Related papers: Ground-state Wigner functional of linearized gravi…
We generalize previous work by considering a novel gravitational model with an action given by an arbitrary function of the Ricci scalar, the matter Lagrangian density, a scalar field and a kinetic term constructed from the gradients of the…
We treat a system (a molecule or a solid) in which electrons are coupled linearly to any number and type of harmonic oscillators and which is further subject to external forces of arbitrary symmetry. With the treatment restricted to the…
A generalized Weyl quantization formalism for a particle on the circle investigated in \cite{1} is developed. A Wigner function for the state $\hat{\varrho}$ and the kernel $\mathcal{K}$ for a particle on the circle is defined and its…
Quantum gravity is fundamentally different from the non-gravitational quantum field theories in the sense that most of the techniques derived for the latter cannot be easily extended to the former. For example, correlation functions in…
Based on certain assumptions for the expectation value of a product of the quantum fluctuating metric at two points, the gravitational and scalar field Lagrangians are evaluated. Assuming a vanishing expectation value of the first order…
The original Wigner function provides a way of representing in phase space the quantum states of systems with continuous degrees of freedom. Wigner functions have also been developed for discrete quantum systems, one popular version being…
Gauge-invariant Wigner theory describes the quantum-mechanical evolution of charged particles in the presence of an electromagnetic field in phase space, which is spanned by position and kinetic momentum. This approach is independent of the…
A quantum hamiltonian which evolves the gravitational field according to time as measured by constant surfaces of a scalar field is defined through a regularization procedure based on the loop representation, and is shown to be finite and…
The rules for superfield Lagrangian quantization method for general gauge theories on a basis of their generalization to special superfield models within a so-called $\theta$-superfield theory of fields ($\theta$-STF) are formulated. The…
The phenomenology of quantum systems in curved space-times is among the most fascinating fields of physics, allowing --often at the gedankenexperiment level-- constraints on tentative theories of quantum gravity. Determining the dynamics of…
Nonholonomic distributions and adapted fame structures on (pseudo) Riemannian manifolds of even dimension are employed to build structures equivalent to almost Kahler geometry and which allows to perform a Fedosov-like quantization of…
We apply the generalized Wigner function formalism to detect and characterize a range of quantum phase transitions in several cyclic, finite-length, spin-$\frac{1}{2}$ one-dimensional spin-chain models, viz., the Ising and anisotropic $XY$…
In the beginning of the 1950's, Wigner introduced a fundamental deformation from the canonical quantum mechanical harmonic oscillator, which is nowadays sometimes called a Wigner quantum oscillator or a parabose oscillator. Also, in quantum…
A new representation for canonical gravity and supergravity is presented, which combines advantages of Ashtekar's and the Wheeler~DeWitt representation: it has a nice geometric structure and the singular metric problem is absent. A formal…
We have recently undergone an analysis of gravitational theories as defined in first order formalism, where the metric and the connection are treated as independent fields. The physical meaning of the connection field has historically been…
An approach to quantization of fields and gravity based on the De Donder-Weyl covariant Hamiltonian formalism is outlined. It leads to a hypercomplex extension of quantum mechanics in which the algebra of complex numbers is replaced by the…
By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a…
We describe a deformation of the observable algebra of quantum gravity in which the loop algebra is extended to framed loops. This allows an alternative nonperturbative quantization which is suitable for describing a phase of quantum…
The ground-state wave function and the energy gap are calculated for various layer separations d and for up to 24 electrons by the density matrix renormalization group (DMRG) method. Two-particle distribution function and excitonic…
Review of the most basic issues appearing in the most conservative approaches to quantum theory of gravity is given. The most part of the review is devoted to issues of perturbative quantization based on functional integral technique.…