Related papers: Magnetic translation groups in n dimensions
For any given finite abelian group, we give factorizations of the group determinant in the group algebra of any subgroup. The factorizations are an extension of Dedekind's theorem. The extension leads to a generalization of Dedekind's…
Irrespective of whether n is prime, prime power with exponent >1, or composite, the group U_n of units of Z_n can sometimes be obtained as the direct product of cyclic groups generated by x, x+k and x+2k, for x, k in Z_n. Indeed, for many…
The Poincar\'e group can be interpreted as the group of isometries of a minkowskian space. This point of view suggests to consider the group of isometries of a given space as the suitable group to construct a gauge theory of gravity. We…
If we replace the general spacetime group of diffeomorphisms by transformations taking place in the tangent space, general relativity can be interpreted as a gauge theory, and in particular as a gauge theory for the Lorentz group. In this…
A detailed study of certain apspects of some 2+1 dimensional field theories is presented with special emphasis on the role of Wigner's little group for massless particles in generating gauge transformations. The planar models considered…
Ferrofluids containing nonmagnetic particles are called inverse ferrofluids. On the basis of the Ewald-Kornfeld formulation and the Maxwell-Garnett theory, we theoretically investigate the magnetophoretic force exerting on the nonmagnetic…
We propose a gauge-invariant formulation of magnetic translation (GMT) operators, eliminating the gauge dependence that conventional definitions suffer from due to specific gauge choices. We extend this framework by incorporating so(3,1)…
We show in elementary terms the equivalence in a general gauge of a U(1)-gauge theory of a scalar charged particle on a torus T^n = R^n/L to the analogous theory on R^n constrained by quasiperiodicity under translations in the lattice L.…
Braman [B08] described a construction where third-order tensors are exactly the set of linear transformations acting on the set of matrices with vectors as scalars. This extends the familiar notion that matrices form the set of all linear…
We have generalised the properties with the tensor product, of one 4x4 matrix which is a permutation matrix, and we call a tensor commutation matrix. Tensor commutation matrices can be constructed with or without calculus. A formula allows…
In continuation of Part I, we study translative integral formulas for certain translation invariant functionals, which are defined on general convex bodies. Again, we consider local extensions and use these to show that the translative…
We plan to translate the successful description of three-dimensional gravity as a gauge theory in the noncommutative framework, making use of the covariant coordinates. We consider two specific three-dimensional fuzzy spaces based on SU(2)…
Generalized gauge fields are tensor fields with mixed symmetries. For gravity and higher spins in dimensions greater than four, the fundamental field in the "magnetic representation" is a generalized gauge field. It is shown that the analog…
We show that the translational subgroup of Wigner's little group for massless particles in 3+1 dimensions generate gauge transformation in linearized Einstein gravity. Similarly a suitable representation of the 1-dimensional translational…
We deduce a simple representation and the invariant factor decompositions of the subgroups of the group $\Bbb{Z}_m \times \Bbb{Z}_n$, where $m$ and $n$ are arbitrary positive integers. We obtain formulas for the total number of subgroups…
When n is odd, consider the finite general linear and unitary groups of rank n, extended by the inverse transpose automorphism. There are elements in the extended groups which square to a regular unipotent element, and we evaluate the…
Factor model is an appealing and effective analytic tool for high-dimensional time series, with a wide range of applications in economics, finance and statistics. This paper develops two criteria for the determination of the number of…
Let $A$ be a ring, and let $M$ and $N$ be $A$-modules. Then $N$ can be viewed as a group object in the category $A$-Mod/$M$ of $A$-modules over $M$ and Ext$^1(M, N)$ can be interpreted as the set of isomorphism classes of $N$-torsors.…
A matrix modeling formulation for translation-invariant noncommutative gauge theories is given in the setting of differential graded algebras and quantum groups. Translation-invariant products are discussed in the setting of…
The magnetic field is traditionally presented as a (pseudo)vector quantity, tied closely to the cross product. Though familiar to experts, many students find these ideas challenging and full of subtleties. Building on earlier work in…