Related papers: Polymer and Fock representations for a Scalar fiel…
We consider theories of gravity that include many coupled scalar fields with arbitrary couplings, in the geometric framework of wave maps. We examine the possibility of obtaining acceptable cosmological solutions without the inclusion of a…
The effect of coupling non-compact $U(1)$ gauge fields to four dimensional simplicial quantum gravity is studied using strong coupling expansions and Monte Carlo simulations. For one gauge field the back-reaction of the matter on the…
We extend the recently developed kinematical framework for diffeomorphism invariant theories of connections for compact gauge groups to the case of a diffeomorphism invariant quantum field theory which includes besides connections also…
It is well known that the quantum double structure plays an important role in three dimensional quantum gravity coupled to matter field. In this paper, we show how this algebraic structure emerges in the context of three dimensional…
Conventional quantum field theory is a method for studying structureless elementary particles. Non-elementary particles, on the other hand, are those with internal structure or particles that are made up of elementary constituents like the…
For decades, a lot of work has been devoted to the problem of constructing a non-trivial quantum field theory in four-dimensional space time. This letter addresses the attempts to construct an algebraic quantum field theory in the framework…
A homogeneous and isotropic quantum cosmological system (universe) initially filled with a uniform scalar field that has a potential in the power law representation is considered. Depending on the epoch, this scalar field yields barotropic…
The U(N) framework and the spinor representation for loop quantum gravity are two new points of view that can help us deal with the most fundamental problems of the theory. Here, we review the detailed construction of the U(N) framework…
The nature of the classical canonical phase-space variables for gravity suggests that the associated quantum field operators should obey affine commutation relations rather than canonical commutation relations. Prior to the introduction of…
The volume operator plays a central role in both the kinematics and dynamics of canonical approaches to quantum gravity which are based on algebras of generalized Wilson loops. We introduce a method for simplifying its spectral analysis,…
The problem of finding the quantum theory of the gravitational field, and thus understanding what is quantum spacetime, is still open. One of the most active of the current approaches is loop quantum gravity. Loop quantum gravity is a…
A model aimed at understanding quantum gravity in terms of Birkhoff's approach is discussed. The geometry of this model is constructed by using a winding map of Minkowski space into a $\mathbb{R}^{3} \times S^{1}$-cylinder. The basic field…
We are concerned with the issue of quantization of a scalar field in a diffeomorphism invariant manner. We apply the method used in Loop Quantum Gravity. It relies on the specific choice of scalar field variables referred to as the polymer…
We study the relational cosmological dynamics emerging from interacting group field theory (GFT) models minimally coupled to a massless clock scalar field and a self-interacting scalar field. We focus on two broad classes of GFT…
The article gives an account of several aspects of the space known as the Bohr compactification of the line, featuring as the quantum configuration space in loop quantum cosmology, as well as of the corresponding configuration space…
We study the semiclassical dynamics of a polymer quantized scalar field with a cubic potential in cosmology. The cosmological spacetime is chosen to be homogeneous and isotropic, and we work in the polymer quantization scheme where the…
We revisit the quantization of U(1) holonomy algebras using the abelian C* algebra based techniques which form the mathematical underpinnings of current efforts to construct loop quantum gravity. In particular, we clarify the role of…
These notes have been triggered by physicist's considerations on (1)'Pre-quantized wave equations' for matter fields, (2) Conservation laws, (3) Gauge Field extensions. All starting from variational principles. These notes do not contain…
Gravity is commonly thought of as one of the four force fields in nature. However, in standard formulations its mathematical structure is rather different from the Yang-Mills fields of particle physics that govern the electromagnetic, weak,…
The representations of the observable algebra of a low dimensional quantum field theory form the objects of a braided tensor category. The search for gauge symmetry in the theory amounts to finding an algebra which has the same…