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Non-Hermitian Hamiltonians with unitary and antiunitary symmetries
(Academic Press Inc Elsevier Science, 2014-03)
We analyse several non-Hermitian Hamiltonians with antiunitary symmetry from the point of view of their point-group symmetry. It enables us to predict the degeneracy of the energy levels and to reduce the dimension of the ...
Local symmetries in gauge theories in a finite-dimensional setting
(ELSEVIER SCIENCE BVAMSTERDAM, 2012)
It is shown that the correct mathematical implementation of symmetry in the geometric formulation of classical field theory leads naturally beyond the concept of Lie groups and their actions on manifolds, out into the realm ...
Non-Hermitian oscillators with Td symmetry
(Academic Press Inc Elsevier Science, 2015-02)
We analyse some PT-symmetric oscillators with Td symmetry that depend on a potential parameter g. We calculate the eigenvalues and eigenfunctions for each irreducible representation and for a range of values of g. Pairs ...
Application of the λ-symmetries approach and time independent integral of the modified Emden equation
(2012-06-01)
In this paper we derive the time-independent integral for a nonlinear dissipative system, namely the modified Emden equation, from Lie point symmetries. We employ the recently introduced λ-symmetries method [C. Muriel, ...
Integrability and conformal symmetry in higher dimensions: A model with exact hopfion solutions
(2002-11-11)
We use ideas on integrability in higher dimensions to define Lorentz invariant field theories with an infinite number of local conserved currents. The models considered have a two-dimensional target space. Requiring the ...
Unsuitable use of spin and pseudospin symmetries with a pseudoscalar Cornell potential
(Iop Publishing Ltd, 2014-09-01)
The concepts of spin and pseudospin symmetries has been used as mere rhetorics to decorate the pseudoscalar potential [Chin. Phys. B 22 090301 (2013)]. It is also pointed out that a more complete analysis of the bound ...
On symmetries of singular implicit ODEs
(2014)
We study implicit ODEs, cubic in derivative, with infinitesimal symmetry at singular points. Cartan showed that even at regular points the existence of nontrivial symmetry imposes restrictions on the ODE. Namely, this ...
Existence and symmetry of least energy nodal solutions for Hamiltonian elliptic systems
(Gauthier-Villars/ElsevierParis, 2015-12)
In this paper we prove existence of least energy nodal solutions for the Hamiltonian elliptic system with Hénon-type weights −Δu = '|X| POT. β' '|V| POT. Q-1' v, −Δv = '|X|POT. α' '|U| POT. P−1' u in Ω, u= v = 0 on ∂Ω, ...
Geometric Singular Perturbation Theory for Systems with Symmetry
(2020-01-01)
In this paper we focus on a class of symmetric vector fields in the context of singularly perturbed fast-slow dynamical systems. Our main question is to know how symmetry properties of a dynamical system are affected by ...
Symmetry of mountain pass solutions of some vector field equations
(SpringerNew YorkEUA, 2006)