Document Type : Original Article


Department of Physics, Razi University, Kermanshah, Iran


The quantum formulation of a physical system is essentially based on the associated creation and annihilation operators. In this article, we introduce these ladder operators for a movement particle on the circle and 2-dimensional sphere by Berezin’s quantization .This approach is derived from the resolution of the unity condition in coherent states. In other words, the coherent states provide a straight forward quantization scheme from a classical state to corresponding quantum state. In this article, we study the coherent states of these systems from heat kernel function point of view.


  1. R J Glauber, Phys .Rev. 131(1963) 2766.

  2. J P Gazeau , “Coherent states in quantum physics”, Wiley-VCH, Berlin (2009).

  3. K Kowalski, J Remielinski, and L C Papaloucas, J . Phys.A: Math.Gen 29 (1996) 4149. 

  4. A Perelomov, “Generalized coherent states and their application”, Springer-verlag, Berlin, Heidelerge, Newyork, London, Parise, Tokyo (1986).

  5. K Kowalski and J Remielinski, J. Phys. A : Math. Gen, 33 (2000) 6035.

  6. A O Barut, “Dynamic group and generalized symmetries in quantum theory” University of Canterbury, Christchurch (1971) .

  7. E A Berezin, Common. Math .Phy. 40 (1975) 153.

  8. B Hall and J J Mitchell, J. Math. Phys. 43 (2002).

  9. T Thiemann, Class. Quantum Grav, 23 (2006) 2063.

  10. T Thiemann, “Modern canonical quantum general relativity”,Cambridge University Press, (2007).

  11. B ‎I S Gradshteyn ‎and ‎I M Ryshik, ‎Tables of Integrals, Series and Products, Fizmatgiz, Moscow. Lett. A ‎(‎1994)‎‎‎‎‎‎‎‎‎‎‎.


ارتقاء امنیت وب با وف ایرانی