Saint Louis University

Dr. Santhanam's Homepage

Thalanayar S. Santhanam
Department of Physics
College of Arts and Sciences
Saint Louis University
Shannon Hall
St. Louis, MO 63103

Phone: (314) 977-8423
Fax: (314) 977-8384


  • B.SC., Kumbakonam Government College, Madras University, India. (57-60). Distinction in Physics and Mathematics, Proficiency in Physics (60). Moopanar-Beauchamp Prize-Winner, First Rank in the College.
  • M.Sc., Madras Christian College, Madras University (60-62), India. First Rank in the whole University (among five colleges affiliated to the University). Dr.K.S.Krishnan Gold-Medalist. P.E.Subramania Iyer Commemoration Medal and Jagirdar of Arni Prince of Wales Commemoration Medal.
  • Research Degree in Theoretical Physics(1966). International School of Advanced Studies & International Centre For Theoretical Physics, I.C.T.P, Trieste, Italy. Advisor: Professor Abdus Salam, Nobel Laureate.
  • Doctor of Philosophy. Madras University (70), India. Advisor: Professor Alladi Ramakrishnan


  • Associate Member, International Centre For Theoretical Physics, Trieste, Italy,1991.
  • Senior Honorary Associate, .I.C.T.P, Trieste Italy, 1984-88.
  • Life Member and Fellow of Tamilnadu Academy of Sciences, Madras, India,1987.
  • Full Member [President-Elect 98] [President 99], Sigma-Xi Scientific Society,1991.
  • Parks College Rank & Tenure Committee [Chairman 98-99], 1994.


  • Professor, MATSCIENCE, The Institute of Mathematical Sciences, Madras, India, 1977-91.
  • Professor, Saint Louis University, 1991- Present.


  • Journal of Mathematical Physics, Calcutta Mathematical Society, Journal of Physics (Delhi), Physics Essays (Canada).


  • Assisted with the Ph.D.Candidates: D.Radhakrishnan (Delhi),1968.
  • P.S.Chandrasekharan (Madras),1972.
  • Nalini.B.Menon (Madras),1973.
  • A.R.Tekumalla(Madras),1974.
  • Supervisor for the Ph.D Students: M.V.Satyanarayana (Madras),1986.
  • S.Madivananne (Madras),1988.


Long Term

  • Fellow, I.C.T.P, Trieste, Italy, 1965-66.
  • Visiting Scientist, Physikalisches Institut, Bonn, Germany, 1970.
  • Visiting Scientist, Physikalisches Institut, Wurzburg, Germany, 1974-77.
  • Senior Research Fellow, Australian National University, Canberra, Australia, 1978-80.
  • Visiting Professor, Southern Illinois University, Carbondale, 1981, 82-83, 88.

Short Visits

  • Visiting Scientist, I.C.T.P Trieste, Italy,69,74,75,82,83,84,86.
  • Associate Member, I.C.T.P Trieste, Italy,1971.
  • Guest Professor, Bonn, Germany, 73, 83, 87.
  • Visiting Scientist, University of Texas, Austin, TX USA 72, 89..
  • Visitor, University of Geneva, Switzerland,1976.
  • Visiting Scientist, Australian National University, Australia,1988.

Very Short Visits

  • Guest Professor, NORDITA, Denmark, 1973.
  • Visitor, Stanford Linear Accelerator Center, Stanford, USA 1981.
  • Visitor, University of Alberta, Canada, 1981, 1982.
  • Visiting Professor, McGill University, Canada,1982.
  • Visitor, C.E.R.N Geneva, Switzerland,66, 73, 87.
  • Visitor, University of Paris, France, 1982.
  • Visitor, Arnold Sommerfeld TeChnical University, Clausthal, Zellerfeld, Germany,1987.
  • Visitor, University of Adelaide, Australia, 79, 88.

Countries Visited & Lectured

  • Australia: Adelaide, Brisbane, Hobart, La Trobe, Melbourne, New Castle, Wollangang
  • Austria: Vienna
  • Belgium: Brussels, Liege
  • Britain: Aberystwyth, Cambridge, Canterbury, Liverpool, London, York, South Hampton
  • Bulgaria: Schumen
  • Canada: Edmonton, Montreal
  • Denmark: Copenhagen
  • France: Paris
  • Finland: Helsinki
  • Germany: Aachen, Bonn, Clausthal, DESY (Hamburg), Giessen, Frankfurt, Freiburg, Kaiserslautern, Mainz, Tubingen, Wurzburg
  • Iran: Tehran
  • Ireland: Dublin
  • Italy: Bologna, Milano, Napoli, Padua, Parma, Pisa, Roma, Torino, Trieste
  • Japan: Kyoto, Tokyo
  • South Korea: Seoul
  • Lebanon: Beirut
  • New Zealand: Auckland, Christ Church, Hamilton
  • The Netherlands: Amsterdam, Nijmegan
  • Sweden: Goteborg, Stockholm
  • Switzerland: Bern, Geneva
  • US: Austin, U.C.L.A, Berkeley, Carbondale, City Univ New York, Rochester, St. Louis, Urbana, Optical Soc.of America.


