Related papers: Magnetic translation groups in n dimensions
It is shown that, when there is a magnetic field present, in the framework of classical or quantum mechanics, the active translations differ from the passive ones and that the canonical momentum is not the generator of them. It is also…
The group algebra of the permutation group is spanned by a set of elements called projectors. The coordinates of permutations expanded in projectors are matrix elements of irreducible representations. The projectors of the permutation group…
Given a magnetic finite group, we consider the similarity classes of magnetic equivariant central simple graded algebras over the complex numbers. We call this set the magnetic equivariant graded Brauer group and its structure as an abelian…
The transformation properties of irreducible tensor operators and the applicability of the Wigner-Eckart theorem to finite magnetic groups have been studied.
In standard quantum field theory, the one-particle states are classified by the unitary representations of the Poincar\'e group, whereas the causal fields' classification employs the finite-dimensional (non-unitary) representations of the…
Given a finite-dimensional faithful representation $V$ of a linearly reductive group $G$ over a field $K=\bar K$, we consider the growth of the number of irreducible factors of $V^{\otimes n}$ when $n$ is large. We prove that there exist…
We give a finite presentation by generators and relations for the group O_n(Z[1/2]) of n-dimensional orthogonal matrices with entries in Z[1/2]. We then obtain a similar presentation for the group of n-dimensional orthogonal matrices of the…
A simple algebraic model for charged particle moving in two dimensional space under influence of singular magnetic field is given. The fundamental assumption for the model is that every charged particle coupled to the magnetic field is…
It is shown that in the case of free electron in a spatially periodic magnetic field the concept of magnetic translations operators is still valid and, moreover, these operators can be defined in the same way as for a Bloch electron in a…
We provide a brief overview of tensor models and group field theories, focusing on their main common features. Both frameworks arose in the context of quantum gravity research, and can be understood as higher-dimensional generalizations of…
The groups distinguish their von Neumann algebras, in the case when these are factors.
Within a gauge formulation of 3+1 gravity relying on a nonlinear realization of the group of isometries of space-time, a natural expansion of the metric tensor arises and a simple choice of the gravity dynamical variables is possible. We…
Group algebras of permutations have proved highly useful in solving a number of problems in large N gauge theories. I review the use of permutations in classifying gauge invariants in one-matrix and multi-matrix models and computing their…
We have expressed the tensor commutation matrix n\otimes n as linear combination of the tensor products of the generalized Gell-Mann matrices. The tensor commutation matrices 3\otimes 2 and 2\otimes 3 have been expressed in terms of the…
Invariant tensors play an important role in gauge theories, for example, in dualities of N=1 gauge theories. However, for theories with fields in representations larger than the fundamental, the full set of invariant tensors is often…
We consider the quantum mechanics of an electron confined to move on an infinite cylinder in the presence of a uniform radial magnetic field. This problem is in certain ways very similar to the corresponding problem on the infinite plane.…
Fractons emerge as charges with reduced mobility in a new class of gauge theories. Here, we generalise fractonic theories of $U(1)$ type to what we call $(k,n)$-fractonic Maxwell theory, which employs symmetric order-$n$ tensors of…
Tensor models are measures for random tensors. They generalise matrix models and were developed to study random geometry in arbitrary dimension. Moreover, they are strongly connected to quantum gravity theories as additionally to the…
In this paper we analize a family of one dimensional fully analytically solvable models, named the n-cluster models in a transverse magnetic field, in which a many-body cluster interaction competes with a uniform transverse magnetic field.…
In Tensor Field Theory (TFT), observables are defined through tensor field contractions that produce unitary invariants for complex-valued tensor fields. Traditionally, these observables are constructed using tensor fields of a fixed order…