arXiv 0906.23852009-06-12hep-th

弯曲空间上量子电动力学的非微扰性质和矩阵引力的研究

Non-Perturbative Aspects of Quantum Electrodynamics on Curved Space and Investigations in Matrix Gravity

Guglielmo Fucci

备注：: Ph.D. Thesis, LaTeX 268 pages

摘要：

在本论文的第一部分，我们利用热核渐近展开技术研究了黎曼流形上量子电动力学的非微扰性质。在这里，我们建立了一个新的非微扰热核渐近展开的Laplace型算子上的齐次阿贝尔丛平行曲率的存在性，我们明确评估的前三个系数。作为应用，我们计算了量子电动力学中非微扰有效作用量的虚部，并推广了经典Schwinger关于在引力场诱导的电磁场中产生标量和旋量粒子的结果.我们还发现了由于引力修正而产生的新的红外发散，这代表了一种全新的物理效应。在论文的第二部分，我们研究了一个新发展的非对易的引力场理论--矩阵引力理论。矩阵引力有两种形式，第一种称为矩阵广义相对论，其作用量泛函是通过将希尔伯特-爱因斯坦泛函推广到矩阵值量而得到的。第二种称为谱矩阵引力，它是由非Laplace型二阶偏微分算子的前两个谱不变量构造的。对于第一个版本，我们找到了理论的动力学方程，而对于第二个版本，我们计算了爱因斯坦方程在弱变形极限下的第一个非对易修正。此外，我们在矩阵引力中发展了测试粒子的运动学，并找到了对通常的黎曼测地线流的一阶和二阶修正。

英文摘要：

In the first part of this Dissertation, we study non-perturbative aspects of quantum electrodynamics on Riemannian manifolds by using heat kernel asymptotic expansion techniques. Here, we established the existence of a new non-perturbative heat kernel asymptotic expansion for a Laplace type operator on homogeneous Abelian bundles with parallel curvature, and we evaluated explicitly the first three coefficients. As an application, we computed the imaginary part of the non-perturbative effective action in quantum electrodynamics and derived a generalization of the classical Schwinger's result for the creation of scalar and spinor particles in an electromagnetic field induced by the gravitational field. We also discovered new infrared divergences due to the gravitational corrections, which represents a completely new physical effect. In the second part of the Dissertation, we studied some aspects of a newly developed non-commutative theory of the gravitational field called Matrix Gravity. There are two versions of Matrix Gravity, in the first one, called Matrix General Relativity, the action functional is obtained by generalizing the Hilbert-Einstein functional to matrix-valued quantities. In the second one, called Spectral Matrix Gravity, the action is constructed form the first two spectral invariants of a non-Laplace type second order partial differential operator. For the first version, we found the dynamical equations of the theory, while, for the second version, we computed the first non-commutative corrections to Einstein equations in the weak deformation limit. Furthermore, we developed the kinematics of test particles in Matrix Gravity and found the first and second order corrections to the usual Riemannian geodesic flow.

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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