Related papers: An introduction to spin systems for mathematicians
The roles that spin networks play in gauge theories, quantum gravity and topological quantum field theory are briefly described, with an emphasis on the question of the relationships among them. It is argued that spin networks and their…
We give a short introduction for elementary mathematical tools used in the context of Quantum Field Theory. These notes were motivated by a reading group in Lyon on Talagrand's book {\guillemotleft}What is Quantum Field Theory, A First…
Spin-density-functional theory (SDFT) is the most widely implemented and applied formulation of density-functional theory. However, it is still finding novel applications, and occasionally encounters unexpected problems. In this paper we…
Spherical field theory is a new non-perturbative method for studying quantum field theories. It uses the spherical partial wave expansion to reduce a general d-dimensional Euclidean field theory into a set of coupled one-dimensional…
The Spin Foam approach to quantum gravity aims at providing a covariant path-integral formulation of canonical Loop Quantum Gravity. Since spin foam amplitudes are defined through discretisations of spacetime, understanding the continuum…
A structural explanation of the coupling constants in the standard model, i.e the fine structure constant and the Weinberg angle, and of the gauge fixing contributions is given in terms of symmetries and representation theory. The coupling…
The majority of current understanding of the quantum correlations is in the field of non-relativistic quantum mechanics. To develop quantum information and computation tasks fully, one must inevitably take into account the relativistic…
In this short note, I review some recent results about gapped ground state phases of quantum spin systems and discuss the notion of topological order.
We investigate the impact of an isotropic antiferromagnetic Heisenberg perturbation on the toric code, focusing on the resulting quantum phase transition and the nature of the phase that emerges beyond topological order. Using…
The concept of twisted Poincar\'e symmetry, as well as some implications, are reviewed. The spin-statistics relation and the nonlocality of NC QFT are discussed in the light of this quantum symmetry. The possibility of a twisted symmetry…
These are a set of lecture notes on generalized global symmetries in quantum field theory. The focus is on invertible symmetries with a few comments regarding non-invertible symmetries. The main topics covered are the basics of higher-form…
Quantum field theory is the application of quantum physics to fields. It provides a theoretical framework widely used in particle physics and condensed matter physics. One of the most distinct features of quantum physics with respect to…
This is a short introduction to Hilbert space frame theory and its applications for those outside the area who want to enter the subject. We will emphasize finite frame theory since it is the easiest way to get into the subject.
We use machine learning to classify rational two-dimensional conformal field theories. We first use the energy spectra of these minimal models to train a supervised learning algorithm. We find that the machine is able to correctly predict…
The numerical emulation of quantum systems often requires an exponential number of degrees of freedom which translates to a computational bottleneck. Methods of machine learning have been used in adjacent fields for effective feature…
In this paper we study the effect of non-trivial spatial topology on quantum entanglement by examining the degenerate ground states of a topologically ordered system on torus. Using the string-net (fixed-point) wave-function, we propose a…
We consider the FRW cosmological model in which the matter content of universe (playing a role of inflaton or quintessence) is given by a novel generalization of the massive scalar field. The latter is a scalar version of the recently…
A mathematically rigorous Hamiltonian formulation for classical and quantum field theories is given. New results include clarifications of the structure of linear fields, and a plausible formulation for nonlinear fields. Many mathematical…
En nous laissant guider par la notion de champ qui en fait domine toute la physique nous d\'efinissons la nature physique d'un syst\`eme, ses propri\'et\'es et ses \'etats possibles. Nous proposons alors un cadre tr\`es g\'en\'erale…
In this Perspective article, we explore some of the promising spin and topology material platforms (e.g. spins in semi- and superconductors, skyrmionic, topological and 2D materials) being developed for such quantum components as qubits,…