# PUBLICATIONS

1. N. R. Ranganathan and R. Jagannathan
Generalized Clifford groups and their physical relevance
Proc. II Int. Colloq. Group Theoretical Methods in Physics (University of Nijmegen, the Netherlands, 1973) Vol.B, 232-241

2. R. Jagannathan and N. R. Ranganathan
On generalized Clifford groups - I
Rep. Math. Phys. 5 (1974) 131-143

3. R. Jagannathan and N. R. Ranganathan
On generalized Clifford groups - II
Rep. Math. Phys. 7 (1975) 229-238

4. R. Jagannathan and H. N. V. Dutt
A negative energy relativistic wave equation
J. Math. Phys. Sci. 9 (1975) 301-302

5. R. Jagannathan
On certain numerical and combinatorial aspects of Clifford algebra, its applications and associated structures
Proc. Conf. Numerical Analysis and Combinatorial Methods (The Institute of Mathematical Sciences, Madras) MATSCIENCE Report 79 (1975) 60-78

6. Alladi Ramakrishnan and R. Jagannathan
A new approach to matrix theory or many facets of the matrix decomposition theorem
Topics in Numerical Analysis - II (Proc. Royal Irish Academy Conf. Numerical Analysis, Dublin, Ireland, 1974) Ed. J H Miller (Academic Press, London, 1976) 133-139

7. R. Jagannathan and N. R. Ranganathan
A new form of magnetic Bloch functions and applications to magnetic band structure calculations
Phys. Stat. Solidi B 74 (1976) 667-672

8. R. Jagannathan
Matrix approach to certain number theoretical problems
Proc. Conf. Matrix algebra, Computational Methods and Number Theory (The Institute of Mathematical Sciences, Madras) MATSCIENCE Report 87 (1977) 6-18

9. R. Jagannathan
Comments on some physical applications of generalized Clifford algebras: Problems of quantum canonical transformations, lattice dynamics, and Bloch electrons in a homogeneous magnetic field
Proc. Conf. Structure of Matter: Mathematics and Phenomenology (The Institute of Mathematical Sciences, Madras) MATSCIENCE Report 93 (1978) 41-56

10. R. Jagannathan and R. Vasudevan
A note on representations of para-fermi algebra
J. Math. Phys. 19 (1978) 1493-1494

11. V. A. Chinnappan, R. Jagannathan and G. A. Savari Raj
Isotopic invariants of nonlinear symmetrical XY$_2$ and planar symmetrical XY$_3$ molecules
Indian J. Pure and Appl. Phys. 16 (1978) 668-672

12. R. Jagannathan
Contributions to Clifford algebra, its generalizations and new kinds of representations of the Dirac equation
Proc. Conf. Mathematical Methods in Physics (The Institute of Mathematical Sciences, Madras) MATSCIENCE Report 96A (1979) 51-73

13. R. Jagannathan and R. Vasudevan
Representations of a parabose algebra using only a single Bose field
J. Math. Phys. 20 (1979) 390-392

14. R. Jagannathan and R. Vasudevan
On $kq$-representations in quantum mechanics
J. Phys. A : Math. Gen. 12 (1979) 1367-1373

15. R. Jagannathan and R. Vasudevan
New representations of para-fermi and parabose fields
Proc. Conf. Probability, Stochastic Processes and Statistical Mechanics (The Institute of Mathematical Sciences, Madras) MATSCIENCE Report 97 (1979) 1-11

16. R. Jagannathan
A matrix approach to certain inverses of arithmetical functions
Proc. Conf. Number Theory (The Institute of Mathematical Sciences, Madras) MATSCIENCE Report 101 (1980) 75-81

17. R. Jagannathan, V. A. Chinnappan and G. A. Savari Raj
On isotopic invariants of polyatomic molecules
Indian J. Pure and Appl. Phys. 18 (1980) 964-969

18. R. Jagannathan
On the use of matrix methods in certain number theoretical problems
Proc. Conf. Number Theory (The Institute of Mathematical Sciences, Madras) MATSCIENCE Report 104 (1981) 131-138

19. R. Jagannathan and R. Vasudevan
Boson, paraboson and boson-fermion representations of some graded Lie algebras
J. Math. Phys. 22 (1981) 2294-2299

20. R. Jagannathan, T. S. Santhanam and R. Vasudevan
Finite-dimensional quantum mechanics of a particle
Int. J. Theor. Phys. 20 (1981) 755-773

21. R. Jagannathan and T. S. Santhanam
Finite-dimensional quantum mechanics of a particle - II
Int. J. Theor. Phys. 21 (1982) 351-362

