Related papers: The classical evaluation of relativistic spin netw…
We consider a compact Lie group as a framed manifold equipped with the left invarianat framing $\mathscr{L}$. In a previous paper we have proved that the Adams $e_\mathbb{C}$-invariant value of $SU(2n)$ $(n\ge 2)$ gives a generator of the…
In these continuation papers (VI and VII) we are interested in approach the problem of spin from a classical point of view. In this first paper we will show that the spin is neither basically relativistic nor quantum but reflects just a…
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…
We compute the Lens space index for 4d supersymmetric gauge theories involving symplectic gauge groups. This index can distinguish between different gauge groups from a given algebra and it matches across theories related by supersymmetric…
We analyze a supersymmetric system with four flat directions. We observe several interesting properties, such as the coexistence of the discrete and continuous spectrum in the same range of energies. We also solve numerically the classical…
In this paper, starting from pure group-theoretical point of view, we develop a regular approach to describing particles with different spins in the framework of a theory of scalar fields on the Poincare group. Such fields can be considered…
We define for any 4-tetrahedron (4-simplex) the simplest finite closed piecewise flat manifold consisting of this 4-tetrahedron and of the one else 4-tetrahedron identical up to reflection to the present one (call it bisimplex built on the…
We numerically study the SU(2)$\otimes$SU(2) symmetric spin-orbit coupled model as a lower symmetric generalization of the SU(4) exchange model. On the symmetric line with respect to the spin and orbit, our result shows the essentially…
We give alternate proofs of the classical branching rules for highest weight representations of a complex reductive group $G$ restricted to a closed regular reductive subgroup $H$, where $(G,H)$ consist of the pairs $(GL(n+1),GL(n))$, $…
We introduce a classical limit of the dynamics of quantum spin systems based on coherent states of SU($N$), where $N$ is the dimension of the local Hilbert space. This approach, that generalizes the well-known Landau-Lifshitz dynamics from…
We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…
In the framework of the Schwinger boson representation for the su(2)-algebra, the closed form is derived for the total spin eigenstates which result from the coupling of n su(2)-spins. In order to demonstrate its usefulness, the orthogonal…
The Hamiltonian formulation of the Holst action in vacuum and in the presence of matter fields is analyzed in a generic local Lorentz frame. It is elucidated how the SU(2) gauge symmetry is inferred by reducing the set of constraints to a…
Following the Poincare algebra for a free spinning particle and using the Casimirs of the algebra in the Hamiltonian approach, we construct systematically a set of Lagrangians for the relativistic spinning particle which includes the…
Covariantly we reformulate the description of a spinning particle in terms of the Poincar\'{e} group. We also construct a Lagrangian which entails all possible constraints explicitly; all constraints can be obtained just from the…
We start developing a formalism which allows to construct supersymmetric theories systematically across space-time signatures. Our construction uses a complex form of the supersymmetry algebra, which is obtained by doubling the spinor…
We prove Langlands functoriality for the generic spectrum of general spin groups (both odd and even). Contrary to other recent instances of functoriality, our resulting automorphic representations on the general linear group will not be…
We discuss how to recognize the constellations seen in the Majorana representation of quantum states. Then we give explicit formulas for the metric and symplectic form on SU(2) orbits containing general number states. Their metric and…
We investigate 2-dimensional Viscoelastic equations with a view of Lie groups. In this sense, we answer question of the symmetry classification. We provide the algebra of symmetry and build the optimal system of Lie subalgebras. Reductions…
We categorify one half of the small quantum sl(2) at a prime root of unity. An extension of this construction to an arbitrary simply-laced case is proposed.