Related papers: Generalised Symmetries in Particle Physics
We discuss the possible applications supersymmetric theories might find in the field of elementary particle physics. The supersymmetric generalization of the $SU(3)\times SU(2)\times U(1)$ standard model is discussed in detail. Special…
These notes are an expanded version of lectures given at the 2022 TASI summer school in Boulder, Colorado. One goal of these lecture notes is to (partially) bridge the gap between what one learns in typical introductory quantum field theory…
These are introductory notes on symmetries in quantum field theory and how they apply to particle physics. The notes cover the fundamentals of group theory, their representations, Lie groups, and Lie algebras, along with an elaborate…
We present a class of three-dimensional quantum field theories whose ordinary global symmetries mix with higher-form symmetries to form a continuous 2-group. All these models can be obtained by performing a gauging procedure in a parent…
We explore the notion of approximate global symmetries in quantum field theory and quantum gravity. We show that a variety of conjectures about quantum gravity, including the weak gravity conjecture, the distance conjecture, and the…
The model of point particle in general external fields is considered and the generalized equivalence principle is suggested identifying all backgrounds which give rise to equivalent particle dynamics. The equivalence transformations for…
We present a comprehensive theoretical analysis of the General Standard Model (GSM), a recently proposed framework that unifies particle physics and cosmology within the Gravitational Quantum Field Theory (GQFT). Constructed from first…
The concept of symmetries in physics is briefly reviewed. In the first part of these lecture notes, some of the basic mathematical tools needed for the understanding of symmetries in nature are presented, namely group theory, Lie groups and…
A generalized symmetry of a system of differential equations is an infinitesimal transformation depending locally upon the fields and their derivatives which carries solutions to solutions. We classify all generalized symmetries of the…
In general quantum field theories (QFTs), ordinary (0-form) global symmetries and 1-form symmetries can combine into 2-group global symmetries. We describe this phenomenon in detail using the language of symmetry defects. We exhibit a…
Generalisations of geometry have emerged in various forms in the study of field theory and quantization. This mini-review focuses on the role of higher geometry in three selected physical applications. After motivating and describing some…
This is an elementary set of lectures on generalized global symmetries originally given at the Jena TPI School on QFT and Holography, designed to be accessible to the reader with a basic knowledge of quantum field theory. Topics covered…
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…
Generalized global symmetries, in particular non-invertible and categorical symmetries, have become a focal point in the recent study of quantum field theory (QFT). In this paper, we investigate aspects of symmetry topological field…
Non-invertible symmetries of a quantum field theory (QFT) are a natural generalization of unitary symmetries, but in which the product of operators does not satisfy a group multiplication law. We show that such symmetry operations on states…
We generalize the spherical harmonics for l=1 and give the differential equation that the generalized forms satisfy. The new forms have an obvious interpretation in the context of quantum mechanics.
Recent advances in our understanding of symmetry in quantum many-body systems offer the possibility of a generalized Landau paradigm that encompasses all equilibrium phases of matter. This is a brief and elementary review of some of these…
Symmetries are important guiding principle for phase transitions. We systematically construct field theory models with local quantum fields that exhibit the following phase transitions: (1) different symmetry protected topological (SPT)…
In spite of the enormous success of the Standard Model (SM), we have strong reasons to expect the presence of new physics beyond the SM at higher energies. The idea of the Grand Unification of all the known interactions in nature is perhaps…
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…