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arXiv 1107.2664hep-th
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标准模型扩展的CPT偶电磁扇区的降维

Dimensional reduction of the CPT-even electromagnetic sector of the Standard Model Extension

Rodolfo Casana, Eduardo S. Carvalho, Manoel M. Ferreira

摘要:

标准模型扩展的CPT偶阿贝尔规范扇区由麦克斯韦项加上$(K_{F})_{μνρσ}F^{μν}F^{ρσ}$表示,其中洛伦兹破坏背景张量$(K_{F})_{μνρσ}$具有黎曼张量的对称性。在目前的工作中,我们研究了这个理论的平面版本,通过一个典型的降维过程$(1+2)$尺寸。由此产生的平面电动力学是由一个规范部门包含六个洛伦兹违反系数,一个标量场赋予一个非正则动力学项,和一个耦合项,连接标量和规范部门。色散关系被精确地确定,揭示了与纯电磁扇区相关的六个参数不产生任何阶的双折射。在这个模型中,双折射只表现为与连接规范扇区和标量扇区的耦合张量有关的二阶效应,运动方程在定常状态下写出并求解。洛仑兹破坏参数不改变场的渐近行为,但引起的角度依赖性没有观察到的麦克斯韦平面理论。

英文摘要:

The CPT-even abelian gauge sector of the Standard Model Extension is represented by the Maxwell term supplemented by $(K_{F})_{μνρσ}F^{μν}F^{ρσ}$, where the Lorentz-violating background tensor, $(K_{F})_{μνρσ}$, possesses the symmetries of the Riemann tensor. In the present work, we examine the planar version of this theory, obtained by means of a typical dimensional reduction procedure to $(1+2)$ dimensions. The resulting planar electrodynamics is composed of a gauge sector containing six Lorentz-violating coefficients, a scalar field endowed with a noncanonical kinetic term, and a coupling term that links the scalar and gauge sectors. The dispersion relation is exactly determined, revealing that the six parameters related to the pure electromagnetic sector do not yield birefringence at any order. In this model, the birefringence may appear only as a second order effect associated with the coupling tensor linking the gauge and scalar sectors.The equations of motion are written and solved in the stationary regime. The Lorentz-violating parameters do not alter the asymptotic behavior of the fields but induce an angular dependence not observed in the Maxwell planar theory.

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