Related papers: Combinatorics of random tensor models
Field theory is an area in physics with a deceptively compact notation. Although general purpose computer algebra systems, built around generic list-based data structures, can be used to represent and manipulate field-theory expressions,…
We develop a reformulation of the functional integral for bosons in terms of bilocal fields. Correlation functions correspond to quantum probabilities instead of probability amplitudes. Discrete and continuous global symmetries can be…
We construct the ordinary irreducible representations of the group of automorphisms of a finite rooted tree and we get a natural parametrization of them. To achieve this goals, we introduce and study the combinatorics of tree compositions,…
Based on local gauge invariance, four different kinds of fundamental interactions in Nature are unified in a theory which has $SU(3)_c \otimes SU(2)_L \otimes U(1) \otimes_s Gravitational Gauge Group$ gauge symmetry. In this approach,…
A pedagogical introduction to some of the main ideas and results of field theories on quantized spacetimes is presented, with emphasis on what such field theories may teach us about the problem of quantizing gravity. We examine to what…
A generalization of the matrix model idea to quantum gravity in three and higher dimensions is known as group field theory (GFT). In this paper we study generalized GFT models that can be used to describe 3D quantum gravity coupled to point…
I give a very brief introduction to the use of effective field theory techniques in quantum calculations of general relativity. The gravitational interaction is naturally organized as a quantum effective field theory and a certain class of…
In this paper we put forward a systematic and unifying approach to construct gauge invariant composite fields out of connections. It relies on the existence in the theory of a group valued field with a prescribed gauge transformation. As an…
We construct the space of vector fields on a generic quantum group. Its elements are products of elements of the quantum group itself with left invariant vector fields. We study the duality between vector fields and 1-forms and generalize…
A foundation is laid for a theory of combinatorial groupoids, allowing us to use concepts like ``holonomy'', ``parallel transport'', ``bundles'', ``combinatorial curvature'' etc. in the context of simplicial (polyhedral) complexes, posets,…
We introduce group field theory networks as a generalization of spin networks and of (symmetric) random tensor networks and provide a statistical computation of the R\'enyi entropy for a bipartite network state using the partition function…
A compact formulation of the field-strengths, Bianchi identities and gauge transformations for tensor hierarchies in gauged maximal supergravity theories is given. A key role in the construction is played by the recently-introduced tensor…
It has been proposed that random wide neural networks near Gaussian process are quantum field theories around Gaussian fixed points. In this paper, we provide a novel map with which a wide class of quantum mechanical systems can be cast…
The integrability of the generalized Benney hierarchy with three primary fields is investigated from the point of view of two-dimensional topological field theories coupled to gravity. The associated primary free energy and correlation…
The proposed theory of causally structured discrete fields studies integer values on directed edges of a self-similar graph with a propagation rule, which we define as a set of valid combinations of integer values and edge directions around…
Combinatorial enumeration leads to counting generating functions presenting a wide variety of analytic types. Properties of generating functions at singularities encode valuable information regarding asymptotic counting and limit…
We present a random matrix model suitable for the quantum mechanical description of a particle confined to move inside a two-dimensional domain. Here, the ensemble average corresponds to an average over domain shapes. Although this approach…
We introduce a linearized version of group field theory. It can be viewed either as a group field theory over the additive group of a vector space or as an asymptotic expansion of any group field theory around the unit group element. We…
The quantum gravity is formulated based on principle of local gauge invariance. The model discussed in this paper has local gravitational gauge symmetry and gravitational field appears as gauge field. The problems on quantization and…
The fundamental interactions of nature, the electroweak and the quantum chromodynamics, are described in the Standard Model by the Gauge Theory under internal symmetries that maintain the invariance of the functional action. The fundamental…