Related papers: Differential Invariants and Hidden Symmetry
Symmetry Protected Topological (SPT) phases describe trivially-acting symmetries. We argue that a symmetry-based description of SPT phases ought to include the topological twist fields associated to the symmetry. Doing so allows us to…
In this paper, we further consider the symmetry-based method for seeking nonlocally related systems for partial differential equations. In particular, we show that the symmetry-based method for partial differential equations is the natural…
Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multi-scale physics in a compact and symbolic representation. This…
The connection between symmetries and linearizations of discrete-time dynamical systems is being inverstigated. It is shown, that existence of semigroup structures related to the vector field and having linear representations enables…
It is shown for a simple ODE that it has many symmetry groups beyond its usual Lie group symmetries, when its generalized solutions are considered within the nowhere dense differential algebra of generalized functions.
We propose the symmetry reduction method of partial differential equations to the system of differential equations with fewer number of independent variables. We also obtain generalized sufficient conditions for the solution found by…
Deformed special relativity is embedded in deformed general relativity using the methods of canonical relativity and loop quantum gravity. Phase-space dependent deformations of symmetry algebras then appear, which in some regimes can be…
We found an additional symmetry hidden in the fermion and Higgs sectors of the Standard Model. It is connected to the centers of the SU(3) and SU(2) subgroups of the gauge group. A lattice regularization of the whole Standard Model is…
By relating the two-dimensional U(N) Principal Chiral Model to a simple linear system we obtain a free-field parametrisation of solutions. Obvious symmetry transformations on the free-field data give symmetries of the model. In this way all…
Lie symmetry transformations that leave a differential equation invariant play a fundamental role in science and mathematics. Such Lie symmetry groups uniquely determine their Lie symmetry algebras. Exact differential elimination algorithms…
We introduce the notion of hidden quantum correlations. We present the mean values of observables depending on one classical random variable described by the probability distribution in the form of correlation functions of two (three, etc.)…
This paper studies pattern formations in coupled elliptic PDE systems governed by transparent boundary conditions. Such systems unify diverse areas, including inverse boundary problems (via a single passive/active boundary measurement),…
Recent advancements in generalized symmetries have drawn significant attention to gapped phases of matter exhibiting novel symmetries, such as noninvertible symmetries. By leveraging the duality transformations, the classification and…
We show that there is a special choice of parameters for which the galileon theory is invariant under an enhanced shift symmetry whose non-linear part is quadratic in the coordinates. This symmetry fixes the theory to be equivalent to one…
We show that nonlocal reductions of systems of integrable nonlinear partial differential equations are the special discrete symmetry transformations.
In quantum mechanics, accidental degeneracy refers to energy degeneracy that occurs coincidentally, without any protection by symmetry. Here, we prove a theorem stating that any two-fold degeneracy (accidental or not) in a quantum system is…
We consider first order symmetry operators for the equations of motion of differential $p$-form fields in general $D$-dimensional background geometry of any signature for both massless and massive cases. For $p=1$ and $p=2$ we give the…
We discuss physical constructions, and the boundary properties of various symmetry protected topological phases that involve 1-form symmetries, from one spatial dimension (1d) to four spatial dimensions (4d). For example, the prototype 3d…
Symmetry properties of conservation laws of partial differential equations are developed by using the general method of conservation law multipliers. As main results, simple conditions are given for characterizing when a conservation law…
We present a method of constructing discrete integrable systems with crystallographic reflection group (Weyl) symmetries, thus clarifying the relationship between different discrete integrable systems in terms of their symmetry groups.…