Abstract
We formally prove the existence of a quantization procedure that makes the path integral of a general diffeomorphism-invariant theory of gravity, with fixed total spacetime volume, equivalent to that of its unimodular version. This is achieved by means of a partial gauge fixing of diffeomorphisms together with a careful definition of the unimodular measure. The statement holds also in the presence of matter. As an explicit example, we consider scalar-tensor theories and compute the corresponding logarithmic divergences in both settings. In spite of significant differences in the coupling of the scalar field to gravity, the results are equivalent for all couplings, including non-minimal ones.
Highlights
We formally prove the existence of a quantization procedure that makes the path integral of a general diffeomorphism-invariant theory of gravity, with fixed total spacetime volume, equivalent to that of its unimodular version
This is achieved by means of a partial gauge fixing of diffeomorphisms together with a careful definition of the unimodular measure
The unimodularity condition (1.1) restricts the invariance group from diffeomorphisms (Diff ) to special diffeomorphisms (SDiff ),4 and one may expect that this could lead to different quantum theories
Summary
The starting point of our analysis is the (Euclidean) path integral defined by a gravitational action SDiff (gμν), gμν = gμν(g; h) being the metric, gμν a fixed background metric and hμν the fluctuating field which is integrated over. In most practical calculations within a continuum quantum-field theoretic setting, a gauge-fixing term must be introduced in (2.1) This is typically achieved by the Faddeev-Popov procedure. Following the standard steps we use the gauge invariance of the measure, of the Faddeev-Popov determinant and the action and redefine the integration variable, to get DφDhμν VDiff. In order to complete the gauge-fixing procedure, one applies again the Faddeev-Popov method for a gauge condition which fixes the SDiff invariance This is achieved, e.g., by taking the standard linear covariant gauges in quantum gravity and applying the transverse projector to it. We expect that gravity-matter systems in a full diffeomorphisminvariant setting are equivalent, quantum-mechanically, to gravity-matter systems in the unimodular framework
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
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 call
