arXiv 0906.20842009-06-11hep-th

O（N）扩展超对称粒子的拉格朗日高自旋场论

Lagrangian higher spin field theories from the O(N) extended supersymmetric particle

Robert Marnelius

备注：: 68 pages

摘要：

O（N）扩展超对称粒子模型的量子理论中的波函数描述了自旋为N/2的无质量自由场。本文仅用基本量子算符，包括分次外微分、迹算符、指数结构算符及其导数，精确地求解了任意偶数维规范场的量子理论。所得到的规范场的方程是一阶（N奇数）或二阶（N偶数）的，并且被证明是广义的（Fang）-Fronsdal方程，它是完全规范不变的，因为它们以一种自然的方式包含了补偿场。局部规范不变的行动首先推导出类似的推导Francia和Sagnotti在对称的情况下。然后给出了一个最小公式，在此公式内容易建立规范不变作用量，并在此提出了上述方程的适当作用量。在第二部分中，它是存在的投影运营商从状态的场强（波函数）的Weyl状态（Weyl张量）只表示在跟踪运营商和他们的整数自旋或在伽玛跟踪运营商和他们的半整数自旋。这些外尔态不仅是完全规范不变的，而且在广义外尔变换下也是不变的。如果让方程由定义为这些外尔张量的平方的作用决定，那么理论是共形不变的，并且对于精确理论中定义的规范场，方程是N阶的。在d=4时，这种高阶共形理论符合弗拉德金、蔡特林和林茨基建立的共形高自旋理论的框架。

英文摘要：

The wave function in the quantum theory of the O(N) extended supersymmetric particle model describes a massless free field with spin N/2. This quantum theory is here exactly solved in terms of gauge fields in arbitrary even dimensions using only the basic quantum operators which include graded external differentials, trace operators, index structure operators and their duals. The resulting equations for the gauge fields are of first (N odd) or second order (N even) and are shown to be generalized (Fang)-Fronsdal equations which are fully gauge invariant since they include compensator fields in a natural way. Local gauge invariant actions are first derived in analogy with the derivation by Francia and Sagnotti in the symmetric case. Then a minimal formulation is given within which it is easy to set up gauge invariant actions and here appropriate actions for the above equations are proposed. In a second part it is shown that there exist projection operators from the states of the field strengths (wave functions) to Weyl states (Weyl tensors) expressed only in terms of the trace operators and their duals for integer spins or in terms of the gamma trace operators and their duals for half-integer spins. These Weyl states are not just fully gauge invariant but also invariant under generalized Weyl transformations. If one lets the equations be determined by the actions defined to be the squares of these Weyl tensors then the theory is conformally invariant and the equations are of order N for the gauge fields defined as in the exact theory. In d=4 this higher order conformal theory fits into the framework for conformal higher spin theories set up by Fradkin, Tseytlin and Linetski.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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