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We derive an action whose equations of motion contain the Poisson equation of Newtonian gravity. The construction requires a new notion of Newton--Cartan geometry based on an underlying symmetry algebra that differs from the usual Bargmann…
A recently proposed variational approach for general relativity where, in addition to the metric tensor, two independent affine connections enter the action as dynamical variables, is revised. Field equations always reduce to the Einstein…
Trace-free Einstein gravity is a theory of gravity that is an alternative to general relativity, wherein the cosmological constant arises as an integration constant. However, there are no fully diffeomorphism-invariant action principles…
Various authors have invoked discretized fractional Brownian (fBm) motion as a model for chain polymers with long range interaction of monomers along the chain. We show that for these, in contrast to the Brownian case, linear forces are…
We study Hamiltonian form of unfree gauge symmetry where the gauge parameters have to obey differential equations. We consider the general case such that the Dirac-Bergmann algorithm does not necessarily terminate at secondary constraints,…
The polynomial affine gravity is an alternative model of gravity whose fundamental field is the affine connection, and it is invariant under the complete group of diffeomorphisms. In 3+1 dimensions the field equations generalise those of…
Following Feynman's treatment of the non-relativistic polaron problem, similar techniques are used to study relativistic field theories: after integrating out the bosonic degrees of freedom the resulting effective action is formulated in…
An explicit, geometric description of the first-class constraints and their Poisson brackets for gravity in the Palatini-Cartan formalism (in space-time dimension greater than three) is given. The corresponding Batalin- Fradkin-Vilkovisky…
Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a non-differentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables. Owing to…
We consider a generic gauge system, whose physical degrees of freedom are obtained by restriction on a constraint surface followed by factorization with respect to the action of gauge transformations; in so doing, no Hamiltonian structure…
We present a covariant multisymplectic formulation for the Einstein-Palatini (or Metric-Affine) model of General Relativity (without energy-matter sources). As it is described by a first-order affine Lagrangian (in the derivatives of the…
It is known that Ashtekar's formulation for pure Einstein gravity can be cast into the form of a topological field theory, namely the $SU(2)$ BF theory, with the B-fields subject to an algebraic constraint. We extend this relation between…
The Hamilton-Jacobi analysis of three dimensional gravity defined in terms of Ashtekar-like variables is performed. We report a detailed analysis where the complete set of Hamilton-Jacobi constraints, the characteristic equations and the…
We study Einstein gravity in a finite spatial region. By requiring a well-defined variational principle, we identify all local boundary conditions, derive surface observables, and compute their algebra. The observables arise as induced…
General relativity can be formulated as a SU(2) BF-theory with constraints, as has been shown, by Pleba\'nski. The cosmological constant term can be obtained from the constraint term, following from the consistency of the equations of…
Recently the so-called mimetic gravity approach has been used to obtain corrections to Friedmann equation of General Relativity similar to the ones present in loop quantum cosmology. In this paper, we propose an alternative way to derive…
We give a derivation of general relativity and the gauge principle that is novel in presupposing neither spacetime nor the relativity principle. We consider a class of actions defined on superspace with two key properties. The first is…
An action principle is presented for Vasiliev's Bosonic higher spin gauge theory in four spacetime dimensions. The action is of the form of a broken topological field theory, and arises by an extension of the MacDowell-Mansouri formulation…
We present the Hamiltonian formalism for $f(T)$ gravity, and prove that the theory has $\frac{n(n-3)}{2}+1$ degrees of freedom (d.o.f.) in $n$ dimensions. We start from a scalar-tensor action for the theory, which represents a scalar field…
We propose a new model of gravity where the Ricci scalar (R) in Einstein-Hilbert action is replaced by an arbitrary function of R and of the norm of energy-momentum tensor i.e., $f(R,T_{\mu\nu}T^{\mu\nu})$. Field equations are derived in…