相关论文: There is no "Theory of Everything" inside E8

We give a complete description of which non-torsion generators are not in the image of the Thom morphism from complex cobordism to integral cohomology for the classifying space of exceptional Lie groups except for E_8. We then show that the…

From what is known today about the elementary particles of matter, and the forces that control their behavior, it may be observed that still a host of obstacles must be overcome that are standing in the way of further progress of our…

Gauge theories describe the interactions of the fundamental building blocks of nature with great success. The Standard Model achieves a partial unification of the electromagnetic and weak interactions, and it also acomodates the strong…

We propose a construction of the spherical subalgebra of a symplectic reflection algebra of an arbitrary rank corresponding to a star-shaped affine Dynkin diagram. Namely, it is obtained from the universal enveloping algebra of a certain…

Given a number field $k$, we show that, for many finite groups $G$, all the Galois extensions of $k$ with Galois group $G$ cannot be obtained by specializing any given finitely many Galois extensions $E/k(T)$ with Galois group $G$ and $E/k$…

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…

Outlined in this paper is a description of \emph{equivariance} in the world of 2-dimensional extended topological quantum field theories, under a topological action of compactLie groups. In physics language, I am gauging the theories ---…

We show that the data needed for the method of the embedding tensor employed in gauging supergravity theories are precisely those of a Leibniz algebra (with one of its induced quotient Lie algebras embedded into a rigid symmetry Lie algebra…

Borrowing ideas from the relation between simply laced Lie algebras and Dynkin diagrams, a weighted graph theory representation of quantum information is addressed. In this way, the density matrix of a quantum state can be interpreted as a…

We prove that there does not exist any connected topological proper loop homeomorphic to a quasi-simple Lie group and having a compact Lie group as the group topologically generated by its left translations. Moreover, any connected…

We discuss some physical consequences of what might be called ``the ultimate ensemble theory'', where not only worlds corresponding to say different sets of initial data or different physical constants are considered equally real, but also…

A description of how a theory of gravity can be considered as a gauge theory (in the sense of Trautman) of the Poincare' group is given. As a result, it is shown that a gauge theory of this kind is consistent with the Equivalence Principle…

We introduce a gauge and diffeomorphism invariant theory on Yang-Mills phase space. The theory is well defined for an arbitrary gauge group with an invariant bilinear form, it contains only first class constraints, and the spacetime metric…

The connections between Euler's equations on central extensions of Lie algebras and Euler's equations on the original, extended algebras are described. A special infinite sequence of central extensions of nilpotent Lie algebras constructed…

While many observations support the validity of Einstein's general relativity as the theory of gravity, there are yet many that suggest the presence of new physics. In order to explain the high-redshift supernovae Ia observations together…

We give tables of noncompact real forms of maximal reductive subalgebras of complex simple Lie algebras of rank up to 8. These were obtained by computational methods that we briefly describe. We also discuss applications in theoretical…

This is an expository paper in which we explain how basic, standard, results about simple Lie algebras can be obtained by geometric arguments, following ideas of Cartan, Richardson and others.

We address the issue of the fallacy of the gauge concept in electromagnetism. The role of groupthink in the perpetuation of this concept in the physics literature is also discussed. Brief, elementary arguments suffice to demonstrate the…

Given a representation V of a group G, there are two natural ways of defining a representation of the group algebra k[G] in the external power V^{\wedge m}. The set L(V) of elements of k[G] for which these two ways give the same result is a…

The Steenrod algebra can not be realised as an enveloping of any Lie superalgebra. We list several problems that suggest a need to modify the definition of the enveloping algebra, for example, to get rid of certain strange deformations…