Related papers: Precanonical Quantum Gravity: quantization without…
A key problem in the attempt to quantize the gravitational field is the choice of boundary conditions. These are mixed, in that spatial and normal components of metric perturbations obey different sets of boundary conditions. In the…
Cosmological solutions for covariant canonical gauge theories of gravity are presented. The underlying covariant canonical transformation framework invokes a dynamical space-time Hamiltonian consisting of the Einstein-Hilbert term plus a…
We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes…
The problem of formulating a manifest covariant Hamiltonian theory of General Relativity in the presence of source fields is addressed, by extending the so-called "DeDonder-Weyl" formalism to the treatment of classical fields in curved…
We replace the usual Hamiltonian constraint of quantum gravity H|psi>=0 by a weaker one <psi|H|psi>=0. This allows |psi> to satisfy the time-dependent functional Schrodinger equation. In general, only the phase of the wave function appears…
We continue recent work and formulate the gravitational vacuum Einstein equations over a locally finite spacetime by using the basic axiomatics, techniques, ideas and working philosophy of Abstract Differential Geometry. The whole…
We provide a quantization of the Schwarzschild spacetime in the presence of a cosmological constant, based on midisuperspace methods developed in the spherically symmetric sector of loop quantum gravity, using in particular the 'improved…
Standard approaches to quantum gravity start with a pre-spacetime structure and attempt, in accordance with Bohr's correspondence principle, to recover the pseudo-Riemannian manifold in the low energy limit. These approaches assume there is…
A quantization of field theory based on the DeDonder-Weyl covariant Hamiltonian formulation is discussed. A hypercomplex extension of quantum mechanics, in which the space-time Clifford algebra replaces that of the complex numbers, appears…
The Gauss-Bonnet gravity is a special case of so-called Quadratic Gravity, which is an extension of Einstein's theory with additional terms in action that are quadratic combinations of the Riemann tensor and its contractions. These…
Precanonical quantization of pure Yang-Mills fields, which is based on the covariant De Donder-Weyl (DW) Hamiltonian formalism, and its connection with the functional Schrodinger representation in the temporal gauge are discussed. The YM…
We show that the Schr\"odinger wave functional may be obtained as the product integral of precanonical wave functions on the space of field and space-time variables. The functional derivative Schr\"odinger equation underlying the canonical…
We perform the manifestly covariant quantization of a scale invariant gravity with a scalar field, which is equivalent to the well-known Brans-Dicke gravity via a field redefinition of the scalar field, in the de Donder gauge condition (or…
We advance here a new gravity quantization procedure that explicitly utilizes York's analysis of the geometrodynamic degrees of freedom. This geometrodynamic procedure of quantization is based on a separation of the true dynamic variables…
This is an introduction to the by now fifteen years old research field of canonical quantum general relativity, sometimes called "loop quantum gravity". The term "modern" in the title refers to the fact that the quantum theory is based on…
We present the manifestly covariant quantization of quadratic gravity or higher-derivative gravity in the de Donder gauge condition (or harmonic gauge condition) for general coordinate invariance on the basis of the BRST transformation. We…
Conventional approaches to quantum gravity regard quantum principles, such as nonlocality and superposition, as fundamental properties of nature and therefore argue that gravity must also be quantized. In contrast, this work introduces a…
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…
The covariant Hamiltonian formulation for general relativity is studied in terms of self-dual variables on a manifold with an internal and lightlike boundary. At this inner boundary, new canonical variables appear: a spinor and a…
The problem of time emerging in the canonical quantization procedure of gravity signals a necessity to properly define a relational time parameter. Previous approaches, which are here briefly discussed, make use of the dependence of the…