量子真空能及其对引力规范理论的启示

Abstract

电磁规范理论及其推广(Yang-Mills理论)在量子场论和粒子物理领域取得了成功要求引力理论也应当是某种局域规范对称下的规范场论；对于量子真空能巨大引力效应与宇宙学观察事实之间的矛盾等问题的探究表明传统引力理论可能是一个低能唯象理论，可能还存在新的高能引力相互作用基本理论。本文介绍了一个新的自旋联络引力规范理论，它以局域Lorentz群为规范对称群、以自旋仿射联络作为非Abel规范场。在低能条件下，我们可以获得一个度规的三阶微分方程作为引力场方程，而爱因斯坦引力场方程作为其一个首次积分解呈现。在该理论中，量子真空能巨大引力效应不再存在，并产生了一个等效宇宙学常数(作为首次积分解的积分常数)，这可能为解决宇宙学常数之谜提供了一条思路。对引力规范理论本身及其在宇宙学中的运用作了一些讨论, 如该引力规范理论会呈现一种准流体(它在四维宇宙中类似暗辐射；在五维宇宙中，则呈现更为丰富的物态)，因此基于该引力规范理论的五维宇宙学在不需要引入真实暗物质和暗能量的条件下也能产生等效的暗物质和暗能量效应。Since electromagnetic gauge theory and its generalization (Yang-Mills gauge field theory) have succeeded in quantum field theory and particle physics, it requires that the theory of gravitation also be a gauge field theory under certain local gauge symmetries, e.g., local Lorentz or Poincare invariance. The discrepancy between unusually large quantum vacuum energy density and ob-servational cosmology may indicate that the generic gravity theory of Einstein is a low-energy phenomenological theory, and a more fundamental theory of gravity might be hidden behind it. A new spin-connection gauge theory for gravitational interaction at high energies (close to the Planck energy scale) is introduced. In such a gravitational gauge field theory, the local Lorentz group is the gauge symmetry group, and the spin-affine connection serves as a non-Abel gauge field (fundamental dynamical variable). A third-order differential equation of metric can be obtained as the gravitational gauge field equation, where the Einstein field equation of gravitation is a first-integral solution. As the vacuum energy density is a constant, the covariant derivative of its energy-momentum tensor unavoidably vanishes. Therefore, the quantum vacuum energy term disappears in the gravitational gauge field equation, and the anomalously large vacuum energy density does not make a practical contribution to gravity. This would enable us to seek for a new route to the longstanding vacuum-energy cosmological constant problem. Some topics relevant to gravitational gauge theory and its applications in cosmology are also addressed. For example, the five-dimensional cosmology within the framework of the present gravitational gauge theory, in which a quasi fluid is emergent, can exhibit the effects of equivalent dark matter and dark energy.