3 years ago

On Gauge Invariance and Covariant Derivatives in Metric Spaces.

Kaushik Ghosh

In this manuscript, we will discuss the construction of covariant derivative operator in a quantum theory of gravity. We will find it is appropriate to use affine connections more general than the metric compatible connections even in free quantum gravity. We will demonstrate this for the canonical quantization procedure. The conventional Palatini action is not sufficient to describe the free theory of gravity with connections more general than the metric compatible Levi-Civita connections. We will discuss a potential formalism and possible extensions of the action to have nonmetricity in the free theory. General affine connections can be described by a third rank tensor with one contravariant and two covariant indices. The antisymmetric part in the lower indices gives torsion with a half factor. In the Palatini formalism or its generalizations considered here, the symmetric part in the lower indices is finite when torsion is finite. This part can give a scalar field in a potential formalism. We will have to extend the energy-momentum conservation law and electric charge conservation law when we use general affine connections. General affine connections can become significant to solve cosmological problems.

Publisher URL: http://arxiv.org/abs/1702.02384

DOI: arXiv:1702.02384v22

You might also like
Discover & Discuss Important Research

Keeping up-to-date with research can feel impossible, with papers being published faster than you'll ever be able to read them. That's where Researcher comes in: we're simplifying discovery and making important discussions happen. With over 19,000 sources, including peer-reviewed journals, preprints, blogs, universities, podcasts and Live events across 10 research areas, you'll never miss what's important to you. It's like social media, but better. Oh, and we should mention - it's free.

  • Download from Google Play
  • Download from App Store
  • Download from AppInChina

Researcher displays publicly available abstracts and doesn’t host any full article content. If the content is open access, we will direct clicks from the abstracts to the publisher website and display the PDF copy on our platform. Clicks to view the full text will be directed to the publisher website, where only users with subscriptions or access through their institution are able to view the full article.