22. R. Jagannathan
Dynamics of Bloch electrons in a homogeneous magnetic field: A pseudopotential formalism

23. R. Jagannathan and T. S. Santhanam
On a number theoretical problem involved in the study of the physics of spin systems
Proc. Conf. Number Theory (The Institute of Mathematical Sciences, Madras), Ed. K. Alladi, Springer Lecture Notes in Mathematics 938 (1982) 82-92

24. R. Jagannathan
New forms of the Dirac equation with the Dirac matrices replaced by operators involving internal variables
Proc. Conf. Particle Interactions and Astrophysics (The Institute of Mathematical Sciences, Madras) MATSCIENCE Report 108 (1982) 203-213

25. N. Subramaniam, R. Srinivasamoorthy, G. A. Savari Raj and R. Jagannathan
Molecular constants using isotopic frequency shifts

26. R. Jagannathan
On some new concepts in probability theory
Proc. Winter School on Stochastic Processes (University of Hyderabad, Hyderabad) , Eds. G. S. Agarwal and S. Datta Gupta, Springer Lecture Notes in Physics 184 (1983) 54-60

27. R. Jagannathan
Finite-dimensional quantum mechanics of a particle - III: The Weylian quantum mechanics of confined quarks
Int. J. Theor. Phys. 22 (1983) 1105-1121

28. R. Jagannathan
A note on the Lorentz transformation in three dimensions
J. Math. Anal. Appl. 94 (1983) 242-245

29. N. Subramaniam, R. Srinivasamoorthy and R. Jagannathan
On the application of perturbation theory for the calculation of molecular constants from isotopic frequency shifts
Indian J. Pure and Appl. Phys. 21 (1983) 731-732

30. N. Subramaniam, R. Srinivasamoorthy, G. A. Savari Raj and R. Jagannathan
On the use of root location theorems for matrices in the problem of determination of molecular force constants
Indian J. Phys. 58B (1984) 349-352

31. R. Jagannathan
On projective representations of finite abelian groups
Proc. Conf. Number Theory (The Institute of Mathematical Sciences, Madras), Ed. K. Alladi, Springer Lecture Notes in Mathematics 1122 (1985) 130-139

32. R. Jagannathan, R. Simon, E. C. G. Sudarshan and R Vasudevan
Dynamical maps and nonnegative phase-space distribution functions in quantum mechanics
Phys. Lett. A 120 (1987) 161-164

33. R. Jagannathan, R. Simon, E. C. G. Sudarshan and N. Mukunda
Quantum theory of magnetic electron lenses based on the Dirac equation
Phys. Lett. A 134 (1989) 457-464

34. R. Jagannathan
Quantum theory of electron lenses based on the Dirac equation
Phys. Rev. A 42 (1990) 6674-6689

35. R. Chakrabarti and R. Jagannathan
On the representations of $GL_q(n)$ using the Heisenberg-Weyl relations
J. Phys. A: Math. Gen. 24 (1991) 1709-1720

36. R. Chakrabarti and R. Jagannathan
On the representations of $GL_{p,q}(2)$, $GL_{p,q}(1|1)$ and the noncommutative spaces
J. Phys. A: Math. Gen. 24 (1991) 5683-5701

37. R. Chakrabarti and R. Jagannathan
A $(p,q)$-oscillator realization of two-parameter quantum algebras
J. Phys. A: Math. Gen. 24 (1991) L711-L718

38. K. Srinivasa Rao, J. Van der Jeugt, J. Raynal, R. Jagannathan and V. Rajeswari
Group theoretical basis for the terminating} $_3F_2(1)$ series
J. Phys. A: Math. Gen. 25 (1992) 861-876

39. K. S. Viswanathan, R. Parthasarathy and R. Jagannathan
Generalized $q$-fermion oscillators and $q$-coherent states
J. Phys. A: Math. Gen. 25 (1992) L335-L339

40. R. Chakrabarti and R. Jagannathan
A $(p,q)$-deformed Virasoro algebra
J. Phys. A: Math. Gen. 25 (1992) 2607-2614

41. R. Chakrabarti and R. Jagannathan
On the number operators of single-mode} $q$-oscillators
J. Phys. A: Math. Gen. 25 (1992) 6393-6398

42. R. Chakrabarti and R. Jagannathan
A two-parameter deformation of the Jaynes-Cummings model: A path integral representation
J. Phys. A: Math. Gen. 25 (1992) 6399-6408

43. R. Jagannathan, R. Sridhar, R. Vasudevan, S. Chaturvedi, M. Krishnakumari, P. Shanta and V. Srinivasan
On the number operators of multimode systems of deformed oscillators covariant under quantum groups
J. Phys. A: Math. Gen. 25 (1992) 6429-6453

