Related papers: The Spectral Action Principle
Scaling symmetries have previously been examined for classical field theories described by singular Lagrangians; in this article, we apply these results to the first-order formulation of General Relativity. It is shown that the dynamical…
In this work, a subclass of the generalized Kerr-Schild class of spacetimes is specified, with respect to which the Ricci tensor (regardless of the position of indices) proves to be linear in the so-called profile function of the geometry.…
As is well known, in order for the Einstein--Hilbert action to have a well defined variation, and therefore to be used for deriving field equation through the stationary action principle, it has to be amended by the addition of a suitable…
In this article we prove a generalization of Weyl's criterion for the spectrum of a self-adjoint nonnegative operator on a Hilbert space. We will apply this new criterion in combination with Cheeger-Fukaya-Gromov and Cheeger-Colding theory…
A connection-independent formulation of general relativity is presented, in which the dynamics does not depend on the choice of connection. The gravity action in this formulation includes one additional scalar term in addition to the…
In this paper, we study the effective action, the mass spectrum and the first law of entanglement entropy for a novel doubly holographic model called wedge holography. We work out the effective action of quantum gravity on the branes. In…
We consider a free massless scalar field coupled to an infinite tower of background higher-spin gauge fields via minimal coupling to the traceless conserved currents. The set of Abelian gauge transformations is deformed to the non-Abelian…
A first-order formulation of gravity is developed in which the fundamental fields consist of an SL(2,C) connection and two spinor-valued 1-forms. It is shown that the first term of an expansion of the Einstein-Hilbert action leads to an…
We propose a method for the spectral analysis of unbounded operator matrices in a general setting which fully abstains from standard perturbative arguments. Rather than requiring the matrix to act in a Hilbert space $\mathcal{H}$, we extend…
This article surveys the noncommutative-geometric (NCG) approach to fundamental physics, in which geometry is encoded spectrally by a generalized Dirac operator and where dynamics arise from the spectral action. I review historically how…
We construct an effective action for gravity in which all homogeneous solutions are nonsingular. In particular, there is neither a big bang nor a big crunch. The action is a higher derivative modification of Einstein's theory constructed in…
We discuss the calculation of the 1-loop effective action on four dimensional, canonically deformed Euclidean space. The theory under consideration is a scalar $\phi^4$ model with an additional oscillator potential. This model is known to…
By integrating the Seiberg-Witten differential equation in a special path, we write ordinary gauge fields in terms of their non-commutative counterparts up to three non-commutative gauge fields. We then use this change of variables to write…
We construct a model unifying gravity with weak $SU(2)$ gauge and "Higgs" scalar fields. We assume the existence of a visible and an invisible (hidden) sector of the Universe. We used the extension of Plebanski's 4-dimensional gravitational…
We consider the (gauged) Weyl gravity action, quadratic in the scalar curvature ($\tilde R$) and in the Weyl tensor ($\tilde C_{\mu\nu\rho\sigma}$) of the Weyl conformal geometry. In the absence of matter fields, this action has spontaneous…
We examine the hypothesis that space-time is a product of a continuous four-dimensional manifold times a finite space. A new tensorial notation is developed to present the various constructs of noncommutative geometry. In particular, this…
We consider the twistor description of conformal higher spin theories and give twistor space actions for the self-dual sector of theories with spin greater than two that produce the correct flat space-time spectrum. We identify a ghost-free…
The gravitating matter is studied within the framework of the non-commutative geometry. The non-commutative Einstein-Hilbert action on the product of a four dimensional manifold with a discrete space gives the models of matter fields…
The evolution equation is used as the fundamental equation of field theory, which is described entirely by the geometry of the four-dimensional space. The evolution kernel determines the covariant action of physical fields by the proper…
We study different quantum one dimensional systems with noncanonical commutation rule $[x,p]=i\hbar (1+sH),$ where $H$ is the one particle Hamiltonian and $s$ is a parameter. This is carried-out using semiclassical arguments and the surmise…