标题： 几何量子力学的形变量子化 显示英文标题

标题： Deformation Quantization of Geometric Quantum Mechanics

摘要： 对经典非相对论单粒子系统的二次量子化被考虑为薛定谔无自旋场的形变量子化。 在假设薛定谔场的相空间为$C^{\infty}$的前提下，讨论并比较了Weyl-Wigner-Moyal和Berezin形变量子化方法。 然后，在假设相空间为$CP^{\infty}$并带有Fubini-Study凯勒度量的情况下，也使用Berezin方法对几何量子力学进行了量子化。 最后，得到了任意粒子态的Wigner函数及其演化方程。 如所示，这种新的“二次量子化”与以前的结果有本质的不同。 例如，每个态都是总粒子数算符的本征态，对应的本征值总是${1 \over \hbar}$。 显示英文摘要

摘要： Second quantization of a classical nonrelativistic one-particle system as a deformation quantization of the Schrodinger spinless field is considered. Under the assumption that the phase space of the Schrodinger field is $C^{\infty}$, both, the Weyl-Wigner-Moyal and Berezin deformation quantizations are discussed and compared. Then the geometric quantum mechanics is also quantized using the Berezin method under the assumption that the phase space is $CP^{\infty}$ endowed with the Fubini-Study Kahlerian metric. Finally, the Wigner function for an arbitrary particle state and its evolution equation are obtained. As is shown this new "second quantization" leads to essentially different results than the former one. For instance, each state is an eigenstate of the total number particle operator and the corresponding eigenvalue is always ${1 \over \hbar}$.