Publications

Order by: publication date number of citations

• Quantum Field Theory Anomalies in Condensed Matter Physics

  R. Arouca, Andrea Cappelli, T. H. Hansson

  SciPost Phys. Lect. Notes 62 (2022) · published 8 September 2022 | Toggle abstract · pdf

  We give a pedagogical introduction to quantum anomalies, how they are calculated using various methods, and why they are important in condensed matter theory. We discuss axial, chiral, and gravitational anomalies as well as global anomalies. We illustrate the theory with examples such as quantum Hall liquids, Fermi liquids, Weyl semi-metals, topological insulators and topological superconductors. The required background is basic knowledge of quantum field theory, including fermions and gauge fields, and some familiarity with path integral and functional methods. Some knowledge of topological phases of matter is helpful, but not necessary.

  6 citations

• Nested Algebraic Bethe Ansatz in integrable models: recent results

  Stanislav Pakuliak, Eric Ragoucy, Nikita Slavnov

  SciPost Phys. Lect. Notes 6 (2018) · published 29 October 2018 | Toggle abstract · pdf

  This short note summarizes the works done in collaboration between S. Belliard (CEA, Saclay), L. Frappat (LAPTh, Annecy), S. Pakuliak (JINR, Dubna), E. Ragoucy (LAPTh, Annecy), N. Slavnov (Steklov Math. Inst., Moscow) and more recently A. Hutsalyuk (Wuppertal / Moscow) and A. Liashyk (Kiev / Moscow). It presents the construction of Bethe vectors, their scalar products and the form factors of local operator for integrable models based on the (super)algebras $gl_n$, $gl_{m|p}$ or their quantum deformations. It corresponds to two talks given by E.R. and N.S. at \textsl{Correlation functions of quantum integrable systems and beyond}, in honor of Jean-Michel Maillet for his 60's (ENS Lyon, October 2017).

  6 citations

• Notes on 8 Majorana Fermions

  David Tong, Carl Turner

  SciPost Phys. Lect. Notes 14 (2020) · published 30 March 2020 | Toggle abstract · pdf

  Eight Majorana fermions in $d=1+1$ dimensions enjoy a triality that permutes the representation of the $SO(8)$ global symmetry in which the fermions transform. This triality plays an important role in the quantization of the superstring, and in the analysis of interacting topological insulators and the associated phenomenon of symmetric mass generation. The purpose of these notes is to provide an introduction to the triality and its applications, with careful attention paid to various ${\bf Z}_2$ global and gauge symmetries and their coupling to background spin structures.

  6 citations

• Aspects of high energy scattering

  Chris D. White

  SciPost Phys. Lect. Notes 13 (2020) · published 7 February 2020 | Toggle abstract · pdf

  Scattering amplitudes in quantum field theories are of widespread interest, due to a large number of theoretical and phenomenological applications. Much is known about the possible behaviour of amplitudes, that is independent of the details of the underlying theory. This knowledge is often neglected in modern QFT courses, and the aim of these notes - aimed at graduate students - is to redress this. We review the possible singularities that amplitudes can have, before examining the generic behaviour that can arise in the high-energy limit. Finally, we illustrate the results using examples from QCD and gravity.

  5 citations

• Dark Matter direct detection of classical WIMPs

  Jodi Cooley

  SciPost Phys. Lect. Notes 55 (2022) · published 20 May 2022 | Toggle abstract · pdf

  One of the highest priorities in particle physics today is the identification of the constituents of dark matter. This manuscript is a supplement to pedagogical lectures given at the 2021 Les Houches Summer School on Dark Matter. The lectures cover topics related to the direct detection of WIMP dark matter, including the distribution of dark matter, nuclear scattering, backgrounds, planning and designing of experiments, and a sampling of planned and ongoing experiments.

  5 citations

• An introduction to higher-form symmetries

  Pedro R. S. Gomes

  SciPost Phys. Lect. Notes 74 (2023) · published 11 September 2023 | Toggle abstract · pdf

  These notes are intended to be a pedagogical introduction to higher-form symmetries, which are symmetries whose charged objects are extended operators supported on lines, surfaces, and etc. This subject has been one of the most popular and effervescent topics of theoretical physics in recent years. Gauge theories are central in the study of higher-form symmetries, with Wilson and 't Hooft operators corresponding to the charged objects. Along these notes, we discuss in detail some basic aspects, including Abelian Maxwell and Chern-Simons theories, and $SU(N)$ non-Abelian gauge theories. We also discuss spontaneous breaking of higher-form symmetries.

  5 citations

• The unitary representations of the Poincar\'e group in any spacetime dimension

  Xavier Bekaert, Nicolas Boulanger

  SciPost Phys. Lect. Notes 30 (2021) · published 14 June 2021 | Toggle abstract · pdf

  An extensive group-theoretical treatment of linear relativistic field equations on Minkowski spacetime of arbitrary dimension $D\geqslant 3$ is presented. An exhaustive treatment is performed of the two most important classes of unitary irreducible representations of the Poincar\'e group, corresponding to massive and massless fundamental particles. Covariant field equations are given for each unitary irreducible representation of the Poincar\'e group with non-negative mass-squared.

  5 citations

• Magnetisation and Mean Field Theory in the Ising Model

  Dalton A R Sakthivadivel

  SciPost Phys. Lect. Notes 35 (2022) · published 19 January 2022 | Toggle abstract · pdf

  In this set of notes, a complete, pedagogical tutorial for applying mean field theory to the two-dimensional Ising model is presented. Beginning with the motivation and basis for mean field theory, we formally derive the Bogoliubov inequality and discuss mean field theory itself. We proceed with the use of mean field theory to determine a magnetisation function, and the results of the derivation are interpreted graphically, physically, and mathematically. We give a new interpretation of the self-consistency condition in terms of intersecting surfaces and constrained solution sets. We also include some more general comments on the thermodynamics of the phase transition. We end by evaluating symmetry considerations in magnetisation, and some more subtle features of the Ising model. Together, a self-contained overview of the mean field Ising model is given, with some novel presentation of important results.

  5 citations

• Sterile neutrinos as dark matter candidates

  Joachim Kopp

  SciPost Phys. Lect. Notes 36 (2022) · published 19 January 2022 | Toggle abstract · pdf

  In these brief lecture notes, we introduce sterile neutrinos as dark matter candidates. We discuss in particular their production via oscillations, their radiative decay, as well as possible observational signatures and constraints.

  5 citations

• An introduction to kinks in $\varphi^4$-theory

  Mariya Lizunova, Jasper van Wezel

  SciPost Phys. Lect. Notes 23 (2021) · published 3 February 2021 | Toggle abstract · pdf

  As a low-energy effective model emerging in disparate fields throughout all of physics, the ubiquitous $\varphi^4$-theory is one of the central models of modern theoretical physics. Its topological defects, or kinks, describe stable, particle-like excitations that play a central role in processes ranging from cosmology to particle physics and condensed matter theory. In these lecture notes, we introduce the description of kinks in $\varphi^4$-theory and the various physical processes that govern their dynamics. The notes are aimed at advanced undergraduate students, and emphasis is placed on stimulating qualitative insight into the rich phenomenology encountered in kink dynamics. The appendices contain more detailed derivations, and allow enquiring students to also obtain a quantitative understanding. Topics covered include the topological classification of stable solutions, kink collisions, the formation of bions, resonant scattering of kinks, and kink-impurity interactions.

  5 citations