Related papers: Magnetic translation groups in n dimensions
Covariant forms are given to a gauge theory of massive tensor field. This is accomplished by introducing another auxiliary field of scalar type to the system composed of a symmetric tensor field and an auxiliary field of vector type. The…
Units of measure with prefixes and conversion rules are given a formal semantic model in terms of categorial group theory. Basic structures and both natural and contingent semantic operations are defined. Conversion rules are represented as…
Using the real time formalism of the finite temperature field theory we calculate the 1-loop polarization tensor in the presence of a background magnetic field in a medium. The expression is obtained to linear order in the background field…
Factored neural machine translation (FNMT) is founded on the idea of using the morphological and grammatical decomposition of the words (factors) at the output side of the neural network. This architecture addresses two well-known problems…
Kaluza-Klein (KK) gravitons emission rates due to plasmon-graviton conversion in magnetic field are computed within the ADD model of TeV-scale gravity. Plasma is described in the kinetic approach as the system of charged particles and…
This is an introduction for nonspecialists to the noncommutative geometric approach to Planck scale physics coming out of quantum groups. The canonical role of the `Planck scale quantum group' $C[x]\bicross C[p]$ and its observable-state…
The central objects in a quantum field theory are its n-point correlation functions and matrix elements. Their structure is determined by Lorentz invariance and leads to tensor decompositions whose Lorentz-invariant coefficient functions…
We define and study multivariate exponential functions, symmetric with respect to the alternating group A_n, which is a subgroup of the permutation (symmetric) group S_n. These functions are connected with multivariate exponential…
In the recently proposed generalization of the Yang-Mills theory the group of gauge transformation gets essentially enlarged. This enlargement involves an elegant mixture of the internal and space-time symmetries. The resulting group is an…
The massless field of spin 1 is defined on the eight-dimensional configuration space; this space is a direct product of Minkowski space and of a two-dimensional complex sphere. Field equations for the spin-one field are derived from a…
We call rectangle Gell-Mann matrices rectangle matrices which make generalization of the expression of a tensor commutation matrix $n \otimes n$ in terms of tensor products of square Gell-Mann matrices.
In a "naive" attempt to create algebraic quantum field theories on the circle, we obtain a family of unitary representations of Thompson's groups T and F for any subfactor. The Thompson group elements are the "local scale transformations"…
The meaning of quantum group transformation properties is discussed in some detail by comparing the (co)actions of the quantum group with those of the corresponding Lie group, both of which have the same algebraic (matrix) form of the…
The symmetry-constrained response tensors on transport, optical, and electromagnetic effects are of central importance in condensed matter physics because they can guide experimental detections and verify theoretical calculations. These…
Originally motivated by questions of P. Etingof related to growth rates of tensor powers in symmetric tensor categories, we obtain general bounds on the order of finite subgroups of ${\rm GL}(n,\mathbb{C})$ with restricted composition…
We investigate the magnetic field distribution inside a Type II superconductor which has point group symmetry $O$ such as Li$_2$Pt$_3$B. The absence of inversion symmetry as a departure from perfect cubic group $O_h$ causes a magnetization…
The magnetic field of a homogeneously magnetized cylindrical tile geometry, i.e. an angular section of a finite hollow cylinder, is found. The field is expressed as the product between a tensor field describing the geometrical part of the…
During the last century the tensor theory of the gravitational field was developed. We propose and develop the novel, pure mathematical, matrix theory of the field in n-dimensional metric space. The definition of the mathematical field…
By an {\em isotropy group} of a tensor $t\in V_1 \otimes V_2\otimes V_3=\widetilde V$ we mean the group of all invertible linear transformations of $\widetilde V$ that leave $t$ invariant and are compatible (in an obvious sense) with the…
As Einstein's $E = mc^{2}$ unifies the energy-momentum relation for massive and massless particles, Wigner's little group unifies their internal space-time symmetries. It is pointed out that translational symmetries play essential roles…