Conservation of Gravitational Energy Momentum and Renormalizable Quantum Theory of Gravitation

• 作者: Christian Wiesendanger
• 来源期刊: 现代物理(英文)
• 学科: 数学
• 关键词: Path INTEGRAL QUANTIZATION GAUGE Theory Volume-Preserving DIFFEOMORPHISMS
• 年，卷（期）: 2013,（8）
• 页码范围: 133-152
• 页数: 20页
• 分类号: O1

摘要

Viewing gravitational energy-momentum as equal by observation, but different in essence from inertial energymomentum naturally leads to the gauge theory of volume-preserving diffeomorphisms of an inner Minkowski space which can describe gravitation at the classical level. This theory is quantized in the path integral formalism starting with a non-covariant Hamiltonian formulation with unconstrained canonical field variables and a manifestly positive Hamiltonian. The relevant path integral measure and weight are then brought into a Lorentz- and gauge-covariant form allowing to express correlation functions—applying the De Witt-Faddeev-Popov approach—in any meaningful gauge. Next the Feynman rules are developed and the quantum effective action at one loop in a background field approach is renormalized which results in an asymptotically free theory without presence of other fields and in a theory without asymptotic freedom including the Standard Model (SM) fields. Finally the BRST apparatus is developed as preparation for the renormalizability proof to all orders and a sketch of this proof is given.