相关论文: Snowmass White Paper: Generalized Symmetries in Qu…
Symmetries are playing a very prominent role in natural sciences. In mathematics as the language of physics, symmetries are treated within the framework of group theory, which provides the tools to classify natural laws and physical objects…
Symmetries are widely used in modeling quantum systems but they do not contribute in postulates of quantum mechanics. Here we argue that logical, mathematical, and observational evidence require that symmetry should be considered as a…
In this talk I review various notions of generalised global symmetry: higher-form, higher-group, and non-invertible symmetry. All these notions have had profound impact on quantum field theory research in the last decade. I highlight…
Generalized symmetries (also known as categorical symmetries) is a newly developing technique for studying quantum field theories. It has given us new insights into the structure of QFT and many new powerful tools that can be applied to the…
It was recently argued that quantum field theories possess one-form and higher-form symmetries, labelled `generalized global symmetries.' In this paper, we describe how those higher-form symmetries can be understood mathematically as…
We study generalized symmetries in a simplified arena in which the usual quantum field theories of physics are replaced with topological field theories and the smooth structure with which the symmetry groups of physics are usually endowed…
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…
Defects are both physically rich objects and powerful tools in modern quantum field theory. They are extended operators, such as boundaries, impurities, and probe particles, embedded in many-body systems. In this dissertation, we study the…
The generalized definition of symmetry is formulated. Application of this definition for symmetric analysis of theoretical physics equations is considered. The version of electrodynamics is constructed permitting the faster-than-light…
We give a modern geometric viewpoint on anomalies in quantum field theory and illustrate it in a 1-dimensional theory: supersymmetric quantum mechanics. This is background for the resolution of worldsheet anomalies in orientifold…
We introduce a framework for internal topological symmetries in quantum field theory, including "noninvertible symmetries" and "categorical symmetries". This leads to a calculus of topological defects which takes full advantage of…
We examine the notion of symmetry in quantum field theory from a fundamental representation theoretic point of view. This leads us to a generalization expressed in terms of quantum groups and braided categories. It also unifies the…
Spacetime and internal symmetries can be used to severely restrict the form of the equations for the fundamental laws of physics. The success of this approach in the context of general relativity and particle physics motivates the…
Quantum gravity places important consistency conditions on low-energy effective field theory, such as the absence of global symmetries. These may have important consequences in the search for particle physics beyond the Standard Model. We…
Quantum groups play the role of hidden symmetries of some two-dimensional field theories. We discuss how they appear in this role in the Wess-Zumino-Witten model of conformal field theory.
Dynamical quantum field theories (QFTs), such as those in which spacetimes are equipped with a metric and/or a field in the form of a smooth map to a target manifold, can be formulated axiomatically using the language of…
A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries…
In standard quantum theory, symmetry is defined in the spirit of Klein's Erlangen Program: the background space has a symmetry group, and the basic operators should commute according to the Lie algebra of that group. We argue that the…
The relation between symmetry reduction before and after quantization of a field theory is discussed using a toy model: the axisymmetric Klein-Gordon field. We consider three possible notions of symmetry at the quantum level: invariance…
Supersymmetry plays prominent roles in the study of quantum field theory and in many proposals for potential new physics beyond the standard model, while lattice field theory provides a non-perturbative regularization suitable for strongly…