# Classical and quantum conformal gravity

## Abstract

Conformal gravity, based on the action quadratic in the Weyl conformal curvature, constitutes a scale-invariant, classically-confining, asymptotically-free theory of gravitation. This theory is examined with a view toward assessing its viability as an alternative to Einstein gravity at the fundamental level. First, by extending the manifestly-covariant, six-dimensional formalism of Dirac, it is shown that conformal gravity arises uniquely as the local gauge theory of the conformal group SU(2,2). The exact, spherically-symmetric, electrovac solutions of the classical theory are obtained. Next, it is argued that the phenomenologically-required breakdown of conformal invariance is a consequence of divergent quantum fluctuations and the resulting energy-momentum tensor trace anomaly. A non-local effective gravitational action reproducing this anomaly is constructed. Finally, the effect of asymptotic freedom and the consequential local confinement of energy-momentum is analyzed.

- Authors:

- Publication Date:

- Research Org.:
- California Univ., San Diego (USA)

- OSTI Identifier:
- 6844972

- Resource Type:
- Thesis/Dissertation

- Resource Relation:
- Other Information: Thesis (Ph. D.)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; GRAVITATION; CONFORMAL GROUPS; QUANTUM GRAVITY; ANALYTICAL SOLUTION; CONFORMAL INVARIANCE; ENERGY-MOMENTUM TENSOR; FLUCTUATIONS; SYMMETRY BREAKING; FIELD THEORIES; INVARIANCE PRINCIPLES; LIE GROUPS; QUANTUM FIELD THEORY; SYMMETRY GROUPS; TENSORS; VARIATIONS; 645400* - High Energy Physics- Field Theory; 657003 - Theoretical & Mathematical Physics- Relativity & Gravitation

### Citation Formats

```
Riegert, R J.
```*Classical and quantum conformal gravity*. United States: N. p., 1986.
Web.

```
Riegert, R J.
```*Classical and quantum conformal gravity*. United States.

```
Riegert, R J. Wed .
"Classical and quantum conformal gravity". United States.
```

```
@article{osti_6844972,
```

title = {Classical and quantum conformal gravity},

author = {Riegert, R J},

abstractNote = {Conformal gravity, based on the action quadratic in the Weyl conformal curvature, constitutes a scale-invariant, classically-confining, asymptotically-free theory of gravitation. This theory is examined with a view toward assessing its viability as an alternative to Einstein gravity at the fundamental level. First, by extending the manifestly-covariant, six-dimensional formalism of Dirac, it is shown that conformal gravity arises uniquely as the local gauge theory of the conformal group SU(2,2). The exact, spherically-symmetric, electrovac solutions of the classical theory are obtained. Next, it is argued that the phenomenologically-required breakdown of conformal invariance is a consequence of divergent quantum fluctuations and the resulting energy-momentum tensor trace anomaly. A non-local effective gravitational action reproducing this anomaly is constructed. Finally, the effect of asymptotic freedom and the consequential local confinement of energy-momentum is analyzed.},

doi = {},

url = {https://www.osti.gov/biblio/6844972},
journal = {},

number = ,

volume = ,

place = {United States},

year = {1986},

month = {1}

}