哈密顿重整化的性质及其在圆周上量子力学中的应用
Properties of the Hamiltonian Renormalisation and its application to quantum mechanics on the circle
AI总结：
该研究针对离散化一维物理理论的哈密顿重整化群流，分析嵌入映射选择对连续极限的影响，探讨重整化流与算符代数的相互作用，提出优选重整化方案并引入弱分布等价性概念，解释不同嵌入下幺正不等价连续极限的弱等价关系。
摘要：
我们研究离散化一维物理理论的哈密顿重整化群流。具体而言，我们探究了不同嵌入映射的选择对重整化群（RG）流及由此产生的连续极限的影响，并阐明了作为物理理论，它们在何种意义上等价、又在何种意义上不等价。此外，我们还阐明了重整化群流与算符在离散和连续情形下所满足代数之间的相互作用。进一步地，我们提出了算符代数的优选重整化方案，在假设合适的延拓性质时，该方案可保证在连续极限下得到优选的代数关系。最后，我们引入了一种更弱形式的分布等价性，并证明了因选择不同嵌入映射而产生的、幺正不等价的连续极限，在此意义下仍可具有弱等价性。
英文摘要：
We consider the Hamiltonian renormalisation group flow of discretised one-dimensional physical theories. In particular, we investigate the influence the choice of different embedding maps has on the RG flow and the resulting continuum limit, and show in which sense they are, and in which sense they are not equivalent as physical theories. We are furthermore elucidating the interplay of the RG flow and the algebras operators satisfy, both on the discrete and the continuum. Further, we propose preferred renormalisation prescriptions for operator algebras guaranteeing to arrive at preferred algebraic relations in the continuum, if suitable extension properties are assumed. Finally, we introduce a weaker form of distributional equivalence, and show how unitarily inequivalent continuum limits, which arise due to a choice of different embedding maps, can still be weakly equivalent in that sense.
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