论文标题
一种新的非交通仪理论的方法
A novel approach to non-commutative gauge theory
论文作者
论文摘要
我们提出了一个在非共同时空定义的字段理论模型，该模型具有非稳定的非承诺参数$θ（x）$，它满足了两个主要要求：它是规范不变的，并在换向限制中，$θ\ to $θ\至0 $，标准$ u（1）$ geguge $ eguge理论。我们在缓慢变化的场近似中工作，其中忽略了星换入器中的较高衍生物项，而后者则由泊松支架近似，$ -i [f，g] _ \ star _ \ star \ ofst \ oft \ of \ of {f {f，g \ \} $。我们得出了对Abelian仪表转换的NC变形的明确表达，该变换封闭了代数$ [δ_f，δ_g] a =δ_ =δ_ {\ {f，g \}} a $，nc field field强度$ {\ cal f} $，在这些转换下f}，f \} $。 NC Chern-Simons方程等于要求NC场强度$ {\ cal f} $的要求相同。这样的方程是非拉格朗日的。 Yang-Mills理论的NC变形是从规格不变动作中获得的，$ s = \ int {\ cal f}^2 $。作为指导示例，详细研究了$ su（2）$的情况 - 像非交换性一样，与旋转不变的NC空间相对应。
We propose a field theoretical model defined on non-commutative space-time with non-constant non-commutativity parameter $Θ(x)$, which satisfies two main requirements: it is gauge invariant and reproduces in the commutative limit, $Θ\to 0$, the standard $U(1)$ gauge theory. We work in the slowly varying field approximation where higher derivatives terms in the star commutator are neglected and the latter is approximated by the Poisson bracket, $-i[f,g]_\star\approx\{f,g\}$. We derive an explicit expression for both the NC deformation of Abelian gauge transformations which close the algebra $[δ_f,δ_g]A=δ_{\{f,g\}}A$, and the NC field strength ${\cal F}$, covariant under these transformations, $δ_f {\cal F}=\{{\cal F},f\}$. NC Chern-Simons equations are equivalent to the requirement that the NC field strength, ${\cal F}$, should vanish identically. Such equations are non-Lagrangian. The NC deformation of Yang-Mills theory is obtained from the gauge invariant action, $S=\int {\cal F}^2$. As guiding example, the case of $su(2)$-like non-commutativity, corresponding to rotationally invariant NC space, is worked out in detail.
