arXiv math-ph/05120172005-12math-phmath.MP

规范自然场论和Noether定理：正则协变守恒流

Gauge-natural field theories and Noether Theorems: canonical covariant conserved currents

Marcella Palese, Ekkehart Winterroth

备注：: 16 pages, abstract rewritten, body slightly revised, Proc. Winter School "Geometry and Physics" (Srni,CZ 2005)
发表信息：: Rend. Circ. Matem. Palermo, Serie II, Suppl. 79 (2006) 161--174

摘要：

最近我们发现正则规范自然超势是纤维流形$\bY_{\zet} \times_{\bX} \mathfrak{K}$上的{ \em约化} $(n-2)$ -度和$(2s-1)$ -阶商层的整体截面，其中$\mathfrak{K}$是无穷小右不变自同构$\barΞ$的向量丛的适当子丛.在本文中，我们提供了另一种证明的事实，即自然属性$\cL_{j_{s}\barΞ_{H}}ω(λ, \mathfrak{K})=0$保持真实的{ \em新}拉格朗日$ω(λ, \mathfrak{K})$收缩欧拉-拉格朗日形式的原始拉格朗日与$\barΞ_{V}\in \mathfrak{K}$。作为基本工具，我们使用的垂直态射的不变分解公式，由于Kolánziness和纤维丛的部分的迭代李导数的理论。因此，我们恢复了与$ω(λ, \mathfrak{K})$相关的正则广义能量-动量守恒张量密度的存在性。

英文摘要：

Recently we found that canonical gauge-natural superpotentials are obtained as global sections of the {\em reduced} $(n-2)$-degree and $(2s-1)$-order quotient sheaf on the fibered manifold $\bY_{\zet} \times_{\bX} \mathfrak{K}$, where $\mathfrak{K}$ is an appropriate subbundle of the vector bundle of (prolongations of) infinitesimal right-invariant automorphisms $\barΞ$. In this paper, we provide an alternative proof of the fact that the naturality property $\cL_{j_{s}\barΞ_{H}}ω(λ, \mathfrak{K})=0$ holds true for the {\em new} Lagrangian $ω(λ, \mathfrak{K})$ obtained contracting the Euler--Lagrange form of the original Lagrangian with $\barΞ_{V}\in \mathfrak{K}$. We use as fundamental tools an invariant decomposition formula of vertical morphisms due to Kolář and the theory of iterated Lie derivatives of sections of fibered bundles. As a consequence, we recover the existence of a canonical generalized energy--momentum conserved tensor density associated with $ω(λ, \mathfrak{K})$.

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