISBN 9781438108070.
- The Nobel Prize in Physics 1957. NobelPrize.org. Nobel Media. Retrieved 26 February 2011.
- Mehra, J. (1994). The beat of a different drum: The life and science of Richard Feynman.
*Clarendon Press Oxford,*p. 477.

# Tachyons

A tachyon is a hypothetical particle that always travels faster than light. Most physicists believe that faster-than-light particles cannot exist because they are not consistent with the known laws of physics. E. C. G. Sudarshan, V.K Deshpande, and Baidyanath Misra were the first to propose the existence of particles faster than light and named them “meta-particles.”

In special relativity, a faster-than-light particle would have space-like four-momentum, unlike ordinary particles with time-like four-momentum. Although in some theories, the mass of tachyons is regarded as imaginary, in some modern formulations, the mass is considered real, the formulas for the momentum and energy being redefined to this end.

Moreover, since tachyons are constrained to the space-like portion of the energy-momentum graph, they could not slow down to subluminal speeds.

**References**

- Randall, Lisa. (2006). Warped Passages: Unraveling the Mysteries of the Universe’s Hidden Dimensions.
*Ecco.*ISBN-13 – 978-0060531096 - Tipler, Paul A., Llewellyn, Ralph A. (2008). Modern Physics (5th ed.).
*New York: W.H. Freeman & Co.*p. 54. ISBN 978-0-7167-7550-8. - Feinberg, G. (1967). Possibility of Faster-Than-Light Particles. Physical Review. 159 (5): 1089–1105. Bibcode:1967PhRv..159.1089F. doi:10.1103/PhysRev.159.1089.
- Recami, E. (2007). Classical tachyons and possible applications.
*Rivista del Nuovo Cimento*.*9*(6): 1–178. Bibcode:1986NCimR…9e…1R. doi:10.1007/BF02724327. ISSN 1826-9850. S2CID 120041976. - Vieira, R. S. (2011). An introduction to the theory of tachyons.
*Rev. Bras. Ens. Fis*.*34*(3). arXiv:1112.4187. Bibcode:2011arXiv1112.4187V. - Hill, James M., Cox, Barry J. (2012). Einstein’s special relativity beyond the speed of light.
*Proc. R. Soc. A*.*468*(2148): 4174–4192. Bibcode:2012RSPSA.468.4174H. doi:10.1098/rspa.2012.0340. ISSN 1364-5021.

# Quantum Zeno Effect

The quantum Zeno effect (also known as the Turing paradox) is a feature of quantum-mechanical systems allowing a particle’s time evolution to be arrested by measuring it frequently enough with respect to some chosen measurement setting.

The meaning of the term has since expanded, leading to a more technical definition, in which time evolution can be suppressed not only by measurement: the quantum Zeno effect is the suppression of unitary time evolution in quantum systems provided by a variety of sources: measurement, interactions with the environment, stochastic fields, among other factors.

The name comes from Zeno’s arrow paradox, which states that because an arrow in flight is not seen to move during any single instant, it cannot possibly be moving at all. The quantum Zeno effect’s first rigorous and general derivation was presented in 1974 by Degasperis, Fonda, and Ghirardi, although Alan Turing had previously described it.

The comparison with Zeno’s paradox is due to a 1977 article by George Sudarshan and Baidyanath Misra.

**References**

- Sudarshan, E. C. G., Misra, B. (1977). The Zeno’s paradox in quantum theory.
*Journal of Mathematical Physics*.*18*(4), 756–763. Bibcode:1977JMP….18..756M. doi:10.1063/1.523304. - Nakanishi, T., Yamane, K., Kitano, M. (2001). Absorption-free optical control of spin systems: the quantum Zeno effect in optical pumping.
*Physical Review A*.*65*(1): 013404. arXiv:quant-ph/0103034. Bibcode:2002PhRvA..65a3404N. doi:10.1103/PhysRevA.65.013404. - Degasperis, A., Fonda, L., Ghirardi, G. C. (1974). Does the lifetime of an unstable system depend on the measuring apparatus?. Il Nuovo Cimento A. 21 (3): 471–484. Bibcode:1974NCimA..21..471D. doi:10.1007/BF02731351.
- Hofstadter, D. (2004). Teuscher, C. (ed.). Alan Turing: Life and Legacy of a Great Thinker. Springer. p. 54. ISBN 978-3-540-20020-8.

# Quantum Optics

Quantum optics is a field of research that uses semi-classical and quantum-mechanical physics to investigate phenomena involving light and its interactions with matter at submicroscopic levels. In other words, it is quantum mechanics applied to photons or light.

Following the work of Dirac in quantum field theory, John R. Klauder, George Sudarshan, Roy J. Glauber, and Leonard Mandel applied quantum theory to the electromagnetic field in the 1950s and 1960s to gain a more detailed understanding of photodetection and the statistics of light.

This led to the introduction of the coherent state as a concept that addressed variations between laser light, thermal light, exotic squeezed states, etc. as it became understood that light cannot be fully described just referring to the electromagnetic fields describing the waves in the classical picture.

A frequently encountered state of the light field is the coherent state, as introduced by E.C. George Sudarshan in 1960. This state, which can be used to approximately describe the output of a single-frequency laser well above the laser threshold, exhibits Poissonian photon-number statistics.

Via specific nonlinear interactions, a coherent state can be transformed into a squeezed coherent state by applying a squeezing operator that can display super- or sub-Poissonian photon statistics. Such light is called squeezed light.

Sudarshan’s most significant work may have been his contribution to the field of quantum optics. His theorem proves the equivalence of classical wave optics to quantum optics. The theorem makes use of the Sudarshan representation. This representation also predicts optical effects that are purely quantum and cannot be explained classically.

**References**

- Gerry, Christopher., Knight, Peter. (2004). Introduction to Quantum Optics. Cambridge University Press. ISBN
*052152735X*.

# Which are the Awards and Honors won by E. C. G. Sudarshan?

The awards and honors received by E. C. G. Sudarshan are as follows;

- Honorary doctorate by the University of Kerala.
- Kerala Sastra Puraskaram for lifetime accomplishments in science. (2013)
- Dirac Medal of the ICTP. (2010)
- Padma Vibhushan, the second-highest civilian award from the Government of India. (2007)
- Majorana Prize. (2006)
- First Prize in Physics. (1985)
- TWAS Prize. (1985)
- Bose Medal. (1977)
- Padma Bhushan, the third-highest civilian award from the Government of India. (1976)
- C V Raman Award. (1970)

**References**

- KU to confer honorary doctorates on Narlikar, Kris Gopalakrishnan. The Hindu. 21 August 2019. Retrieved 5 November 2020.
- Padma Awards (PDF). (2015). Ministry of Home Affairs, Government of India. Archived from the original (PDF) on 15 October 2015. Retrieved 21 July 2015.

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