Remarks on the Bose description of the Pauli spin operators

Some remarks on the fragmentation of Bose condensates

We show how fragmentation of a Bose-Einstein condensate can occur given repulsive inter-particle interactions and a non-uniform external potential.

Influence of the Fermionic Exchange Symmetry beyond Pauli's Exclusion Principle

Pauli's exclusion principle has a strong impact on the properties of most fermionic quantum systems. Remarkably, the fermionic exchange symmetry implies further constraints on the one-particle picture. By exploiting those generalized Pauli constraints we derive a measure which quantifies the influence of the exchange symmetry beyond Pauli's exclusion principle. It is based on a geometric hierarchy induced by the exclusion principle constraints. We provide a proof of principle by applying our measure to a simple model. In that way, we conclusively confirm the physical relevance of the generaliz…

BCS-BEC 交叉中的等自旋和反自旋密度-密度关联：规范对称性、泡利不相容原理、威克定理与实验

Equal-spin and opposite-spin density-density correlations in the BCS-BEC crossover: Gauge Symmetry, Pauli Exclusion Principle, Wick's Theorem and Experiments

基于规范不变性和泡利原理，建立了自旋相关密度-密度关联的约束，并通过二维零温BCS到玻色区间的计算，揭示了两粒子不可约贡献（集体激发、多粒子散射和顶点修正）对描述实验的关键作用，特别是解释了反自旋密度-密度关联中实验观测到的极小值。

Spin and Statistics on the Groenewold-Moyal Plane: Pauli-Forbidden Levels and Transitions

The Groenewold-Moyal plane is the algebra A_θ(R^(d+1)) of functions on R^(d+1) with the star-product as the multiplication law, and the commutator [x_μ,x_ν] =i θ_{μν} between the coordinate functions. Chaichian et al. and Aschieri et al. have proved that the Poincare group acts as automorphisms on A_θ(R^(d+1))$ if the coproduct is deformed. (See also the prior work of Majid, Oeckl and Grosse et al). In fact, the diffeomorphism group with a deformed coproduct also does so according to the results of Aschieri et al. In this paper we show that for this new action, the Bose and Fermi commutation r…

Pauli乘积对角算符的非局域到局域本征基置换

Non-Local to Local Eigenbasis Permutations of Pauli Product Diagonal Operators

本研究通过证明非局域稀疏对角量子哈密顿量经本征基置换映射为局域形式并非总能实现，驳斥了准粒子局域性猜想，并发现该映射概率的急剧转变与哈密顿稀疏度及天体物理熵变相关。

Rotational invariance and the spin-statistics theorem

In this article the rotational invariance of entangled quantum states is investigated as a possible cause of the Pauli exclusion principle. First, it is shown that a certain class of rotationally invariant states can only occur in pairs. This is referred to as the coupling principle. This in turn suggests a natural classification of quantum systems into those containing coupled states and those that do not. Surprisingly, it would seem that Fermi-Dirac statistics follows as a consequence of this coupling while the Bose-Einstein follows by breaking it. In section 5, the above approach is related…