44. S. Chaturvedi, R. Jagannathan, R. Sridhar and V. Srinivasan
Nonrelativistic quantum mechanics in a noncommutative space
J. Phys. A: Math. Gen. 26 (1993) L105-L112

45. R. Chakrabarti, R. Jagannathan and R. Vasudevan
A new look at the $q$-deformed calculus
Mod. Phys. Lett. A 8 (1993) 2695-2701

46. S. Chaturvedi, R. Jagannathan and V. Srinivasan
Tamm-Dancoff deformation of bosonic oscillator algebras
Mod. Phys. Lett. A 8 (1993) 3727-3734

47. R. Jagannathan
Dirac equation and electron optics
Dirac and Feynman: Pioneers in Quantum Mechanics, Eds. R. Dutt and A. K. Ray (Wiley Eastern, New Delhi, 1993) 75-82

48. S. A. Khan and R. Jagannathan
Theory of relativistic electron beam transport based on the Dirac equation
Proc. Third National Seminar on Physics and Technology of Particle Accelerators and their Applications(PATPAA93) (Calcutta, 1993) Ed. S. N. Chintalapudi (Inter-University Consortium of Department of Atomic Energy Facilities (IUC-DAEF) Publ.) 102-107

49. R. Chakrabarti and R. Jagannathan
On $U_{p,q}(gl(2))$ and a $(p,q)$-Vira-soro algebra
J. Phys. A: Math. Gen. 27 (1994) 2023-2035

50. R. Chakrabarti and R. Jagannathan
A $q$-deformation of the parasupersymmetric quantum mechanics
Int. J. Mod. Phys. A 9 (1994) 1411-1421

51. R. Chakrabarti and R. Jagannathan
Parabosons, Virasoro-type algebras and their deformations
J. Phys. A: Math. Gen. 27 (1994) L277-L283

52. P. Shanta, S. Chaturvedi, V. Srinivasan and R. Jagannathan
Unified approach to the analogues of single-photon and multiphoton coherent states for generalized boson oscillators
J. Phys. A: Math. Gen. 27 (1994) 6433-6442

53. S. A. Khan and R. Jagannathan
Quantum mechanics of charged-particle beam transport through magnetic lenses
Phys. Rev. E 51 (1995) 2510-2515

54. R. Chakrabarti and R. Jagannathan
On a nonstandard two-parametric quantum algebra and its connections with $U_{p,q}(gl(2))$ and $U_{p,q}(gl(1|1))$
Z. Phys. C: Particles and Fields 66 (1995) 523-528
(e-Print: arXiv:hep-th/9410163)

55. R. Jagannathan and J. Van der Jeugt
Finite-dimensional representations of the quantum group $GL_{p,q}(2)$ using the exponential map from $U_{p,q}(gl(2))$
J. Phys. A: Math. Gen. 28 (1995) 2819-2831
(e-Print: arXiv:hep-th/9411200)

56. J. Van der Jeugt and R. Jagannathan
Polynomial deformations of $osp(1/2)$ and generalized parabosons
J. Math. Phys. 36 (1995) 4507-4518
(e-Print: arXiv:hep-th/9410145)

57. R. Jagannathan and S. A. Khan
Wigner functions in charged particle optics
Selected Topics in Mathematical Physics - Professor R. Vasudevan Memorial Volume, Eds. R. Sridhar, K. Srinivasa Rao and V. Lakshminarayanan (Allied Publishers, Madras, Delhi, 1995) 308-321

58. J. Van der Jeugt and R. Jagannathan
The exponential map for representations of $U_{p,q}(gl(2))$
Proc. of the 4th International Colloquium on Quantum Groups and Integrable Systems, Prague, 1995: Czech. J. Phys. 46 (1996) 269-275
(e-Print: arXiv:q-alg/9507009)

59. R. Chakrabarti and R. Jagannathan
On the Hopf structure of $U_{p,q}(gl(1|1))$ and the universal ${\cal T}$-matrix of $Fun_{p,q}(GL(1|1))$
Lett. Math. Phys. 37 (1996) 191-199
(e-Print: arXiv:hep-th/9409161)

60. R. Jagannathan and S. A. Khan
Quantum theory of the optics of charged particles
Advances in Imaging and Electron Physics Vol.97, Ed. P. W. Hawkes (Academic Press, San Diego, 1996) 257-358

61. M. Conte, R. Jagannathan, S. A. Khan and M. Pusterla
Beam optics of the Dirac particle with anomalous magnetic moment
Part. Accel. 56 (1996) 99-125

