In order to entangle the functions to be transformed, we proposed the entangled. Fourier integration transformation (EFIT) which has the property of keeping modulus-invariant for its inverse transformation. Then we… Click to show full abstract
In order to entangle the functions to be transformed, we proposed the entangled. Fourier integration transformation (EFIT) which has the property of keeping modulus-invariant for its inverse transformation. Then we then studied Wigner operator’s EFIT and found that a function’s EFIT is just related to its Weyl-corresponding operator’s matrix element, in so doing we also derived new operator re-ordering formulas δx−Py−Q=1π::e−2iP−xQ−y::$$ \delta \left(x-P\right)\left(y-Q\right)=\frac{1}{\pi }{\displaystyle \begin{array}{c}:\\ {}:\end{array}}{e}^{-2i\left(P-x\right)\left(Q-y\right)}\ {\displaystyle \begin{array}{c}:\\ {}:\end{array}} $$;δy−Qx−P=1π::e2iP−xQ−y::$$ \delta \left(y-Q\right)\left(x-P\right)=\frac{1}{\pi }{\displaystyle \begin{array}{c}:\\ {}:\end{array}}{e}^{2i\left(P-x\right)\left(Q-y\right)}\ {\displaystyle \begin{array}{c}:\\ {}:\end{array}} $$, where P, Q are momentum and coordinate operator respectively, the symbol ::::$$ {\displaystyle \begin{array}{c}:\\ {}:\end{array}}\ {\displaystyle \begin{array}{c}:\\ {}:\end{array}} $$ denotes Weyl ordering. By virtue of EFIT we also found the operator which can generate fractional squeezing transformation.
               
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