arXiv subjects
Publications and source records attributed to M. Chaves.
In Wilson's Theorem the primality of a number hinges on a congruence. We present a similar test where the primality of a number m hinges, instead, on the indivisibility of 4(m-5)! by m. One implication of this theorem is a necessary and sufficient condition for two numbers to be twin primes, a result reminiscent of Clement's theorem but involving indivisibility. MSC: 11A41 and 11A51.
Local oscillatory and other properties of source-type solutions of doubly nonlinear sixth-order parabolic thin film equations are studied.
We consider a modified form of gravity, which has an extra term quadratic in the Riemann tensor. This term mimics a Yang-Mills theory. The other defining characteristic of this gravity is having the affine connection independent of the metric. (The metricity of the metric is rejected, too, since it implies a Levi-Civita connection.) It is then shown that, in the low density limit, this modified gravity does not differ from the General Theory of Relativity. We then point out that its Lagrangian does not contain partials of the metric, so that the metric is not a quantum field, nor does it contribute propagators to the Feynman diagrams of the theory. We also point out that the couplings of this theory (that determine the topological structure of the Feynman diagrams) all come from the term quadratic in the Riemann tensor. As a result of this situation, the diagrams of this theory and the diagrams of a Yang-Mills theory all have the same topology and degree of divergence, up to numerical coefficients. Since Yang-Mills theories are renormalizable, it follows that this theory should also be renormalizable.
A few years ago H. Morales and the author introduced a type of generalized derivative that contained both vector and scalar boson fields. Here it is shown how to construct a full-fledged generalized Yang-Mills theory through the introduction of "extended field" multiplets. These are mixed fields that include both a vector and a scalar part. It is shown how the standard model of high energy physics appears naturally in a Yang-Mills theory that uses extended field multiplets through two spontaneous symmetry breakings, one due to the VEV of a scalar field and another to the VEV of a vector field.
In generalized Yang-Mills theories scalar fields can be gauged just as vector fields in a usual Yang-Mills theory, albeit it is done in the spinorial representation. The presentation of these theories is aesthetic in the following sense: A physical theory using Yang-Mills theories requires several terms and irreducible representations, but with generalized Yang-Mills theories, only two terms and two irreducible representations are required. These theories are constructed based upon the maximal subgroups of the gauge Lie group. The two terms of the lagrangian are the kinetic energy of fermions and of bosons. A brief review of Yang-Mills theories and covariant derivatives is given, then generalized Yang-Mills theories are defined through a generalization of the covariant derivative. Two examples are given, one pertaining the Glashow-Weinberg-Salam model and another SU(5) grand unification. The first is based upon a $U(3)\supset U(1)\times U(1)\times SU(2)$ generalized Yang-Mills theory, and the second upon a $SU(6)\supset U(1)\times SU(5)$ theory. The possibility of expressing generalized Yang-Mills theories using a five-dimensional formalism is also studied. The situation is unclear in this case. At the end a list of comments and criticisms is given.
The asymptotic decay of passive scalar fields is solved analytically for the Kraichnan model, where the velocity has a short correlation time. At long times, two universality classes are found, both characterized by a distribution of the scalar -- generally non-Gaussian -- with global self-similar evolution in time. Analogous behavior is found numerically with a more realistic flow resulting from an inverse energy cascade.
Generalized Yang-Mills theories have a covariant derivative that employs both scalar and vector bosons. Here we show how grand unified theories of the electroweak and strong interactions can be constructed with them. In particular the SU(5) GUT can be obtained from SU(6) with SU(5)xU(1) as a maximal subgroup. The choice of maximal subgroup also determines the chiral structure of the theory. The resulting Lagrangian has only two terms, and only two irreducible representations are needed, one for fermions and another for bosons.
The generalized covariant derivative, that uses both scalar and vector bosons, is defined. It is shown how a grand unified theory of the Standard Model can be constructed using a generalized Yang-Mills theory.
This paper has been withdrawn by the author because the conclusions reached in it are incorrect.
Software for the resolution of certain kind of problems, those that rate high in the Stringent Performance Objectives adjustment factor (IFPUG scheme), can be described using a combination of game theory and autonomous systems. From this description it can be shown that some of those problems exhibit chaotic behavior, an important fact in understanding the functioning of the related software. As a relatively simple example, it is shown that chess exhibits chaotic behavior in its configuration space. This implies that static evaluators in chess programs have intrinsic limitations.
Generalized Yang-Mills theories are constructed, that can use fields other than vector as gauge fields. Their geometric interpretation is studied. An application to the Glashow-Weinberg-Salam model is briefly review, and some related mathematical and physical considerations are made.
The inflaton field is assumed to possess electric charge. The effect of the charge upon inflation is studied using a parameter ω_0 that acts as a measure of the quantity of inflaton present. It is shown that at the end of inflation the charged inflaton should produce a fractal electromagnetic structure, which could act as a seed for the development of macroscopic galactic structures. Another consequence would be the presence nowadays of residual electromagnetic fields that would encompass galaxies, clusters, and larger structures.
It is odd that chess grandmasters often disagree in their analysis of positions, sometimes even of simple ones, and that a grandmaster can hold his own against an powerful analytic machine such as Deep Blue. The fact that there must exist pure winning strategies for chess is used to construct a control strategy function. It is then shown that chess strategy is equivalent to an autonomous system of differential equations, and conjectured that the system is chaotic. If true the conjecture would explain the forenamed peculiarities and would also imply that there cannot exist a static evaluator for chess.
A generalization of the Yang-Mills covariant derivative, that uses both vector and scalar fields and transforms as a 4-vector contracted with Dirac matrices, is used to simplify and unify the Glashow-Weinberg-Salam model. Since SU(3) assigns the wrong hypercharge to the Higgs boson, it is necessary to use a special representation of U(3) to obtain all the correct quantum numbers. A surplus gauge scalar boson emerges in the process, but it uncouples from all other particles.
We show that a system of bosons in a T=0 quantum field theory can present metastable ground states with spontaneous symmetry breaking, even in the absence of an imaginary mass term. This gives a natural explanation to the Davis-Shellard background field \exp(-i ω_0 t) and adds a new degree of freedom in boson systems, with possible applications in cosmology, condensed matter and high energy physics.