幂计数算子的表示

Representation of power number operators

讨论平方可积Bernoulli泛函空间L^(2)(M)上幂计数算子a^(N)的表示问题,a是任意非负实数.得到4种表示方法:a^(N)的谱表示,a^(N)以{an;n≥0}为其特征值,a^(N)的特征向量全体构成L^(2)(M)的一组标准正交基,当a=2时,2^(N)可用■-QNBs的异型等时混合积算子级数表示;关于L^(2)(M)的标准正交基的表示;利用真空态Zϕ以及■-QNBs,给出a^(N)的■-QNBs-真空态表示;利用一列特殊的■-QNBs,给出a^(N)的极限表示.考虑a^(N)与■-QNBs等时混合积复合后特征根与特征子空间均会随复合顺序发生变化.

The representation of the power number operator a^(N) was proposed,where a is a non-negative real number,a^(N) is densely defined in L^(2)(M),which the space of the square-integrable Bernoulli functional noise.The following conclusions are obtained:the first one was the spectral representation,where{an;n≥0}is the spectrum of a^(N),and the eigenvectors of a^(N) constituted a standard orthogonal basis of L^(2)(M);a^(N) could be represented by the QNBs of L^(2)(M);the vacuum state representation of a^(N) was given using the vacuum state Zϕas well as-QNBs;obtained with the help of the-QNBs{∂σn;n≥0}.The constructure of the composition of a^(N) and{∂σ,∂^(*)_(σ);σ∈}was considered.