场的相干表示与形变量子化
Coherent representation of fields and deformation quantization
摘要：
受量子光学和量子信息理论中相空间描述的一些著名结果的启发，我们的目标是通过在形变量子化程序中明确考虑标量场的全纯表示来描述量子场论的形式。值得注意的是，一个对称有序算子的符号在全纯变量方面可以直接通过与正常有序算子相关联的胡西米分布的量子场模拟来获得。这种关系也允许建立一个$c$之间的Moyal和正常的星产品的等价性。此外，通过将密度算符写成相干态，我们能够直接引入维格纳泛函分布的一系列表示，这可能是方便的，以便计算量子场可观测量的概率分布，而无需进行形式的相空间积分。
英文摘要：
Motivated by some well-known results in the phase space description of quantum optics and quantum information theory, we aim to describe the formalism of quantum field theory by explicitly considering the holomorphic representation for a scalar field within the deformation quantization program. Notably, the symbol of a symmetric ordered operator in terms of holomorphic variables may be straightforwardly obtained by the quantum field analogue of the Husimi distribution associated with a normal ordered operator. This relation also allows establishing a $c$-equivalence between the Moyal and the normal star-products. In addition, by writing the density operator in terms of coherent states we are able to directly introduce a series representation of the Wigner functional distribution which may be convenient in order to calculate probability distributions of quantum field observables without performing formal phase space integrals at all.
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