arXiv subjects

Mauricio Ayala

Publications and source records attributed to Mauricio Ayala.

4 recordsLinked to original sources

arXiv2003

Towards a necessary change in the mathematical principles of natural philosophy

Being mathematics a natural language to Mankind and to physics, it must be constantly adapted to our necessities and our natural perception. Then, mathematical concepts are not absolute to reality. Although mathematical theories are constructions of our mind, and the existence of objects in such theories is a matter of consistency or coherence of the theory (this allows us to study them independently of other theories), in physics its not enough that mathematical structures are coherent or consistent, these must have a much more tangible reference to reality. Therefore any mathematical model not necessarily is appropriate in physics. So, what sense has the concept of a point in physics, that elementary notion used to represent the objects of the reality. If we consider that in a good model of reality, the existence of a mathematical object with a physical reference must be equivalent to the possibility of its construction, perception and verification of physical existence, where the refutaction of the non-existence of an object does not necessarily mean that it is possible to find a test of its existence. Then, one obtains that the mathematical language becomes richer in structures, where the point concept is replaced by more intuitive and perceivable concepts. On the one hand, this possibly can lead us to a physics without infinites, and without paradoxes, on the other hand, one restricts the use of mathematics and the use of mental experiments in physics.

physics.gen-ph↗

arXiv2002

Status of e-Print Servers

We make a short study of the history and evolution of scientific publications, in order to explain the format for near-term e-Prints servers, proposing a new scientific publication scheme via digital network, and exploring the new dynamics of publication.

physics.soc-ph↗

arXiv2002

Group contractions and its consequences upon representations of different spatial symmetry groups

We investigate the group contraction method for various space-time groups, including SO(3)->E_2, SO(3,1)->G_3, SO(5-h,h)->P(3,1) (h=1 or 2), and its consequences for representations of these groups. Following strictly quantum mechanical procedures we specifically pay attention in the asymptotic limiting procedure employed in the contraction G -> G', not only to the respective algebras but to their representations spaces spanned by the eigenvectors of the Cartan subalgebra and the eigenvalues labelling these representation spaces. Where appropriate a physical interpretation is given to the contraction prodecure.

hep-th↗

arXiv2001

OSp(N|4) group and their contractions to P(3,1)xGauge

Starting from SO(n,m) groups, we are in search of groups that: (1.) in a simple way, include N supersymmetric generators(see \cite{Nahm}) (2.) contain as subgroup: the de Sitter group SO(4,1) or the Anti-de Sitter group SO(3,2) (3.) permit nontrivial gauge symmetry groups. The smallest groups satisfyng above conditions are the OSp(N|4) groups, which contain Sp(4)xSO(N) ($Sp(4)\sim SO(3,2)$) or OSp(1|4)xSO(N-1). Because of this, it is possible to generate P(3,1)xG using groups contraction mechanism, which may be: $SO(3,2)\to P(3,1)$ o $OSp(N|4)\to ^SP(3,1|N)$ where P(3,1) is the Poincaré group and G is a gauge group, say SO(N) or SO(N-1). This group contraction mechanism and its consequences upon different groups representations including SO(3,2) or SO(4,1), is clarified and extended to OSp(N|4) representations (see \cite{Nicolai}), contracted to its N-extensión SuperPoincaré group $\ ^SP(3,1|N)$.

hep-th↗