Phase amplitude conformal symmetry in Fourier transforms

30th International Colloquium on Group Theoretical Methods in Physics

Kuwata, S.^1

Department of Frontier Sciences, Graduate School of Information Sciences, Hiroshima City University, Asaminami-ku, Hiroshima

731-3194, Japan^1

关键词: Complex-valued;    Conformal symmetry;    Uncertainty relation;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/597/1/012052/pdf
DOI  :  10.1088/1742-6596/597/1/012052

来源: IOP

【 摘 要 】

For the Fourier transform : L2(R) → L2(R) of a complex-valued even or odd function ψ, it is found that the amplitude invariance |ψ| = |ψ| leads to a phase invariance or inversion as arg(ψ) = ±argψ + θ (θ = constant). The converse holds unless arg ψ = constant. The condition |ψ| = |ψ| is required in dealing with, for example, the minimum uncertainty relation between position and momentum. Without the evenness or oddness of ψ, |ψ| = |ψ| does not necessarily imply arg(ψ) = ±argψ + θ, nor is the converse.