Related papers: Gerbes, Quantum Mechanics and Gravity
Assuming that the mechanism proposed by Gell-Mann and Hartle works as a mechanism for decoherence and classicalization of the metric field, we formally derive the form of an effective theory for the gravitational field in a semiclassical…
We consider the quantum mechanics of a particle on a noncommutative two-sphere with the coordinates obeying an SU(2)-algebra. The momentum operator can be constructed in terms of an $SU(2)\times SU(2)$-extension and the Heisenberg algebra…
Quantum theory does not only predict probabilities, but also relative phases for any experiment, that involves measurements of an ensemble of systems at different moments of time. We argue, that any operational formulation of quantum theory…
Classically, unimodular gravity is known to be equivalent to General Relativity (GR), except for the fact that the effective cosmological constant $\Lambda$ has the status of an integration constant. Here, we explore various formulations of…
We will argue in this paper that the type classification of v.Neumann algebras play an important role in a theory of quantum gravity and quantum space-time physics. We provide arguments that type $II_{\infty}$ and its representation as a…
An earlier proposed theory with linear-gonihedhic action for quantum gravity is reviewed. One can consider this theory as a "square root" of classical gravity with a new fundamental constant of dimension one. We demonstrate also, that the…
We consider classical and quantum mechanics for an extended Heisenberg algebra with additional canonical commutation relations for position and momentum coordinates. In our approach this additional noncommutativity is removed from the…
The classical theory of gravity is formulated as a gauge theory on a frame bundle with spontaneous symmetry breaking caused by the existence of Dirac fermionic fields. The pseudo-Riemannian metric (tetrad field) is the corresponding Higgs…
Semiclassical Gravity replaces the energy momentum tensor $T_{\mu \nu}$ with its expectation value $\langle T_{\mu \nu}\rangle$ in Einstein equations, this making the Einstein tensor $G_{\mu \nu}$ a classical variable thus avoiding the…
The fundamental interactions of nature, the electroweak and the quantum chromodynamics, are described in the Standard Model by the Gauge Theory under internal symmetries that maintain the invariance of the functional action. The fundamental…
In this paper we consider the relation between the super-renormalizable theories of quantum gravity (SRQG) studied in [arXiv:1110.5249v2, arXiv:1202.0008] and an underlying non-commutativity of spacetime. For one particular…
We present a new point of view on the quantization of the gravitational field, namely we use exclusively the quantum framework of the second quantization. More explicitly, we take as one-particle Hilbert space, $H_{graviton}$ the unitary…
This is an introduction to an algebraic construction of a gravity theory on noncommutative spaces which is based on a deformed algebra of (infinitesimal) diffeomorphisms. We start with some fundamental ideas and concepts of noncommutative…
We discuss gravity-like formulations of massive Abelian and non-Abelian gauge field theories in four space-time dimensions with particular emphasis on the issue of gauge invariance. Alternative descriptions in terms of antisymmetric tensor…
The quantum field theory of gravitation is constructed in terms of Lagrangian density of Dirac fields which couple to the electromagnetic field $A_\mu$ as well as the gravitational field $\cal G$. The gravity appears in the mass term as $…
There are fundamental reasons as to why there should exist a reformulation of quantum mechanics which does not refer to a classical spacetime manifold. It follows as a consequence that quantum mechanics as we know it is a limiting case of a…
We extend and strengthen no-go results on pointwise-defined quantum fields to cover general spinors. We show that the weak continuity of quantum fields rules out equal-time canonical conjugate (anti)commutation relations in globally…
In this Letter we construct the noncommutative (NC) gravity model on the $\theta$-constant NC space-time. We start from the NC $SO(2,3)_\star$ gauge theory and use the enveloping algebra approach and the Seiberg-Witten map to construct the…
An Abelian gerbe is constructed over classical phase space. The 2-cocycles defining the gerbe are given by Feynman path integrals whose integrands contain the exponential of the Poincare-Cartan form. The U(1) gauge group on the gerbe has a…
In this paper we couple noncommutative (NC) vielbein gravity to scalar fields. Noncommutativity is encoded in a star product between forms, given by an abelian twist (a twist with commuting vector fields). A geometric generalization of the…