Related papers: On the Equivalence between 2D Induced Gravity and …
It is a well known result that any formulation of unimodular gravity is classically equivalent to General Relativity (GR), however a debate exists in the literature about this equivalence at the quantum level. In this work, we investigate…
The concept of gauge invariance can be considered one of the most subtle and useful concept in theoretical physics since it can permit the comprehension of difficult systems in physics with an arbitrary choice of a reference frame at every…
Tensor networks prepare states that share many features of states in quantum gravity. However, standard constructions are not diffeomorphism invariant and do not support an algebra of non-commuting area operators. Recently, analogues of…
The current understanding of renormalization in quantum gravity (QG) is based on the fact that UV divergences of effective actions in the covariant QG models are covariant local expressions. This fundamental statement plays a central role…
We formulate a 4-dimensional higher gauge theoretic Chern-Simons theory. Its symmetry is encoded in a semistrict Lie 2-algebra equipped with an invariant non singular bilinear form. We analyze the gauge invariance of the theory and show…
Inertial and gravitational mass or energy-momentum need not be the same for virtual quantum states. Separating their roles naturally leads to the gauge theory of volume-preserving diffeomorphisms of an inner four-dimensional space. The…
The framework of the Covariant Canonical Gauge theory of Gravity (CCGG) is described in detail. CCGG emerges naturally in the Palatini formulation, where the vierbein and the spin connection are independent fields. Neither torsion nor…
We study quantum intergrable systems of interacting particles from the point of view, proposed in our previous paper. We obtain Calogero-Moser and Sutherland systems as well their Ruijsenaars relativistic generalization by a Hamiltonian…
Loop quantum gravity is an approach to quantum gravity that starts from the Hamiltonian formulation in terms of a connection and its canonical conjugate. Quantization proceeds in the spirit of Dirac: First one defines an algebra of basic…
We present a comprehensive formalism to derive precise expressions for the induced gravity of the braneworld, assuming the dynamics of the Dirac-Nambu-Goto type. The quantum fluctuations of the brane at short distances give rise to…
In this paper the quantization of the 2$+$1-dimensional gravity couplet to the massless Dirac field is carried out. The problem is solved by the application of the new Dynamic Quantization Method [1,2]. It is well-known that in general…
Following the Hamiltonian structure of bi-gravity and multi-gravity models in the full phase space, we have constructed the generating functional of diffeomorphism gauge symmetry. As is expected, this generator is constructed from the first…
The interaction of matter with gravity in two dimensional spacetimes can be supplemented with a geometrical force analogous to a Lorentz force produced on a surface by a constant perpendicular magnetic field. In the special case of constant…
A family of diffeomorphism-invariant Seiberg--Witten deformations of gravity is constructed. In a first step Seiberg--Witten maps for an SO(1,3) gauge symmetry are obtained for constant deformation parameters. This includes maps for the…
For spacetimes with the topology $\IR\!\times\!T^2$, the action of (2+1)-dimensional gravity with negative cosmological constant $\La$ is written uniquely in terms of the time-independent traces of holonomies around two intersecting…
We construct not only an induced gravity model with the restricted diffeomorphisms, that is, transverse diffeomorphisms which preserves the curvature density, but also that with the full diffeomorphisms. By solving the equations of motion,…
We consider two programs for quantizing gravity in $1+1$ dimensions, which have appeared in the literature: one using a gauge--theoretic approach and the other following a more conventional ``geometric'' approach. We compare the wave…
In this short note we perform canonical analysis of the theory invariant under restricted diffeomorphism so that the action contains kinetic term for determinant of metric. We find corresponding Hamiltonian and determine structure of…
We consider the role of the diffeomorphism constraint in the quantization of lattice formulations of diffeomorphism invariant theories of connections. It has been argued that in working with abstract lattices, one automatically takes care…
Coadjoint orbits of the Virasoro and Kac-Moody algebras provide geometric actions for matter coupled to gravity and gauge fields in two dimensions. However, the Gauss' law constraints that arise from these actions are not necessarily…