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arXiv 0705.0767hep-th
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暴胀过程中的量子修正费米子模函数

The Quantum-Corrected Fermion Mode Function during Inflation

Shun-Pei Miao

摘要:

我的项目计算了无质量狄拉克+爱因斯坦在局部德西特背景下的单圈费米子自能。我采用维数正则化,并获得一个完全重整化的结果,吸收所有的分歧与Bogliubov,Parasiuk,Hepp和Zimmermann(BPHZ)的counterterterterms。我的计算中一个有趣的技术方面是需要一个非不变的反项,因为我们的规范条件打破了德西特不变性。我还解决了在最简单的规范,包括所有的量子引力的单圈修正膨胀过程中的无质量费米子的有效狄拉克方程。在后期,空间平面波的结果表现得好像经典解经受了与时间相关的场强重整化Z_2(t)= 1 - 17(4 π)*G H^2 *ln(a)+ O(G ^2)。我证明了这也是由哈特里近似得出的,尽管数值系数不同。

英文摘要:

My project computed the one loop fermion self-energy for massless Dirac + Einstein in the presence of a locally de Sitter background. I employed dimensional regularization and obtain a fully renormalized result by absorbing all divergences with Bogliubov, Parasiuk, Hepp and Zimmermann (BPHZ) counterterms. An interesting technical aspect of my computation was the need for a noninvariant counterterm, owing to the breaking of de Sitter invariance by our gauge condition. I also solved the effective Dirac equation for massless fermions during inflation in the simplest gauge, including all one loop corrections from quantum gravity. At late times the result for a spatial plane wave behaves as if the classical solution were subjected to a time-dependent field strength renormalization of Z_2(t) = 1 - 17(4 pi) *G H^2 *ln(a) + O(G^2). I showed that this also follows from making the Hartree approximation, although the numerical coefficients differ.

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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