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Luis J. Boya

Publications and source records attributed to Luis J. Boya.

31 records · Page 2Linked to original sources
arXiv2005

Arguments for F-theory

After a brief review of string and $M$-Theory we point out some deficiencies. Partly to cure them, we present several arguments for ``$F$-Theory'', enlarging spacetime to $(2, 10)$ signature, following the original suggestion of C. Vafa. We introduce a suggestive Supersymmetric 27-plet of particles, associated to the exceptional symmetric hermitian space $E_{6}/Spin^{c}(10)$. Several possible future directions, including using projective rather than metric geometry, are mentioned. We should emphasize that $F$-Theory is yet just a very provisional attempt, lacking clear dynamical principles.

hep-th↗
arXiv2004

Spinors and Octonions

Octonions are introduced through some spin representations. The groups $G_2$, $F_4$ and the $E$ series appear in a natural manner; one way to understand octonions is as the "second coming" of the reals, but with the spinors instead of vectors. Some physical applications in $M$- and $F$-theory as putative "theories of everything" are suggested.

math-ph↗
arXiv2004

The Thermal Radiation Formula of Planck (1900)

We review the derivation of Planck's Radiation Formula on the light of recent studies in its centenary. We discuss specially the issue of discreteness, Planck's opinion on his discovery, and the critical analysis on the contributions by Ehrenfest, Einstein, Lorentz, etc. We also address the views of T.S. Kuhn, which conflict with the conventional interpretation that discontinuty was already found by Planck.

physics.hist-ph↗
arXiv2003

New solvable quantum mechanical potentials by iteration of the free V=0 potential

A huge family of solvable potentials can be generated by systematically exploiting the factorization (Darboux) method. Starting from the free case, a large class of the known solvable families is thus reproduced, together with new ones. We explicitly find and solve several new singular potentials obtained by iteration from the V=0 case; some of them have an E=0 bound state and constant phase shift without being explicitly scale invariant. The new potentials are rational functions, and can be related to rational solutions of the KdV family.

quant-ph↗
arXiv2003

Volumes of Compact Manifolds

We present a systematic calculation of the volumes of compact manifolds which appear in physics: spheres, projective spaces, group manifolds and generalized flag manifolds. In each case we state what we believe is the most natural scale or normalization of the manifold, that is, the generalization of the unit radius condition for spheres. For this aim we first describe the manifold with some parameters, set up a metric, which induces a volume element, and perform the integration for the adequate range of the parameters; in most cases our manifolds will be either spheres or (twisted) products of spheres, or quotients of spheres (homogeneous spaces). Our results should be useful in several physical instances, as instanton calculations, propagators in curved spaces, sigma models, geometric scattering in homogeneous manifolds, density matrices for entangled states, etc. Some flag manifolds have also appeared recently as exceptional holonomy manifolds; the volumes of compact Einstein manifolds appear in String theory.

math-ph↗
arXiv2003

Octonions and M-theory

We explain how structures related to octonions are ubiquitous in M-theory. All the exceptional Lie groups, and the projective Cayley line and plane appear in M-theory. Exceptional G_2-holonomy manifolds show up as compactifying spaces, and are related to the M2 Brane and 3-form. We review this evidence, which comes from the initial 11-dim structures. Relations between these objects are stressed, when extant and understood. We argue for the necessity of a better understanding of the role of the octonions themselves (in particular non-associativity) in M-theory.

hep-th↗
arXiv2002

Rejection of the Light Quantum: The Dark Side of Niels Bohr

Evidence is recalled of the strong opposition of Niels Bohr, at the time of the Old Quantum Theory 1.913-25, to the Lichtquanten hypothesis of Einstein. Some episodes with H.A. Kramers, J.C. Slater and W. Heisenberg are recollected; Bohr's changing point of view is traced back to some philosophical antecedents and to his endeavour to deduce quantum results from the Correspondence Principle. Some consequences for the future interpretation of Quantum Mechanics, specially to the Complementarity Principle, are considered.

physics.hist-ph↗
arXiv1999

Clifford Periodicity from Finite Groups

We deduce the periodicity 8 for the type of $Pin$ and $Spin$ representations of the orthogonal groups $O(n)$ from simple combinatorial properties of the finite Clifford groups generated by the gamma matrices. We also include the case of arbitrary signature $O(p,q)$. The changes in the type of representation can be seen as a rotation in the complex plane. The essential result is that adding a $(+)$ dimension performs a rotation by $π/4$ in the counter clock-wise sense, but for each $(-)$ sign in the metric, the rotation is clockwise.

math-ph↗
arXiv1998

Density Matrices and Geometric Phases for n-state Systems

An explicit parameterization is given for the density matrices for $n$-state systems. The geometry of the space of pure and mixed states and the entropy of the $n$-state system is discussed. Geometric phases can arise in only specific subspaces of the space of all density matrices. The possibility of obtaining nontrivial abelian and nonabelian geometric phases in these subspaces is discussed.

quant-ph↗
arXiv1997

Topological charges and the genus of surfaces

We show that the topological charge of the n-soliton solution of the sine-Gordon equation n is related to the genus g > 1 of a constant negative curvature compact surface described by this configuration. The relation is n=2(g-1), where n is even. The moduli space of complex dimension B(g)=3(g-1) corresponds precisely to the freedom to choosing the configuration with n solitons of arbitrary positions and velocities. We speculate also that the odd soliton states will describe the unoriented surfaces.

hep-th↗
arXiv1994

Point Interactions from Flux Conservation

We show that the physical requirement of flux conservation can substitute for the usual matching conditions in point interactions. The study covers an arbitrary superposition of $δ$ and $δ'$ potentials on the real line and can be easily applied to higher dimensions. Our procedure can be seen as a physical interpretation of the deficiency index of some symmetric, but not self-adjoint operators.

hep-th↗