62. R. Chakrabarti and R Jagannathan
The dual $(p,q)$-Alexander-Conway Hopf algebras and the associated ${\cal T}$-matrix
Z. Phys. C: Particles and Fields 72 (1996) 519-524
(e-Print: arXiv:q-alg/9602020)

63. B. Basu-Mallick, P. Ramadevi and R. Jagannathan
Multiparametric and coloured extensions of the quantum group $GL_q(N)$ and the Yangian algebra $Y(gl_N)$ through a symmetry transformation of the Yang-Baxter equation
Int. J. Mod. Phys. A 12 (1997) 945-962
(e-Print: arXiv:q-alg/9511028)

64. R. Jagannathan and S. A. Khan
Quantum mechanics of accelerator optics
ICFA Beam Dynamics Newsletter No. 13 (April, 1997) 21-27
(International Committee for Future Accelerators (ICFA))

65. R. Jagannathan
$(P,Q)$-Special functions
Proc. Workshop on Special Functions & Differential Equations (The Institute of Mathematical Sciences, Chennai, January, 1997), Eds. K. Srinivasa Rao, R. Jagannathan, G. Vanden Berghe and J. Van der Jeugt, (Allied Publishers, New Delhi, 1998) 158-164
(e-Print: arXiv:math.QA/9803142)

66. R. Jagannathan
The Dirac equation approach to spin-1/2 particle beam optics
Proc. 15th Advanced ICFA Beam Dynamics Workshop on Quantum Aspects of Beam Physics (January 1998, Monterey, California, U.S.A), Ed. Pisin Chen (World Scientific, Singapore, 1998) 670-681
(e-Print: arXiv:physics/9803042)

67. J. Van der Jeugt and R. Jagannathan
Realizations of $su(1,1)$ and $U_q(su(1,1))$ and generating functions for orthogonal polynomials
J. Math. Phys. 39 (1998) 5062-5078
(e-Print: arXiv:math-ph/9807019)

68. V. Lakshminarayanan, R. Sridhar and R. Jagannathan
A Lie algebraic treatment of dioptric power and optical aberrations
J. Opt. Soc. America A 15 (1998) 2497-2503

69. V. Sunilkumar, B. A. Bambah, R. Jagannathan, P. K. Panigrahi and V. Srinivasan
Coherent states of nonlinear algebras: Applications in quantum optics
J. Opt. B: Quantum Semiclass. Opt. 2 (2000) 126-132
(e-Print: arXiv:quant-ph/9907075)

70. V. Sunilkumar, B. A. Bambah and R. Jagannathan
Three dimensional quadratic algebras: Some realizations and representations
J. Phys. A: Math. Gen. 34 (2001) 8583-8596
(e-Print: arXiv:math-ph/0108027)

71. R. Jaganathan
Some introductory notes on quantum groups, quantum algebras, and their applications
Proc. the Institutional and Instructional Program on Quantum Groups and their Applications (March 2001, University of Madras, Chennai), Ed. S. Parvathi (Publ. # 10, The Ramanujan Institute, 2002) pp. 1-21
(e-Print: arXiv:math-ph/0105002)

72. V. Sunil Kumar, B. A. Bambah and R. Jagannathan
Jordan-Schwinger realizations of three dimensional polynomial algebras
Mod. Phys. Lett. A 17 (2002) 1559-1566
(e-Print: arXiv:math-ph/0205005)

73. R. Jaganathan
Quantum mechanics of Dirac particle beam optics: Single-particle theory
Proc. 18th Advanced ICFA Beam Dynamics Workshop on Quantum Aspects of Beam Physics (October 2000, Capri, Italy), Ed. Pisin Chen (World Scientific, Singapore, 2002) pp. 568-577
(e-Print: arXiv:physics/0101060)

74. R. Sridhar and R. Jagannathan
On the $q$-analogues of the Zassenhaus formula for disentangling exponential operators
To appear in the Proc. the International Conference on Special Functions - 2002 (IMSc, Chennai) to be published as a special issue of J. Comp. Appl. Math.
(e-Print: arXiv:math-ph/0212068)

75. R. Jaganathan
Quantum mechanics of Dirac particle beam transport through optical elements with straight and curved axes
To appear in the Proc. 28th Advanced ICFA Beam Dynamics Workshop on Quantum Aspects of Beam Physics (January 2003, Hiroshima, Japan) Ed. Pisin Chen (World Scientific, Singapore)
(e-Print: arXiv:physics/0304099)

76. S. A. Khan, R. Jagannathan and R. Simon
Foldy-Wouthuysen transformation and a quasiparaxial approximation scheme for the scalar wave theory of light beams
(e-Print: arXiv:physics/0209082)

For copies of the above publications please send email to: jagan@imsc.res.in