  • The review article "SU(6) and its relativistic generalizations", written in collaboration with W.Ruhl and H.Ruegg received an award from Helvetica. Physica (Switzerland), 1968.
  • The review article on "Bhabha equations" received an award from Fortschrift der Physik, Germany, 1974.

Participation in Conferences

  • Renormalization Theory, Trieste, Italy,1969.
  • High Energy Physics, Heidelberg, Germany, 1970.
  • Differential Geometric methods, Bonn, Germany, 1975, 77.
  • Europhysics Conference, Aachen, Germany, 1977.
  • Group Theoretical Methods, Tubingen, Germany,1977.
  • Nuclear Physics, Canberra, Australia, 1978.
  • Frontiers in Physics, Singapore, 1978.
  • Einstein Centennial Symposium, Carbondale, U.S., 1979.
  • High Energy Physics, Katoomba, Australia, 1979.
  • Group Theoretical Methods, Kent, Canterbury, England, 1981.
  • Group Theoretical Method, Trieste, Italy, 1983.
  • Differential Geometric Methods, Clausthal, Germany, 1983.
  • Differential Geometric Methods, Schumen, Bulgaria, 1984.
  • Yukawa Conference, Kyoto, Japan, 1985.
  • Group Theoretical Methods, Seoul, Korea, 1985.
  • High Energy Physics, Kashmir, India, 1987.
  • Superstrings, Kanpur, India, 1987.
  • Foundations of Quantum Mechanics, New Delhi, India, 1988.
  • Kac-Moody Algebras, Raleigh, N.C.,1988.
  • E.C.G. Sudarshan Conference, Austin, Texas, 1991.
  • Harmonic Oscillators, Mexico, 1994.
  • International Conference on Special Functions, Madras, India, 1997.


A. Particle Physics

  • Some remarks on Symmetries shared by strong and weak Interactions, Nuclear. Physics, 45, 255(1963).
  • Pion Resonances, Symposia on Theoretical Physics, Plenum Press, New York, VolI, 1963, Ed.Alladi Ramakrishnan.
  • Symmetries of Strong and Weak Interactions, Proceedings of Kodaikanal Summer School,1963.
  • Origin of Unitary Symmetry in Strong Interactions, Physical Review. 236B, 1092(1964).
  • P-wave non-leptonic decays and representation mixing in SU(6), Physics Letters21,234(1966).
  • SU(6) and its Relativistic Generalizations, Helv.Phys.Acta. 40, 9(1967).
  • Stueckelberg Fields and Current Algebra Sumrules, Nuovo.Cimento 57A,440(1968).
  • Broken Symmetry and Smushkewich Principle, Nuovo.Cimento 59A,20(1969).
  • Bounds on Pion Renormalization Constant, Proc.Colorado Summer School,1969.
  • Rigorous bounds on the wave function renormalization constant, Physical Review D12, 3403(1970).
  • Recursion relations for the multi-Veneziano amplitude and the residue functions, Z.fur.Phys.235,206(1970).
  • Configuration mixing for the baryon and renormalization in Cabibbo Theory, Nuovo.Cimento Letters 3, 454(1972).
  • The remarkable connection between Multi-Venetiano Integrand and the Character Function of Special Unitary Groups, J.Math.Phys.13,1823(1972).
  • Leptonic quarks and the unified description of weak and electromagnetic interractions, Proc.Nuclear Physics Conference, Mysore, India (1973).
  • A seven quark model for the spectrum of hadrons, Physical Review D14, 3200(1976).
  • Supersymmetry and Exceptional Groups, Lecture Notes in Physics 79,391(1977), Springer-Verlag, Germany.
  • New Particles,and New Physics, Proc.Tamilnadu Acad.Sci.(India)1,35(1978).
  • New Particles, Matscience Report92, 11(1978).
  • Multiplicity scaling and compound Poisson distributions, Proc.Conf on Fewbody problems, Laval Univ.Press(Canada), 1975, p.653.
  • Are the nucleans composite of only three valence quarks? Proc.Tamilnadu.Acad. Sci.4, 1(1981).
  • Unification of fundamental forces and Cosmology, Matscience Report108(1981).
  • On a Number theoretic problem involved in the study of physics of spin systems, Lecture Notes in Mathematics 938, Springer-Verlag, Ed.K.Alladi,p.82.
  • On the classical solution of SO(3) Gauge theory and 't Hooft-Polyakov Momopole, Pramana24,457(1985).
  • Supersymmetric Quantum Mechanics and the Phase problem of the Harmonic Oscillator, Physical Review, D33,3790(1986) Rapid Communications.
  • The concept of Maximum CP-nonconservation in arbitrary number of generations, J.Sc.Tech.Res.49, 174(1990).
  • A Symmetric Mass Matrix, Physical Review D43,945(1991).
  • Supersymmetric Dirac Oscillator, J.Math.Phys.33,1114(1992).

