Related papers: The Immirzi parameter in quantum general relativit…
By parametrizing the action integral for the standard Schrodinger equation we present a derivation of the recently proposed method for quantizing a parametrized theory. The reformulation suggests a natural extension from conventional to…
We embed the Loop Quantum Gravity Barbero-Immirzi parameter and field within an action describing 4D, $\cal N$ = 1 supergravity and thus within a Low Energy Effective Action of Superstring/M-Theory. We use the fully gauge-covariant…
The implications of a Generalized Uncertainty Principle on the Taub cosmological model are investigated. The model is studied in the ADM reduction of the dynamics and therefore a time variable is ruled out. Such a variable is quantized in a…
Beginning with the work of Dirac and Arnowitt, Deser, Misner in the late fifties and early sixties, and then after subsequent development by Kucha\v r, the canonical dynamical structure of general relativity has often been viewed as that of…
We consider first generation scalar-tensor theories of gravitation in a completely generic form, keeping the transformation functions of the local rescaling of the metric and the scalar field redefinition explicitly distinct from the…
We carry out the complete variational analysis of the Barbero--Immirzi--Holst Lagrangian, which is the Holst Lagrangian expressed in terms of the triad of fields $(\theta, A, \kappa)$, where $\theta$ is the solder form/spin frame, $A$ is…
For various theories, in particular gauge field theories, the algebraic form of the Hamiltonian simplifies considerably if one writes it in terms of certain complex variables. Also general relativity when written in the new canonical…
Quantum mechanics with a generalized uncertainty principle arises through a representation of the commutator $[\hat{x}, \hat{p}] = i f(\hat{p})$. We apply this deformed quantization to free scalar field theory for $f_\pm =1\pm \beta p^2$.…
Recent developments concerning canonical quantisation and gauge invariant quantum mechanical systems and quantum field theories are briefly discussed. On the one hand, it is shown how diffeomorphic covariant representations of the…
Let $G$ be a Lie group, $\g$ its Lie algebra, and $U_h(\g)$ the corresponding quantum group. We consider some examples of $U_h(\g)$-invariant one and two parameter quantizations on $G$-manifolds.
In this paper, we extend the quantum geometric tensor for parameter-dependent curved spaces to higher dimensions, and introduce an equivalent definition that generalizes the Zanardi, et al, formulation of the tensor. The parameter-dependent…
We put forward the first analysis of renormalization group flows in an area-metric theory, motivated by spin-foam quantum gravity. Area-metric gravity contains the well-known length-metric degrees of freedom of standard gravity as well as…
A new form of the dynamical equations of vacuum general relativity is proposed. This form involves the canonical Hamiltonian structure but non canonical variables. The new field variables are the electric field $E^{a}{}_{i}$ and the…
Using self dual Ashtekar variables, we investigate (at the effective level) the spherically symmetry reduced model of loop quantum gravity, both in vacuum and when coupled to a scalar field. Within the real Ashtekar-Barbero formulation, the…
It is possible to implement a certain form of modified gravity inspired by loop quantization through non-bijective canonical transformations. The canonical nature might suggest that such modifications are guaranteed to preserve general…
Peculiar phenomena appear in the discretization of a system invariant under reparametrization. The structure of the continuum limit is markedly different from the usual one, as in lattice QCD. First, the continuum limit does not require…
Present day quantum field theory (QFT) is founded on canonical quantization, which has served quite well, but also has led to several issues. The free field describing a free particle (with no interaction term) can suddenly become…
We describe a deformation of the observable algebra of quantum gravity in which the loop algebra is extended to framed loops. This allows an alternative nonperturbative quantization which is suitable for describing a phase of quantum…
We develop the quantization of unimodular gravity in the Plebanski and Ashtekar formulations and show that the quantum effective action defined by a formal path integral is unimodular. This means that the effective quantum geometry does not…
The Hilbert space of a free massless particle moving on a group manifold is studied in details using canonical quantisation. While the simplest model is invariant under a global symmetry, $G \times G$, there is a very natural way to…