Theory of dynamical affine and conformal symmetries as the theory of the gravitational field
Theory of dynamical affine and conformal symmetries as the theory of the gravitational field
复制标题
作为引力场理论的动力学仿射和共形对称理论
DOI：
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发表时间：
1974
期刊：
影响因子：
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通讯作者：
V. Ogievetskiǐ
中科院分区：
文献类型：
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作者：
A. B. Borisov;V. Ogievetskiǐ
无限参数广义协变群下的不变性等价于仿射和共形群下的同时不变性。仿射群的非线性实现（在庞加莱群上线性化）导致对称张量场作为Goldstone场。理论同时对应于共形群的实现的要求也导致了唯一的张量场理论，其方程是爱因斯坦的。这表明引力场理论是仿射对称和共形对称自发破缺的理论，就像手征动力学是手征对称自发破缺的理论一样。这个类比揭示了引力在基本粒子理论中的作用的新方面。
Invariance under the infinite-parameter generally covariant group is equivalent to simultaneous invariance under the affine and the conformal group. A nonlinear realization of the affine group (with linearization on the Poincare group) leads to a symmetric tensor field as Goldstone field. The requirement that the theory correspond simultaneously to a realization of the conformal group as well leads uniquely to the theory of a tensor field whose equations are Einstein’s. This shows that the theory of the gravitational field is the theory of spontaneous breaking of affine and conformal symmetries in the same way as chiral dynamics is the theory of spontaneous breaking of chiral symmetry. This analogy brings out new aspects of the role of gravitation in the theory of elementary particles.