B. Group Theory

  • Some remarks on the construction of invariants of semi-simple Lie groups, J.Math.Phys.7,1886(1966).
  • A compact formula for the C.G.coefficient of SU(3). Nuovo Cimento 45A,1046(1966).
  • Internal multiplicity Structure and Clebsch-Gordan series of Exceptional Group, G(2), J.Math.Phys.8,2206(1967).
  • Lectures on Group Theory and Applications, Matscience Report 61, 1967.
  • Generating Functions of Classical Groups and Evaluation of Partition Functions, J.Math.Phys.10,1704 (1969).
  • General Involutional Transformations and the representation of GL(n),J.Math.Phys.12,377(1971).
  • On the symmetries of Racah Coefficients, J.Math.Pjys.16,1528(1975).
  • Multi-quark model and the Embedding of Groups,J.Math.Phys.18,849(1977).
  • Generalized Inverse and Kostant's partition functions, Matscience Report.(1977).
  • Indecomposable representations of the Algebra of Para-Bose oscillators, J.Math.Phys.24,1032(1983).
  • A unified description of the representations of the Graded Algebra GL(2),J.Math.Phys.25,1253(1984).
  • Indecomposable representations of some Graded Algebras, Springer Lecture Notes in Physics 201,73(1984).
  • An Introduction to the Group Theory underlying the Interacting Boson Model, Proc.Recent Trends in Theor.Nuclear Phys. Macmillan(India),Ed.K.S.Rao,15(1987).
  • Invariant Equations and Indecomposable Representations, Proc.XIV Group Theory Conf., Seoul, Korea, p.280 (1985), World. Scientific(Singapore). Eds.Y.M.Cho..
  • A new recurrence formula for the Racah Coefficient, J.Phys.A20,3041(1987).
  • Kostant's Partition functions in Kac-Moody algebras, Workshop on Particle Physics, Kanpur, India (1988), Ed.H.S.Mani, and R.Ramachandran, World Scientific, Singapore.p.457.
  • Multiplicative Diophantine Equations Journal of Number Theory 42,20(1992).
  • Kostant Partition Functions for Affine Kac-Moody Algebras Internat.J.Math. & Math.Sci.539-552(1997).
  • Kostant's Partition functions for twisted Kac-Moody algebras, ..J.Math. & Math.Sci., In Print (1999).
  • Third Order transport coefficient for charged particle swarms, Journal of Chemical Physics, Vol 100, n 5, 1 Feb 1999, Slobodan B. Vrhovac and Zoran Lj. Petrovic, Larry Viehland and Thalanayar S. Santhanam

C. Clifford Algebras, Generalized Clifford Algebras

  • Clifford Algebra and massless Fields, Progr.Theor.Phys.(Japan},41,264(1969).
  • Representation Theory of Generalized Clifford Algebras, J.Math.Phys.Sci (India),3,307(1969).
  • The Fundamental Theorem in Spinor Theory, Symp. on Theor.Phys.Vol10, Plenum Press, N.Y.(USA)
  • Helicity Matrices and Generalized Clifford Algebras,J.Math.Anal and Appl.26, 275 (1969).
  • Generalized Clifford Algebra and the Unitary Group,J.Math.Anal and Appl.27, 164 (1969).
  • Generalized Idempotent Matrices, J.Math.Anal and Appl.27, 563 (1969).
  • Representation Theory of Generalized Clifford Algebras, Proc.I Mastech Conf.1969.
  • Sylvester Matrix and Symmetrical Components of Electrical Network, Matrix and Tensor Quarterly 21, 121(1971).
  • Evaluation of sprus of products of generalized Clifford elements, Matrix and Tensor Quarterly 23,99 (1973).
  • Traces of Generalized Clifford Elements, Matscience Report 79, 1973.

