Related papers: Functional Integration Over Geometries
We propose that large quantum fluctuations of the conformal factor drastically modify classical general relativity at cosmological distance scales, resulting in a scale invariant phase of quantum gravity in the far infrared. We derive…
The notion of a measure on the space of connections modulo gauge transformations that is invariant under diffeomorphisms of the base manifold is important in a variety of contexts in mathematical physics and topology. At the formal level,…
Recently a scale invariant theory of gravity was constructed by imposing a conformal symmetry on general relativity. The imposition of this symmetry changed the configuration space from superspace - the space of all Riemannian 3-metrics…
The quantum gravity problem of N point particles interacting with the gravitational field in 2+1 dimensions is approached working out the phase-space functional integral. The maximally slicing gauge is adopted for a non compact open…
Let $G$ be a compact connected Lie group and $P \to M$ a smooth principal $G$-bundle. Let a `cylinder function' on the space $\A$ of smooth connections on $P$ be a continuous function of the holonomies of $A$ along finitely many piecewise…
We evaluate the influence functional for two dimensional models of dilaton gravity. This functional is exactly computed when the conformal invariance is preserved, and it can be written as the difference between the Liouville actions on…
A gauge-invariant field is found which describes physical configurations, i.e. gauge orbits, of non-Abelian gauge theories. This is accomplished with non-Abelian generalizations of the Poincare'-Hodge formula for one-forms. In a particular…
A geometric formal method for perturbatively expanding functional integrals arising in quantum gauge theories is described when the spacetime is a compact riemannian manifold without boundary. This involves a refined version of the…
Application of the functional integration methods in equilibrium statistical mechanics of quantum Bose-systems is considered. We show that Gibbs equilibrium averages of Bose-operators can be represented as path integrals over a special…
We present a scale-invariant theory, conformal gravity, which closely resembles the geometrodynamical formulation of general relativity (GR). While previous attempts to create scale-invariant theories of gravity have been based on Weyl's…
The quantization of General Relativity invariant with respect to time-reparametrizations is considered. We construct the Faddeev-Popov generating functional for the unitary perturbation theory in terms of invariants of the kinemetric group…
We study integration over functions on superspaces. These functions are invariant under a transformation which maps the whole superspace onto the part of the superspace which only comprises purely commuting variables. We get a compact…
We consider four-dimensional non-Abelian gauge theory living on a complex projective space $\mathbb{CP}^2$ as a way of gaining insights into (3+1)-dimensional QCD. In particular, we use a complex parametrization of gauge fields on which…
We consider symmetry operations on the four-dimensional vector space that is spanned by the local versions of the Minkowski functionals (or fundamental measures): volume, surface, integral mean curvature, and Euler characteristic, of an…
Conventional functional/path integrals used in physics are most often defined and understood, either explicitly or implicitly, as the infinite-dimensional analog of Fourier transform. In this paper, the infinite-dimensional analog of Mellin…
We consider topological gauge theories in three dimensions which are defined by metric independent lagrangians. It has been claimed that the functional integration necessarily depends nontrivially on the gauge-fixing metric. We demonstrate…
The use in the action integral of a volume element of the form $\Phi d^{D}x$, where $\Phi$ is a metric-independent measure density, can yield new interesting results in all types of known generally coordinate-invariant theories: (1) 4-D…
Employing alternative spacetime volume-forms (generally-covariant integration measure densities) independent of the pertinent Riemannian spacetime metric have profound impact in general relativity. Although formally appearing as…
We find a large internal symmetry within 4-dimensional Poincare gauge theory. In the Riemann-Cartan geometry of Poincare gauge theory the field equation and geodesics are invariant under projective transformation, just as in affine…
A class of decoherence schemes is described for implementing the principles of generalized quantum theory in reparametrization-invariant `hyperbolic' models such as minisuperspace quantum cosmology. The connection with sum-over-histories…