Related papers: Multi-dimensional Virasoro algebra and quantum gra…
We extend a recent classification of three-dimensional spatially isotropic homogeneous spacetimes to Chern--Simons theories as three-dimensional gravity theories on these spacetimes. By this we find gravitational theories for all…
We provide a relatively self-contained introduction to the application of quantum spacetime and quantum Riemannian geometry to theoretical physics. Recent successes include calculation of the vacuum energy of spacetime curvature…
The loop equations in the $U(N)$ lattice gauge theory are represented in the form of constraints imposed on a generating functional for the Wilson loop correlators. These constraints form a closed algebra with respect to commutation. This…
The 2-dimensional space-time sine-Gordon field theory is extended algebraically within the n-dimensional space of extended complex numbers. This field theory is constructed in terms of an adapted extension of standard vertex operators. A…
A class of vector-tensor theories arises naturally in the framework of quadratic gravity in spacetimes with linear vector distortion. Requiring the absence of ghosts for the vector field imposes an interesting condition on the allowed…
In this paper, we present and classify the supersymmetric extensions of extended kinematical algebras, at the basis of non-Lorentzian physics theories. The diverse kinematical superalgebras are here derived by applying non- and…
The fourth derivative models for two dimensional gravity are shown to be equivalent to the special version of the nonlinear sigma models coupled to 2d quantum gravity. The reduction consists in the introduction of the auxiliary scalar…
Determining cosmological field equations represents a still very debated matter and implies a wide discussion around different theoretical proposals. A suitable conceptual scheme could be represented by gravity models that naturally…
We consider a Lie algebra generalizing the Virasoro algebra to the case of two space variables. We study its coadjoint representation and calculate the corresponding Euler equations. In particular, we obtain a bi-Hamiltonian system that…
One of the main technical obstacles in constructing a consistent theory of quantum gravity is that the metric itself defines the causal structure required for quantization. This motivates implementing quantum aspects of gravity through an…
We introduce the generalized Lorentz gauge condition in the theory of quantum electrodynamics into the general vector-tensor theories of gravity. Then we explore the cosmic evolution and the static, spherically symmetric solution of the…
The careful analysis of the duality properties of Riemann's curvature tensor points to possibility of extension of Einstein's General Relativity to the nonabelian Yang-Mills theory. The motion equations of the theory are Yang-Mills'…
We construct the non-linear realisation of the semi-direct product of the very extended algebra A1+++ and its vector representation. This theory has an infinite number of fields that depend on a spacetime with an infinite number of…
We add some comments to our old paper \cite{F-U} where the metric tensor was introduced as the gauge theory of general coordinate transformation. This formulation is more satisfactorily completed than the original one if it is required to…
Possible geometric frameworks for a unified theory of gravity and electromagnetism are investigated: General relativity is enlarged by allowing for an arbitrary complex linear connection and by constructing an extended spinor derivative…
Motivated by recent discussions of fractons, we explore nonrelativistic field theories with a continuous global symmetry, whose charge is a spatial vector. We present several such symmetries and demonstrate them in concrete examples. They…
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.…
General relativity successfully describes space-times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time there have been indications that quantum gravity will…
Generalized Virasoro algebras (defined as the universal central extension of some generalized Witt algebras) and super-Virasoro algebras and modules of the intermediate series are studied and discussed.
The metric $f(R)$ theories of gravity are generalized to five-dimensional spacetimes. By assuming a hypersurface-orthogonal Killing vector field representing the compact fifth dimension, the five-dimensional theories are reduced to their…