代数拓扑中带各种参数的同调理论都可以转化为带层参数的层上同调理论,因此下面我们开始考虑层上同调,同样我们从最简单的情况开始,即从 abelian sheaf 开始。(这里我们都默认 sheaf 是定义在 site 上的。) 根据Tohoku 里面的结论,利用 abelian category 上的同调代数,对于任意一条 abelian sheaf 的正合链: 0\right...
正 由于非阿贝尔(non-Abelian)规范场方程是非线性的,因此它存在一种无源的孤子(Soliton)解和瞬子(Instanton)解。自从't Hooft … wiki.cnki.com.cn|基于32个网页 2. 色荷是非阿贝尔式的 QGP则成为普通浆体(电浆)的类比。此外尚有些不相似之处,肇因於色荷是非阿贝尔式的(non-Abelian),而电荷是阿贝尔 …...
1.如果是U(1)变换,则F_{\mu\nu}表达式中的对易子为零,A_{\mu}为Abelian gauge potential。 2.对于一般的SU(N)变换,更常用生成元T^a来表示转动U(adjoin representation): \\U=e^{i\theta\cdot T}=e^{i\theta^a T^{a}}\approx1+i\theta^a \cdot T^{a} 其中最后的约等于号是无穷小转动的...
推广至场论，需要引入规范势Gauge potential以处理局域规范对称性。拉格朗日量形式化为[公式]，对于复标量场，协变微分是关键，它确保了规范不变性。非阿贝尔情况下，规范势的非交换性质导致了field strength的构造，比如Yang-Mills场强度。同位旋理论中，通过扩展到N个内禀自由度，拉格朗日量和规范势矩阵化，...
Non-abelian Cheshire cat models are investigated in their lagrangian and hamiltonian formulations. The lagrangian bag boundary conditions are used to derive the form of non-abelian soliton operators, through which fermions are represented in bosonic language. These soliton operators are then used to ...
Non-Abelian braiding has attracted substantial attention because of its pivotal role in describing the exchange behaviour of anyons—candidates for realizing quantum logics. The input and outcome of non-Abelian braiding are connected by a unitary matrix
在这个过程中，复标量场的框架被扩展，以适应SU(N)的变换，从而构建出非阿贝尔场强，一个矩阵2-form，它的协变性通过精心设计的算子得以证明，这标志着非Abelian规范场论的独特性质。当U(1)的简单性被SU(N)所替代，规范势也随之进化，成为非阿贝尔的主体。在Yang-Mills理论的舞台，非阿贝尔场强被定义...
Abstract Thouless pumping enables topological transport and the direct measurement of topological invariants. So far, realizations of Thouless pumping rely on the adiabatic evolution of a physical system following a non-degenerate band, but it has been predicted that pumping can become non-Abelian in ...
Non-Abelian "electric" charges appear as sources of A(mu) but as monopoles of (A) over tilde(mu), while their "magnetic" counterparts appear as monopoles of A(mu) but sources of (A) over tilde(mu). Although these results have been derived only for classical fields, it is shown for...
Non Abelian Berry Connection。利用 ∇XFvi=ωij(X)vj,1形式构成的矩阵 ω={ωij} 即物理上算出来的Berry Connection。Berry Curvature按定义为 B(X,Y)=∇XF∇YF−∇YF∇XF−∇[X,Y]F ,其对应的2形式矩阵根据第二结构公式为 Ω=dω+12[ω,ω]...