Recoupling theory for quantum spinors

A quantum fermion realisation of the finite dimensional spinor representation of ${\rm{U}}_q({\mathfrak {osp}}(1|2n))$

The quantum supergroup ${\rm{U}}_q({\mathfrak {osp}}(1|2n))$ admits a finite dimensional spinor representation, which does not have a classical limit. We construct a realisation of this representation on the Fock space of $q$-fermions. We also generalise the construction to the infinite dimensional spinor representations of ${\rm{U}}_q({\mathfrak {osp}}(2m+1|2n))$ for $m, n\ge 1$ by using both quantum bosons and fermions. This leads to a new realisation different from those obtained before by other researchers.

六边形自旋网络与拓扑量子神经网络的精确评估

The exact evaluation of hexagonal spin-networks and topological quantum neural networks

本文提出一种基于重耦合理论与Haar积分的高效算法，精确评估六边形自旋网络的物理标量积，并分析拓扑量子神经网络在经典与量子重耦合下的行为，提供可复现的实现框架。

Classical Spinor Structures on Quantum Spaces

A noncommutative-geometric generalization of the classical concept of spinor structure is presented. This is done in the framework of the formalism of quantum principal bundles. In particular, analogs of the Dirac operator and the Laplacian are introduced and analyzed. A general construction of examples of quantum spaces with a spinor structure is presented.

Spinor representations of $U_q(\hat{\frak o}(N))$

This is an extension of quantum spinor construction of $U_q(\hat {\frak gl}(n))$. We define quantum affine Clifford algebras based on the tensor category and the solutions of q-KZ equations, and construct quantum spinor representations of $U_q(\hat{\frak o}(N))$.

Spinor Representations of $U_q(\hat{\frak gl}(n))$ and Quantum Boson-Fermion Correspondence

This is an extension of quantum spinor construction in \cite{DF2}. We define quantum affine Clifford algebras based on the tensor category and the solutions of q-KZ equations, construct quantum spinor representations of $U_q(\hat{\frak gl}(n))$ and explain classical and quantum boson-fermion correspondence.

General Spinor Structures on Quantum Spaces

A general theory of quantum spinor structures on quantum spaces is presented, within the conceptual framework of the formalism of quantum principal bundles. Quantum analogs of all basic objects of the classical theory are constructed and analyzed. This includes Laplace and Dirac operators, quantum versions of Clifford and spinor bundles, a Hodge *-operator, appropriate integration operators, and mutual relations of these objects. We also present a self-contained formalism of braided Clifford algebras. Quantum phenomena appearing in the theory are discussed, including a very interesting example…