相关论文: A group-theorist's perspective on symmetry groups …

In this survey, we report on the state of the art of some of the fundamental problems in the Lie theory of Lie groups modeled on locally convex spaces, such as integrability of Lie algebras, integrability of Lie subalgebras to Lie…

We give very flexible, concrete constructions of discrete and faithful epresentations of right-angled Artin groups into higher-rank Lie groups. Using the geometry of the associated symmetric spaces and the combinatorics of the groups, we…

Finite Lorentz groups acting on 4-dimensional vector spaces coordinatized by finite fields with a prime number of elements are represented as homomorphic images of countable, rational subgroups of the Lorentz group acting on real…

Wigner found unreasonable the "effectiveness of mathematics in the natural sciences". But if the mathematics we use to describe nature is simply a coded expression of our experience then its effectiveness is quite reasonable. Its…

In this easy introduction to higher gauge theory, we describe parallel transport for particles and strings in terms of 2-connections on 2-bundles. Just as ordinary gauge theory involves a gauge group, this generalization involves a gauge…

Observed physical phenomena can be described well by quantum mechanics or general relativity. People may try to find an unified fundamental theory which mainly aims to merge gravity with quantum theory. However, difficulty in merging those…

If a (possibly finite) compact Lie group acts effectively, locally linearly, and homologically trivially on a closed, simply-connected four-manifold with second Betti number at least three, then it must be isomorphic to a subgroup of S^1 x…

In quantum field theory there is now a well developed technique, effective field theory, which allows one to obtain low energy quantum predictions in ``non-renormalizable'' theories, using only the degrees of freedom and interactions…

This paper introduces Lie groups in degenerate geometric (Clifford) algebras that preserve four fundamental subspaces determined by the grade involution and reversion under the adjoint and twisted adjoint representations. We prove that…

Since some experiments have found superluminality, we assume that the particles in the universe are divided into three classes: the subluminal, luminal and superluminal particles by the speed of light, their energy-momenum relations are E2…

In this era of an increased interest in loop theory, the Einstein velocity addition law has fresh resonance. One of the most fascinating aspects of recent work in Einstein's special theory of relativity is the emergence of special grouplike…

We introduce the key ideas behind the group field theory approach to quantum gravity, and the basic elements of its formalism. We also briefly report on some recent results obtained in this approach, concerning both the mathematical…

Lie theory is, beyond any doubt, an absolutely essential part of differential geometry. It is therefore necessary to seek its generalization to $\mathbb{Z}$-graded geometry. In particular, it is vital to construct non-trivial and explicit…

Fundamentals on Lie group methods and applications to differential equations are surveyed. Many examples are included to elucidate their extensive applicability for analytically solving both ordinary and partial differential equations.

In a recent paper [1], it was introduced a new class of gravitational theories with two local degrees of freedom. The existence of these theories apparently challenges the distinctive role of general relativity as the unique non-linear…

Properties of a given symmetry group G are very important in investigation of a physical system invariant under its action. In the case of finite spin systems (magnetic rings, some planar macromolecules) the symmetry group is isomorphic…

The Standard Model of particle physics may seem complicated and arbitrary, but it has hidden patterns that are revealed by the relationship between three "grand unified theories": theories that unify forces and particles by extending the…

In the second half of the 1920s, physicists and mathematicians introduced group theoretic methods into the recently invented ``new'' quantum mechanics. Group representations turned out to be a highly useful tool in spectroscopy and in…

Few, if any, applications of quantum technology are as widely known as the quantum simulation of quantum matter. Consequently, many interesting questions have been sparked at the intersection of condensed matter, quantum chemistry, and…

Analogies have had and continue to have an important role in the development of theoretical physics. They may start from similarities of physical concepts followed by similarities in the mathematical formalization or it may be a purely…