全态集到广义基的重整化及其恒等式的分解
Renormalization of total sets of states into generalized bases with a resolution of the identity
摘要：
在有限维希尔伯特空间中考虑了一组状态，对于这些状态，我们没有确定的身份（一个“预基”）。一个着装形式主义重新正规化他们到密度矩阵解决的身份，并使他们成为一个“广义基础”，这是实际有用的。穿衣机制的灵感来自于合作博弈论中的Shapley方法，它使用了莫比乌斯变换。在这些广义基中存在着非独立性和冗余性，这是量化的香农型熵。由于这种冗余，基于广义基的计算对物理变化敏感，并且在存在噪声的情况下是鲁棒的。例如，当系数中插入噪声时，在这样的广义基中的任意向量的表示是鲁棒的。此外，在具有在耦合常数的某个值处突然改变的基态的物理系统中，所提出的方法检测到这样的变化，即使当噪声被添加到系统的哈密顿量中的参数时。
英文摘要：
A total set of states for which we have no resolution of the identity (a `pre-basis'), is considered in a finite dimensional Hilbert space. A dressing formalism renormalizes them into density matrices which resolve the identity, and makes them a `generalized basis', which is practically useful. The dresssing mechanism is inspired by Shapley's methodology in cooperative game theory, and it uses Möbius transforms. There is non-independence and redundancy in these generalized bases, which is quantified with a Shannon type of entropy. Due to this redundancy, calculations based on generalized bases, are sensitive to physical changes and robust in the presence of noise. For example, the representation of an arbitrary vector in such generalized bases, is robust when noise is inserted in the coefficients. Also in a physical system with ground state which changes abruptly at some value of the coupling constant, the proposed methodology detects such changes, even when noise is added to the parameters in the Hamiltonian of the system.
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