D. Relativistic Wave Equations

  • The Equations of Motion in Odd space-time and CPT Invariance,J.Math.Phys.11,1122(1970).
  • Relativistic wave Equations describing the Neutrino, Nuovo.Cimento Letters 3,190 (1972).
  • CP and CPT non-invarant Relativistic Equations and the Two-component Neutrino, Nuovo Cimento Letters 6,99 (1973).
  • Linear Relativistic wave Equations for Particles with spin ½, Progr.Theor.Phys(Japan), 47,671(1972).
  • On the new spin ½ Equation, Progr.Theor Phys(Japan)50,992(1973).
  • Bhabha Equations for unique mass and spin, Fortschrift der physik Heft 8,1974.
  • Unitary Foldy-Wouthysen Transformations for Particles of arbitrary spin, Nuovo Cimento Letters10, 737 (1974).
  • Invariant Wave Equations and Indecomposable Representations,Proc.14th Group Theory Conference, Seoul, Korea, World Scientific (Singapore)1986.p.280 Ed.Y.M.Cho.

E. Coherent and Generalized Coherent States

  • Angular Momentum coherent states, Proc. International Conf. On Frontiers of Physics, Singapore, 1978.Singapore National Academy of Sciences,Vol.21978, p.1167-96,Ed.K.K.Phua.
  • Angular Momentum Coherent States, Matscience Report92, 1978.
  • Coherent States of Para-Bose oscillators,J.Aust. Math.Soc.B22,210 (1980).
  • Generalized Coherent States,Proc. Einstein Centennial Celebrations, Carbondale, Illinois, U.S.A.Plenum Press, N.Y., p.337(1980)., Ed.B.Gruber, and R.Millman.
  • Impossibility of squeezed coherent states for a Para-Bose Oscillator, Physical Review 30D,2251(1984).
  • Representation of Rigid Stimulus Transformations by Cortical Activity Patterns in "Geometric Representations of Perceptual Phenomena", Lawrence Erlbaum Associates Publishers, p.61,(1995), Eds.R.Duncan Luce

F. Quantum Mechanics in Finite Dimensions

  • Weyl's Quantum Mechanics and Uncertainty Principle, Proc.Refresher Course for Post-graduate Teachers,1973,Presidency College, Madras, India.Ed.P.Thirugnanasambandam.
  • Quantum Mechanics in Finite Dimensions, Foundations of Physics 6,583(1976).
  • Canonical Commutation Relations for operators with a bounded spectrum, Phys.Letters.56A,345(1976).
  • Quantum Mechanics of B0unded Operators, in "Uncertainty Principle and Foundations of Quantum Mechanics",Eds.W.Price, and S.S.Chissick, John-Wiley, London,227-243, 1977.Werner. Heissenberg Memorial Volume.
  • Quantum Mechanics in Discrete Space and Angular Momentum, Foundations of Physics 7,121 (1977).
  • Does Weyl's Commutation Relation imply a Generalized Statistics? Nuovo Cimento Letters 20, 13 (1977).
  • Quantum Mechanics in Finite Space, Aust.J.Phys.31,233 (1978).
  • Finite Dimensional Quantum Mechanics of a Particle, Int.J.Theor.Phys.20, 755 (1981).
  • Finite Dimensional Quantum Mechanics of a Particle II, Int.J.Theor.Phys.21, 351 (1982).
  • Quantum Mechanics in Finite Space, Physica 114,445 (1982).
  • Finite Fourier Transformations and the Hamistonian of finite dimensional quantum systems, IC/82/12 Trieste..
  • Finite dimensional matrix representations if Differential operators, determinantal form,and zeros of special functions,IC/86/379, Trieste.
  • Matrix representation of differential operators and applications to special functions,Proc. International conference on Special functions and applications, Gorakpur, U.P.,India.1986.
  • Incompatible operators in Discrete Quantum Mechanics, Phys.Letters A 135,235 (1989).
  • A Note on the Angular Fourier Transformation, Proc.International Conference on Harmonic Oscillator, Mexico, 1994. NASA Report, p.249.
  • An algorithm for the basis of the Finite Fourier Transformation, Proc. International workshop on Harmonic Oscillators, Mexico, 1994. NASA Report, p.239.
  • Quantum Groups, deformed oscillators, and Heisenberg-Weyl quantum Mechanics, in Selected Topics in Mathematical Physics, Allied Publishers, Ltd(India),1995, p303.Eds. R.Sridar Prof.Vasudevan Memorial Volume.
  • Finite-Space Quantum Mechanics and Krawtchuk Functions, Proc. International Workshop on Special Functions held in Madras, India, 1997, Eds. K.S. Rao et al., Allied Publishers (India), pg 192.
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