TITLE:
Affine Eikonal, Wavization and Wigner Function
AUTHORS:
Akihiro Ogura
KEYWORDS:
Affine Eikonal, Wavization of Gabor Function, Wigner Function
JOURNAL NAME:
Journal of Modern Physics,
Vol.7 No.13,
September
28,
2016
ABSTRACT: The aim in this paper is to construct an affine transformation using the classical physics analogy between the fields of optics and mechanics. Since optics and mechanics both have symplectic structures, the concept of optics can be replaced by that of mechanics and vice versa. We list the four types of eikonal (generating functions). We also introduce a unitary operator for the affine transformation. Using the unitary operator, the kernel (propagator) is calculated and the wavization (quantization) of the Gabor function is discussed. The dynamic properties of the affine transformed Wigner function are also discussed.