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Galois/monodromy groups attached to parametric systems of polynomial equations provide a method for detecting the existence of symmetries in solution sets. Beyond the question of existence, one would like to compute formulas for these…
We consider localized soliton-like solutions in the presence of a stable scalar condensate background. By the analogy with classical mechanics, it can be shown that there may exist solutions of the nonlinear equations of motion that…
The representation theory of non-centrally extended Lie algebras of Noether symmetries, including spacetime diffeomorphisms and reparametrizations of the observer's trajectory, has recently been developped. It naturally solves some…
We study non-geodesic orbits of test particles endowed with a structure, assuming the Schwarzschild spacetime as background. We develop a formalism which allows one to recognize the geometrical characterization of those orbits in terms of…
The study of the relation between Lie algebras and groups, and especially the derivation of new algebras from them, is a problem of great interest in mathematics and physics, because finding a new Lie group from an already known one also…
The Linearization Theorem for proper Lie groupoids organizes and generalizes several results for classic geometries. Despite the various approaches and recent works on the subject, the problem of understanding invariant linearization…
In this paper, the classical Lie symmetry analysis and the generalized form of Lie symmetry method are performed for a general short pulse equation. The point, contact and local symmetries for this equation are given. In this paper, we…
Methods of Lie group analysis of differential equations are extended to weak solutions of (linear and nonlinear) PDEs, where the term ``weak solution'' comprises the following settings: (a) Distributional solutions. (b) Solutions in…
Many models of beyond Standard Model physics connect flavor symmetry with a discrete group. Having this symmetry arise spontaneously from a gauge theory maintains compatibility with quantum gravity and can be used to systematically prevent…
We analyse the underlying nonlinear partial differential equation which arises in the study of gravitating flat fluid plates of embedding class one. Our interest in this equation lies in discussing new solutions that can be found by means…
We model spherically symmetric black holes within the group field theory formalism for quantum gravity via generalised condensate states, involving sums over arbitrarily refined graphs (dual to 3d triangulations). The construction relies…
For the static spherically symmetric dilatonic black hole described by the Gibbons-Maeda-Garfinkle-Horowitz-Strominger geometry, we analyze the timelike trajectories for electrically charged test particles. Both cases of an electric black…
In this paper, we review the progress in the analysis of magnetic monopoles as generalized states in quantum mechanics. We show that the considered model contains rich algebraic structure that generates symmetries which have been utilized…
This paper describes a new algorithm for determining all discrete contact symmetries of any differential equation whose Lie contact symmetries are known. The method is constructive and is easy to use. It is based upon the observation that…
In this thesis, we study the one parameter point transformations which leave invariant the differential equations. In particular we study the Lie and the Noether point symmetries of second order differential equations. We establish a new…
We investigate Lie symmetries of general Yang-Mills equations. For this purpose, we first write down the second prolongation of the symmetry generating vector fields, and compute its action on the Yang-Mills equations. Determining equations…
The confinement mechanism proposed earlier and then applied successfully to meson spectroscopy by one of the authors is interpreted in classical terms. For this aim the unique solution of the Maxwell equations, an analog of the…
The infinite group of deformed diffeomorphisms of the spacetime continuum is put into the basis of the gauge theory of gravity. This gives rise to some new ways for unification of gravity with other gauge interactions.
The symmetries described by Pin groups are the result of combining a finite number of discrete reflections in (hyper)planes. The current work shows how an analysis using geometric algebra provides a picture complementary to that of the…
We study some Lie algebras defined by solutions to the double shuffle equations with poles and construct families of explicit solutions to these equations in all weights and depths. These provide universal coordinates in which to write down…