标题： 通过Weyl对称性破缺产生质量 显示英文标题

标题： Mass-Generation by Weyl-Symmetry Breaking

摘要： 在Weyl空间W_4中为轻子构建了一个无质量的电弱理论，该理论产生了一个Weyl不变的规范动力学，允许度规和所有具有非零Weyl权重的场的共形重标度，以及相应的表示D(1)或膨胀规范场的Weyl矢量场的变换。 为了研究非零质量的出现，该理论通过拉格朗日量中的一个项被显式破坏，该项涉及W_4的曲率标量R和标量场的质量项。 因此，规范场以及带电费米子场也像标准电弱理论中那样获得质量。 对称性破缺由关系式D Phi^2=0控制，其中Phi是标量场的模，D表示Weyl协变导数。 这种真正的对称性约化在理论中建立了长度尺度，与标准电弱理论中所谓的自发对称性破缺进行比较，实际上这是通过采用代表标量场的陪集空间中的一个原点而得到的一个特定（非线性）规范，该原点在电磁规范群下是不变的。 特别关注在Weyl对称性破缺后度规出现爱因斯坦方程，从W_4和一个具有常数模的标量场得到一个伪黎曼空间V_4，这反过来以类似于Brans-Dicke理论的方式影响爱因斯坦的引力常数。 显示英文摘要

摘要： A massless electroweak theory for leptons is formulated in a Weyl space, W_4, yielding a Weyl invariant gauge dynamics allowing for conformal rescalings of the metric and all fields with nonvanishing Weyl weight together with the corresponding transformations of the Weyl vector fields representing the D(1) or dilatation gauge fields. To study the appearance of nonzero masses this theory is explicitly broken by a term in the Lagrangean involving the curvature scalar R of the W_4 and a mass term for the scalar field. Thereby also the gauge fields as well as the charged fermion field acquire a mass as in the standard electroweak theory. The symmetry breaking is governed by the relation D Phi^2=0, where Phi is the modulus of the scalar field and D denotes the Weyl-covariant derivative. This true symmetry reduction, establishing a scale of length in the theory, is compared to the so-called spontanous symmetry breaking in the standard electroweak theory which is, actually, the choice of a particular (nonlinear) gauge obtained by adopting an origin in the coset space representing the scalar field which is invariant under the electromagnetic gauge group. Particular attention is devoted to the appearance of Einstein's equations for the metric after the Weyl-symmetry breaking yielding a pseudo-Riemannian space V_4 from a W_4 and a scalar field with a constant modulus which in turn affects Einstein's gravitational constant in a manner comparable to the Brans-Dicke theory.