Related papers: Quantized K\"ahler Geometry and Quantum Gravity
We solve the problem of determining the fundamental degrees of freedom underlying a generalized K\"ahler structure of symplectic type. For a usual K\"ahler structure, it is well-known that the geometry is determined by a complex structure,…
The quantum gravity is formulated based on principle of local gauge invariance. The model discussed in this paper has local gravitational gauge symmetry and gravitational field appears as gauge field. The problems on quantization and…
We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…
For a Dirac theory of quantum gravity obtained from the refined algebraic quantization procedure, we propose a quantum notion of Cauchy surfaces. In such a theory, there is a kernel projector for the quantized scalar and momentum…
We study K\"{a}hler gravity on local SU(N) geometry and describe precise correspondence with certain supersymmetric gauge theories and random plane partitions. The local geometry is discretized, via the geometric quantization, to a foam of…
We describe a theory amalgamating quantum theory and general relativity through the identification of a continuous 4-dimensional spacetime arena constructed from the substructures of a generalised multi-dimensional form for proper time. In…
It is commonly accepted that the study of 2+1 dimensional quantum gravity could teach us something about the 3+1 dimensional case. The non-perturbative methods developed in this case share, as basic ingredient, a reformulation of gravity as…
The Berezin quantization on a simply connected homogeneous K\"{a}hler manifold, which is considered as a phase space for a dynamical system, enables a description of the quantal system in a (finite-dimensional) Hilbert space of holomorphic…
We construct a model of quantum gravity in which dimension, topology and geometry of spacetime are dynamical. The microscopic degree of freedom is a real rectangular matrix whose rows label internal flavours, and columns label spatial…
We study a type of geometric theory with a non-dynamical one-form field. Its dynamical variables are an $su(2)$ gauge field and a triad of $su(2)$ valued one-forms. Hamiltonian decomposition reveals that the theory has a true Hamiltonian,…
Gravity theory based on current algebra is formulated. The gauge principle rather than the general covariance combined with the equivalence principle plays the pivotal role in the formalism, and the latter principles are derived as a…
Pure gravity and gauge theories in two dimensions are shown to be special cases of a much more general class of field theories each of which is characterized by a Poisson structure on a finite dimensional target space. A general scheme for…
Yes, there is. - A new kind of gauge theory is introduced, where the minimal coupling and corresponding covariant derivatives are defined in the space of functions pertaining to the functional Schroedinger picture of a given field theory.…
The problem of constructing a quantum theory of gravity is considered from a novel viewpoint. It is argued that any consistent theory of gravity should incorporate a relational character between the matter constituents of the theory. In…
We consider a system with a discrete configuration space. We show that the geometrical structures associated with such a system provide the tools necessary for a reconstruction of discrete quantum mechanics once dynamics is brought into the…
Any acceptable quantum gravity theory must allow us to recover the classical spacetime in the appropriate limit. Moreover, the spacetime geometrical notions should be intrinsically tied to the behavior of the matter that probes them. We…
The geometro-stochastic method of quantization provides a framework for quantum general relativity, in which the principal frame bundles of local Lorentz frames that underlie the fibre-theoretical approach to classical general relativity…
Various extensions to Riemann geometry have been proposed since the inception of general relativity (GR). The aim has been and continues to be to construct a quantum and dynamic spacetime that incorporates the well-known classical (static)…
We introduce mu-scalar curvature for a K"ahler metric with a moment map mu and start up a study on constant mu-scalar curvature K"ahler metric as a generalization of both cscK metric and K"ahler-Ricci soliton and as a continuity path to…
We consider a $SO(d)$ gauge theory in an Euclidean $d$-dimensional space-time, which is known to be renormalizable to all orders in perturbation theory for $2\le{d}\le4$. Then, with the help of a space-time representation of the gauge…