Related papers: Group field theories for all loop quantum gravity
Well defined quantum field theory (QFT) for the electroweak force including quantum electrodynamics (QED) and the weak force is obtained by considering natural unitary representations of a group $K\subset U(2,2)$, where $K$ is locally…
Gauge field theory with rank-one field $T_{\mu}$ is a quantum field theory that describes the interaction of elementary spin-1 particles, of which being massless to preserve gauge symmetry. In this paper, we give a generalized, extended…
In standard quantum field theory, the one-particle states are classified by the unitary representations of the Poincar\'e group, whereas the causal fields' classification employs the finite-dimensional (non-unitary) representations of the…
This thesis provides an introduction to the various category theory ideas employed in topological quantum field theory. These theories are viewed as symmetric monoidal functors from topological cobordism categories into the category of…
This is a pedagogical introduction to the treatment of quantum general relativity as an effective field theory. It starts with an overview of the methods of effective field theory and includes an explicit example. Quantum general relativity…
The physics of quantum gravity is discussed within the framework of topological quantum field theory. Some of the principles are illustrated with examples taken from theories in which space-time is three dimensional.
The quantum theory of fields is largely based on studying perturbations around non-interacting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is…
In this introductory article a brief description of Quantum Field Theories (QFT) is presented with emphasis on the distinction between strongly and weakly coupled theories. A case is made for using numerical simulations to solve QCD, the…
We give a general procedure, in the group field theory (GFT) formalism for quantum gravity, for constructing states that describe macroscopic, spatially homogeneous universes. These states are close to coherent (condensate) states used in…
We study the (generalized) transition probability spaces, in the sense of Mielnik and Cantoni, for spacetime quantum states in loop quantum gravity. First, we show that loop quantum gravity admits the structures of transition probability…
A new, configuration-space picture of a formalism of group quantization, the GAQ formalism, is presented in the context of a previous, algebraic generalization. This presentation serves to make a comprehensive discussion in which other…
Quantum field theory (QFT) based on the principles of special relativity (SR) and it is in fact the \emph{kinematic theory of fields}. The root assumption is that there is "relativistic description" of \emph{any} isolated quantum system in…
We review the status of (scalar) quantum field theory on curved spacetimes using a novel formulation in terms of non linear functionals over the smooth configuration fields. In particular, this entails also a new foundation of locally…
Quantum fields are shown to provide an example of infinite-dimensional quantum groups. A dictionary is established between quantum field and quantum group concepts: the expectation value over the vacuum is the counit, Wick's theorem is the…
The early universe provides an opportunity for quantum gravity to connect to observation by explaining the large-scale structure of the Universe. In the group field theory (GFT) approach, a macroscopic universe is described as a GFT…
Relativistic quantum field theory (QFT) is commonly formulated in terms of operators, asymptotic states, and covariant amplitudes, a perspective that tends to obscure the real-time origin of field dynamics and correlations. Here we…
Quantum cluster approaches offer new perspectives to study the complexities of macroscopic correlated fermion systems. These approaches can be understood as generalized mean-field theories. Quantum cluster approaches are non-perturbative…
In fundamental physics, this has been the century of quantum mechanics and general relativity. It has also been the century of the long search for a conceptual framework capable of embracing the astonishing features of the world that have…
A general formalism is developed that allows the construction of a field theory on quantum spaces which are deformations of ordinary spacetime. The symmetry group of spacetime (Poincar\' e group) is replaced by a quantum group. This…
I review the basic ingredients of discretized gravity which motivate the introduction of Group Field Theory. Thus I describe the GFT formulation of some models and conclude with a few remarks on the emergence of noncommutative structures in…