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Weyl ordering expansion for optical field phase operator and inverse operators

Li Xue-Chao Yang Yang Fan Hong-Yi

Weyl ordering expansion for optical field phase operator and inverse operators

Li Xue-Chao, Yang Yang, Fan Hong-Yi
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  • Using the technique of integration within an ordered product of operators, we derive Weyl ordered expansion for optical field phase operator and inverse of creation and annhilation operators. The results are used to obtain the classical correspondence, new generation function formula of some special functions and new integration formulas. In particular, for the first time we derive complex Gaussian integral formula when the integrand has negative power function.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 10975125, 11175113).
    [1]

    Dirac P A M 1927 Proc. R. Soc. London A 114 243

    [2]

    Carruthers P, Nieto M M 1968 Rev. Mod. Phys. 40 411

    [3]

    Wigner E P 1932 Phys. Rev. 40 749

    [4]

    Klauder J R, Skagerstam B S 1985 Coherent States (Singerpore:World Scientific Publishing)

    [5]

    Scully M O, Zubairy M S 1997 Quantum Optics (United Kingdom:Cambridge University Press)

    [6]

    Glauber R J 1963 Phys. Rev. 130 2529

    [7]

    Weyl H 1927 Z. Phys. A 46 1

    [8]

    Fan H Y 1992 J. Phys. A 25 3443

    [9]

    Fan H Y, Hu L Y 2008 Chin. Phys. B 17 1640

    [10]

    Yuan H C, Xu X X 2010 Acta Phys. Sin. 61 064205 (in Chinese) [袁洪春, 徐学翔 2012 物理学报 61 064205]

    [11]

    Fan H Y 2008 Ann. Phys. 323 1502

    [12]

    Jiang N Q, Fan H Y, Hu L Y 2011 J. Phys. A:Math. Theor. 44 195302

    [13]

    Xu X X,Yuan H C, Hu L Y 2010 Acta Phys. Sin. 59 4661 (in Chinese) [徐学翔, 袁洪春, 胡利云 2010 物理学报 59 4661]

    [14]

    Dirac P A M 1966 Lectures on Quantum Field Theory (New York:Academic)

    [15]

    Fan H Y 1993 Phys. Rev. A 47 4521

  • [1]

    Dirac P A M 1927 Proc. R. Soc. London A 114 243

    [2]

    Carruthers P, Nieto M M 1968 Rev. Mod. Phys. 40 411

    [3]

    Wigner E P 1932 Phys. Rev. 40 749

    [4]

    Klauder J R, Skagerstam B S 1985 Coherent States (Singerpore:World Scientific Publishing)

    [5]

    Scully M O, Zubairy M S 1997 Quantum Optics (United Kingdom:Cambridge University Press)

    [6]

    Glauber R J 1963 Phys. Rev. 130 2529

    [7]

    Weyl H 1927 Z. Phys. A 46 1

    [8]

    Fan H Y 1992 J. Phys. A 25 3443

    [9]

    Fan H Y, Hu L Y 2008 Chin. Phys. B 17 1640

    [10]

    Yuan H C, Xu X X 2010 Acta Phys. Sin. 61 064205 (in Chinese) [袁洪春, 徐学翔 2012 物理学报 61 064205]

    [11]

    Fan H Y 2008 Ann. Phys. 323 1502

    [12]

    Jiang N Q, Fan H Y, Hu L Y 2011 J. Phys. A:Math. Theor. 44 195302

    [13]

    Xu X X,Yuan H C, Hu L Y 2010 Acta Phys. Sin. 59 4661 (in Chinese) [徐学翔, 袁洪春, 胡利云 2010 物理学报 59 4661]

    [14]

    Dirac P A M 1966 Lectures on Quantum Field Theory (New York:Academic)

    [15]

    Fan H Y 1993 Phys. Rev. A 47 4521

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  • Received Date:  02 September 2012
  • Accepted Date:  26 December 2012
  • Published Online:  20 April 2013

Weyl ordering expansion for optical field phase operator and inverse operators

  • 1. School of Science, Anhui University of Science and Technology, Huainan 232001, China;
  • 2. Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China;
  • 3. Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 10975125, 11175113).

Abstract: Using the technique of integration within an ordered product of operators, we derive Weyl ordered expansion for optical field phase operator and inverse of creation and annhilation operators. The results are used to obtain the classical correspondence, new generation function formula of some special functions and new integration formulas. In particular, for the first time we derive complex Gaussian integral formula when the integrand has negative power function.

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