标题: | 尺度不变重力 Scale Invariant Gravity |
作者: | 林世昀 Shih-Yuin Lin 高文芳 吴建宏 Win-Fun Kao Kin-Wang Ng 电子物理系所 |
关键字: | 尺度对称;黑洞;宇宙学;等效位能;scale symmetry;black hole;cosmology;effective potential;Vilkovisky;DeWitt |
公开日期: | 1998 |
摘要: | 从Einstein的几何重力理论出发,Weyl将Einstein的“运动的相对论”观念推广到“量值的相对论”,以具有局部尺度对称的理论来描述重力。在掌握这些尺度不变重力理论的作用量之后,我们试图讨论这些理论的黑洞物理与宇宙学。首先在黑洞方面,我们找到了这些理论的球对称黑洞解,并在Weyl重力理论、它的无质量的特例,以及含有对称破缺项的Weyl理论下,分别证明了这些黑洞的形状并不会受到Weyl规范场与纯量测度场的电荷所影响。然后,由于量子世界中,存在一个绝对的尺度标准─Planck常数,使目前的宇宙没有尺度对称,因此我们在应用Weyl重力论来研究宇宙学之前,得先引入量子修正项来把尺度对称破坏掉。为了避免结果暧昧不明,我们应用Vilkovisky与DeWitt (VD) 的方法来计算系统的量子等效位能,因为这套方法所算出的等效位能形式,和背景场的变换无关,也和规范条件的选取无关。最后我们探讨具有这个VD等效位能的Weyl理论下的宇宙学,我们发现这个理论的宇宙暴涨模型,其相变是以Hawking-Moss瞬子解来描述,而这个理论在暴涨阶段之后的宇宙学性质,则和标准热大爆炸模型相差极微。除了以上成果之外,我们也厘清,一般误认在规范场论下VD等效位能的暧昧性,其实只是所有场论中初始场变数的选取问题而已。 A natural generalization from the idea of "relativity of motion" in Einstein's geometrical theory of gravity is Weyl's "relativity of magnitude" realized by local scale symmetry of space-time. Given the actions of scale invariant gravity, we study the black hole physics and cosmology for these theories. First, we found the spherically symmetric black hole solutions and proved that there is no classical hair of the Weyl's gauge fields and the scalar measuring field in Weyl gravity, its massless limit and the ones with symmetry-breaking potential. Second, by noting that scale symmetry is not appreciated by the quantum nature because of the existence of the absolute Planck scale, we were led to introduce quantum corrections to break the scale symmetry dynamically before the study of the cosmology for Weyl gravity. To get rid of ambiguities, we calculated the one-loop effective potential for Weyl gravity by Vilkovisky-DeWitt (VD) method, which guarantees the field re-parameterization covariance and gauge independence of the results. In the last part of this thesis, a cosmology based on Weyl gravity with one-loop VD effective potential is studied in detail. It is found that the model admits an inflation via Hawking-Moss bubbling. However, the deviation from the standard hot big-bang model is vanishingly small after inflation. We also found that the metric dependence of VD effective potential relates to initial field parameterization rather than gauge symmetry as it was thought of as. |
URI: | http://140.113.39.130/cdrfb3/record/nctu/#NT870429001 http://hdl.handle.net/11536/64420 |
显示于类别: | Thesis |