Abstract
We have recently undergone an analysis of gravitational theories as defined in first order formalism, where the metric and the connection are treated as independent fields. The physical meaning of the connection field has historically been somewhat elusive. In this paper, a complete spin analysis of the torsionless connection field is performed, and its consequences are explored. The main properties of a hypothetical consistent truncation of the theory are discussed as well.
Highlights
This means that either the theory is not a theory of gravity at all, or else all the dynamics of the gravitational field is determined by the three index connection field
The idea that the true dynamics of gravitation is better conveyed by the connection field than by the metric has a long history
We shall find after some roundabout that the physical content of the theory is the same as we previously found in the last paragraph
Summary
Let us make the exercise of reanalyzing this same theory in first order formalism, in which the metric and the connection are independent. We shall find after some roundabout that the physical content of the theory is the same as we previously found in the last paragraph. Where Aαβγ is the quantum field for the connection, which is symmetric in the last two indices as we are restricting ourselves to the torsionless case. We obtain the same result when we treat the theory in second order formalism (2.11) and in first order formalism, for the particular case of the Einstein–Hilbert action
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
