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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.
[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 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 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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[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 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 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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