Related papers: A note on coarse graining and group representation…
The algebraic formulation of the quantum group covariant noncommutative geometry in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider structure groups taking values in the quantum groups and…
In this paper the problem of tomographic reconstruction of states is investigated within the so-called Schwinger's picture of Quantum Mechanics in which a groupoid is associated with every quantum system. The attention is focused on spin…
We introduce a new family of tensorial field theories by coupling different fields in a non-trivial way, with a view towards the investigation of the coupling between matter and gravity in the quantum regime. As a first step, we consider…
We investigate the renormalization group (RG) flow of SU(3) lattice gauge theory in a two coupling space with couplings $\beta_{11}$ and $\beta_{12}$ corresponding to $1\times 1$ and $1\times 2$ loops respectively. Extensive numerical…
In this job, we will present a theory called Quantum Tomography that is the natural extension of the theory of detection of signals in classical telecommunications to Quantum Mechanics. This theory mainly consists in the reconstruction of a…
The current form of quantum mechanics is very successful and is almost certainly correct. It is remarkable, however, that the entire structure-from the mass, spin and charge labels on particlelike states to antisymmetry to broken internal…
The covariantization procedure is usually referred to the translation operator, that is the derivative. Here we introduce a general method to covariantize arbitrary differential operators, such as the ones defining the fundamental group of…
A modified gravitational theory is developed in which the gravitational coupling constants $G$ and $Q$ and the effective mass $m_\phi$ of a repulsive vector field run with momentum scale $k$ or length scale $\ell =1/k$, according to a…
We explore the properties of a recently proposed background independent exact renormalization group approach to gauge theories and gravity. In the process we also develop the machinery needed to study it rigorously. The proposal comes with…
We show how Loop Quantum Cosmology can be derived as an effective semiclassical description of Loop Quantum Gravity. Using the tools of QRLG, a gauge fixed version of LQG, we take the coherent states of the fundamental microscopic theory…
Real-Space renormalization group techniques are developed for tackling large curvature fluctuations in quantum gravity. Within cells of invariant volume $a^4$, only certain types of fluctuations are allowed. Normal coordinates are used to…
The renormalization group method is applied to the study of homogeneous and flat Friedmann-Robertson-Walker type Universes, filled with a causal bulk viscous cosmological fluid. The starting point of the study is the consideration of the…
The basic elements of the geometric approach to a consistent quantization formalism are summarized, with reference to the methods of the old quantum mechanics and the induced representations theory of Lie groups. A possible relationship…
We study renormalization group flows in far-from-equilibrium states. The study is made tractable by focusing on states that are spatially homogeneous, time-independent, and scale-invariant. Such states, in which mode $k$ has occupation…
The phase space given by the cotangent bundle of a Lie group appears in the context of several models for physical systems. A representation for the quantum system in terms of non-commutative functions on the (dual) Lie algebra, and a…
To study materials phenomena simultaneously at various length scales, descriptions in which matter can be coarse grained to arbitrary levels, are necessary. Attempts to do this in the static regime (i.e. zero temperature) have already been…
We survey and analyze different ways in which bornologies, coarse structures and uniformities on a group agree with the group operations.
We give a very brief introduction to the group field theory approach to quantum gravity, a generalisation of matrix models for 2-dimensional quantum gravity to higher dimension, that has emerged recently from research in spin foam models.
The results of the renormalization group are commonly advertised as the existence of power law singularities near critical points. The classic predictions are often violated and logarithmic and exponential corrections are treated on a…
Group field theories represent a 2nd quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs…