Lorentz-covariant four-vector formalism for two-measure theory
Lorentz-covariant four-vector formalism for two-measure theory
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二测度理论的洛伦兹协变四向量形式
DOI：
10.1103/physrevd.87.027702
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发表时间：
2013
影响因子：
5
通讯作者：
S. Rajpoot
中科院分区：
文献类型：
--
作者：
E. Guendelman;H. Nishino;S. Rajpoot
在传统的二测度理论中，标量密度函数 $\ensuremath{\Phi}$ 被取为$\ensuremath{\Phi}\ensuremath{\equiv}{ϵ}^{\ensuremath{\mu}\ensuremath{\nu}\ensuremath{\rho}\ensuremat h{\sigma}}{ϵ}_{abcd}({\ensuremath{\partial}}_{\ensuremath{\mu}}{\ensuremath{\varphi}}^{a})({\ensuremat h{\partial}}_{\ensuremath{\nu}}{\ensuremath{\varphi}}^{b})({\ensuremath{\partial}}_{\ensuremath{\rho}} {\ensuremath{\varphi}}^{c})({\ensuremath{\partial}}_{\ensuremath{\sigma}}{\ensuremath{\varphi}}^{d})$,其中索引 $a,b,c,d=1$, 2, 3, 4 是内部空间索引。将四个标量 ${\ensuremath{\varphi}}^{a}$ 替换为洛伦兹协变四向量 ${\ensuremath{\varphi}}^{m}$ 和局部洛伦兹索引 $m=(0)$, (1), (2), (3) 更为自然。我们接受这种可能性，并表明新提出的拉格朗日不仅尊重洛伦兹协方差，而且尊重全局尺度不变性。传统二测度理论中的关键方程 ${\ensuremath{\partial}}_{\ensuremath{\mu}}L=0$ 也出现在我们的新公式中，即 ${\ensuremath{\varphi}}^{m}$ 场方程。
In the conventional two-measure theory, the scalar density function $\ensuremath{\Phi}$ is taken to be $\ensuremath{\Phi}\ensuremath{\equiv}{ϵ}^{\ensuremath{\mu}\ensuremath{\nu}\ensuremath{\rho}\ensuremath{\sigma}}{ϵ}_{abcd}({\ensuremath{\partial}}_{\ensuremath{\mu}}{\ensuremath{\varphi}}^{a})({\ensuremath{\partial}}_{\ensuremath{\nu}}{\ensuremath{\varphi}}^{b})({\ensuremath{\partial}}_{\ensuremath{\rho}}{\ensuremath{\varphi}}^{c})({\ensuremath{\partial}}_{\ensuremath{\sigma}}{\ensuremath{\varphi}}^{d})$, where the indices $a,b,c,d=1$, 2, 3, 4 are internal-space indices. It is more natural to replace the four scalars ${\ensuremath{\varphi}}^{a}$ by a Lorentz-covariant four-vector ${\ensuremath{\varphi}}^{m}$ with a local Lorentz index $m=(0)$, (1), (2), (3). We entertain this possibility, and show that the newly proposed Lagrangian respects not only Lorentz covariance, but also global-scale invariance. The crucial equation ${\ensuremath{\partial}}_{\ensuremath{\mu}}L=0$ in the conventional two-measure theory also arises in our new formulation, as the ${\ensuremath{\varphi}}^{m}$-field equation.