Related papers: Symmetry as a source of hidden coherent structures…
Symmetry groups are projectively represented in quantum mechanics, and crystalline symmetries are fundamental in condensed matter physics. Here, we systematically present a unified theory of quantum mechanical space groups from two…
We discuss hidden symmetries of three-dimensional field configurations revealed at the one-particle level by the use of pseudoclassical particle models. We argue that at the quantum field theory level, these can be naturally explained in…
We consider the problem of quantum behavior in the finite background. Introduction of continuum or other infinities into physics leads only to technical complications without any need for them in description of empirical observations. The…
This paper is a programmatic article presenting an outline of a new view of the foundations of quantum mechanics and quantum field theory. In short, the proposed foundations are given by the following statements: * Coherent quantum physics…
The Hamiltonian formulation of lattice gauge theories plays a central role in quantum simulations of gauge theories, and understanding their spectrum and other properties is expected to become crucial in the upcoming years. The relevant…
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…
Outer automorphisms of symmetries ("symmetries of symmetries") in relativistic quantum field theories are studied, including charge conjugation (C), space-reflection (P) , and time-reversal (T) transformations. The group theory of outer…
Systems under holonomic constraints are classified within the generalized Hamiltonian framework as second-class constraints systems. We show that each system of point particles with holonomic constraints has a hidden gauge symmetry which…
In this letter we present a theorem on the dynamics of the generalized Hubbard models. This theorem shows that the symmetry of the single particle Hamiltonian can protect a kind of dynamical symmetry driven by the interactions. Here the…
We study the classical and quantum oscillator in the context of a non-additive (deformed) displacement operator, associated with a position-dependent effective mass, by means of the supersymmetric formalism. From the supersymmetric partner…
We introduce and discuss (local) symmetries of geometric structures. These symmetries generalize the classical (locally) symmetric spaces to various other geometries. Our main tools are homogeneous Cartan geometries and their explicit…
We present a general unified approach for finding the coherent states of polynomially deformed algebras such as the quadratic and Higgs algebras, which are relevant for various multiphoton processes in quantum optics. We give a general…
By virtue of the Noether theorems, the vast gauge redundancy of general relativity provides us with a rich algebra of boundary charges that generate physical symmetries. These charges are located at codimension-2 entangling surfaces called…
We describe an infinite-dimensional algebra of hidden symmetries for the self-dual gravity equations. Besides the known diffeomorphism-type symmetries (affine extension of w(infinity) algebra), this algebra contains new hidden symmetries,…
Symmetries play a crucial role in shaping the structure and predictions of multi-Higgs-doublet models. In three-Higgs-doublet models considerable effort has been put into classifying possible symmetry groups and the conditions for their…
Motivated by group-theoretical questions that arise in the context of asymptotic symmetries in gravity, we study model spaces and their quantization from the viewpoint of constrained Hamiltonian systems. More precisely, we propose that a…
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…
It is known that a single quantum harmonic oscillator is characterized by a hidden spectrum generating superconformal symmetry, but its origin has remained rather obscure. We show how this hidden superconformal symmetry can be derived by…
Hidden symmetries are the backbone of Integrable two-dimensional theories. They provide classical solutions of higher dimensional models as well, they seem to survive partially quantisation and their discrete remnants in M-theory called…
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…