, Volume 23, Issue 3, pp 327–332 | Cite as

Cumulant functions in optical coherence theory

  • CL Mehta


Cumulant functions are introduced to describe the statistical state of a radiation field. These functions are simply related to the optical coherence functions but have some interesting features. It is shown that if the cumulant functions of all orders greater than some numberN 0 vanish then they also vanish for all orders greater than 2. Thermal field is the only field having this property. This property holds whether the field is described by a classical stochastic process or by a quantum density operator. Further the particular operator ordering used in defining these cumulant functions for the quantized field affects only the second order cumulant function. To describe the statistical state of a vector field such as partially polarized or unpolarized radiation, one would need to introduce cumulant tensors.


Cumulant functions optical coherence Marcinkiewicz theorem 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Agarwal G S and Wolf E 1970Phys. Rev. D2 2161ADSMathSciNetGoogle Scholar
  2. Davenport W B and Root W L 1958An introduction to the theory of random signals and noise (New York: McGraw Hill)MATHGoogle Scholar
  3. Gabor D 1946J. Inst. Elec. Engrs. 93 429Google Scholar
  4. Glauber R J 1963Phys. Rev. 131 2766CrossRefADSMathSciNetGoogle Scholar
  5. Kano Y 1965J. Math. Phys. 6 1913CrossRefADSMathSciNetGoogle Scholar
  6. Lukacs E 1960Characteristic function (London: C. Griffin).Google Scholar
  7. Mandel L and Wolf E 1965Rev. Mod. Phys. 37 231CrossRefADSMathSciNetGoogle Scholar
  8. Marcinkiewicz J 1939Math. Z. 44 612CrossRefMathSciNetGoogle Scholar
  9. Mehta C L 1967Phys. Rev. Lett. 18 752CrossRefADSGoogle Scholar
  10. Mehta C L 1968J. Phys. A1 385ADSMathSciNetGoogle Scholar
  11. Mehta C L 1970 inProgress in optics (ed.) E Wolf (Amsterdam: North Holland) Vol. 8, p. 431Google Scholar
  12. Mehta C L and Sudarshan E C G 1965Phys. Rev. 138 B274Google Scholar
  13. Messiah A 1961Quantum mechanics (Amsterdam: North Holland) Vol. 1, p. 442Google Scholar
  14. Rice S O 1945Bell Syst. Tech. J. 23 282;24 46MathSciNetGoogle Scholar
  15. Rice S O 1945Bell Syst. Tech. J. 24 41MathSciNetGoogle Scholar
  16. Richter H 1956Wahrscheinlichkeitstheorie (Berlin: Springer Verlag)Google Scholar
  17. Schweber S S 1961An introduction to relativistic quantum field theory (New York: Harper and Row)Google Scholar
  18. Sudarshan E C G 1963Phys. Rev. Lett. 10 277MATHCrossRefADSMathSciNetGoogle Scholar

Copyright information

© Indian Academy of Sciences 1984

Authors and Affiliations

  • CL Mehta
    • 1
  1. 1.Physics DepartmentWest Virginia UniversityMorgantownUSA

Personalised recommendations