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Geometric mechanics provides valuable insights into how biological and robotic systems use changes in shape to move by mechanically interacting with their environment. In high-friction environments it provides that the entire interaction is…
To facilitate the treatment of electromagnetic effects in applications such as dynamically perturbed vortons, this work employs a covariantly formulated string-source Green measure to obtain a coherent relativistic scheme for describing the…
We reevaluate the status of the gauge principle and reposition it as an intermediary structure dependent on the initial conditions we endow on our theory. We explore how the gauge symmetry manifests in the context of basic quantum…
We address the question of how to represent an interacting action for the tower of conformal higher spin fields in a form covariant with respect to a background metric. We use a background metric to define a star product which plays a…
Contrary to the conventional view point of quantization that breaks the gauge symmetry, a gauge invariant formulation of quantum electrodynamics is proposed. Instead of fixing the gauge, some frame is chosen to yield the locally invariant…
We analyse three interacting vacuum dark energy models with the aim of exploring whether the $H_0$ and $\sigma_8$ tensions can be simultaneously resolved in such models. We present the first ever derivation of the covariant gauge-invariant…
I discuss various aspects of background independence in the context of string theory, for which so far we have no manifestly background independent formulation. After reviewing the role of background independence in classical Einstein…
The design of an invariant tracking control law for the kinematic car driving on a sphere is discussed. Using a Lie group framework a left-invariant description on SO(3) is derived. Basic geometric considerations allow a direct comparison…
We develop a gauge invariant canonical perturbation scheme for perturbations around symmetry reduced sectors in generally covariant theories, such as general relativity. The central objects of investigation are gauge invariant observables…
We propose an integral formulation of the equations of motion of a large class of field theories which leads in a quite natural and direct way to the construction of conservation laws. The approach is based on generalized non-abelian Stokes…
We consider a $\sigma$-model formulation of open string theory in the presence of D-branes. We perform two-loop computations and discuss gravitational corrections to Born-Infeld action when branes are non-trivially embedded in a curved…
The cosmological constant problem and the possibility of obtaining a see saw cosmological effect, where the effective vacuum energy is highly suppressed by the existence of a large scale is investigated in the context of scale-invariant,…
The background independent formulation of the gauge theories on D-branes in flat space-time is considered, some examples of the solutions of their equations of motion are presented, the solutions of Dirac equation in these backgrounds are…
Metric independent $\sigma$ models are constructed. These are field theories which generalise the membrane idea to situations where the target space has fewer dimensions than the base manifold. Instead of reparametrisation invariance of the…
This paper examines a proposal for gauging non-linear sigma models with respect to a Lie algebroid action. The general conditions for gauging a non-linear sigma model with a set of involutive vector fields are given. We show that it is…
Small non-spherical perturbations of a spherically symmetric but time-dependent background spacetime can be used to model situations of astrophysical interest, for example the production of gravitational waves in a supernova explosion. We…
The open Wilson lines are gauge-invariant operators made with a gauge transporter along an open path saturated at the end-points with matter fields. Here it is shown that numerical experiments on 3D Z2 Higgs model provide useful guidance in…
We look at the covariant techniques and the ideas on constraints and gauge-invariance, which were recently employed in [gr-qc/0702104] to support earlier work by the same authors. That work was criticised in [gr-qc/0503042]. Using very…
In this paper free quantum theories are derived solely from their underlying symmetry group without reference to a Lagrangean or classical physics and then interactions are introduced by making use of automorphism of the symmetry algebra.…
A single-parameter family of covariant gauge fixing conditions in bosonic string field theory is proposed. It is a natural string field counterpart of the covariant gauge in the conventional gauge theory, which includes the Landau gauge as…