A New Kind of Integration Transformation in Phase Space Related to Two Mutually Conjugate Entangled-State Representations and Its Uses in Weyl Ordering of Operators
LV Cui-Hong1, FAN Hong-Yi1,2
1Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026 2Department of Physics, Shanghai Jiao Tong University, Shanghai 200030
A New Kind of Integration Transformation in Phase Space Related to Two Mutually Conjugate Entangled-State Representations and Its Uses in Weyl Ordering of Operators
LV Cui-Hong1, FAN Hong-Yi1,2
1Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026 2Department of Physics, Shanghai Jiao Tong University, Shanghai 200030
摘要Based on the two mutually conjugate entangled state representations |ξ> and |η>, we propose an integration transformation in ξ-η phase space , and its inverse transformation, which possesses some well-behaved transformation properties, such as being invertible and the Parseval theorem. This integral transformation is a convolution, where one of the factors is fixed as a special normalized exponential function. We generalize this transformation to a quantum mechanical case and apply it to studying the Weyl ordering of bipartite operators, regarding to (Q1-Q2)↔(P1-P2) ordered and simultaneously (P1+P2)↔(Q1+Q2) ordered operators.
Abstract：Based on the two mutually conjugate entangled state representations |ξ> and |η>, we propose an integration transformation in ξ-η phase space , and its inverse transformation, which possesses some well-behaved transformation properties, such as being invertible and the Parseval theorem. This integral transformation is a convolution, where one of the factors is fixed as a special normalized exponential function. We generalize this transformation to a quantum mechanical case and apply it to studying the Weyl ordering of bipartite operators, regarding to (Q1-Q2)↔(P1-P2) ordered and simultaneously (P1+P2)↔(Q1+Q2) ordered operators.
LV Cui-Hong;FAN Hong-Yi;. A New Kind of Integration Transformation in Phase Space Related to Two Mutually Conjugate Entangled-State Representations and Its Uses in Weyl Ordering of Operators[J]. 中国物理快报, 2010, 27(5): 50301-050301.
LV Cui-Hong, FAN Hong-Yi,. A New Kind of Integration Transformation in Phase Space Related to Two Mutually Conjugate Entangled-State Representations and Its Uses in Weyl Ordering of Operators. Chin. Phys. Lett., 2010, 27(5): 50301-050301.
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2010, Vol. 27 
, and its inverse transformation, which possesses some well-behaved transformation properties, such as being invertible and the Parseval theorem. This integral transformation is a convolution, where one of the factors is fixed as a special normalized exponential function. We generalize this transformation to a quantum mechanical case and apply it to studying the Weyl ordering of bipartite operators, regarding to (Q1-Q2)
, and its inverse transformation, which possesses some well-behaved transformation properties, such as being invertible and the Parseval theorem. This integral transformation is a convolution, where one of the factors is fixed as a special normalized exponential function. We generalize this transformation to a quantum mechanical case and apply it to studying the Weyl ordering of bipartite operators, regarding to (Q1-Q2)