50 research outputs found
An infinite supermultiplet of massive higher-spin fields
The representation theory underlying the infinite-component relativistic wave
equation written by Majorana is revisited from a modern perspective. On the one
hand, the massless solutions of this equation are shown to form a
supermultiplet of the superPoincare algebra with tensorial central charges; it
can also be obtained as the infinite spin limit of massive solutions. On the
other hand, the Majorana equation is generalized for any space-time dimension
and for arbitrary Regge trajectories. Inspired from these results, an infinite
supermultiplet of massive fields of all spins and of equal mass is constructed
in four dimensions and proved to carry an irreducible representation of the
orthosymplectic group OSp(1|4) and of the superPoincare group with tensorial
charges.Comment: 29 pages, references [30] added. To appear in JHE
Vertex operator for generalised Kac--Moody algebras associated to the two-sphere and the two-torus
We pursue our study of generalised Kac-Moody and Virasoro algebras defined on
compact homogeneous manifolds.
Extending the well-known Vertex operator in the case of the two-torus or the
two-sphere, we obtain explicit bosonic realisations of the semi-direct product
of the extension of Kac-Moody and Virasoro algebras on and , respectively. As for the fermionic realisation
previously constructed, in order to have well defined algebras, we introduce,
beyond the usual normal ordering prescription, a regulator and regularise
infinite sums by means of the Riemann -function.Comment: 9 page
Generalized harmonic functions and unitary representations of low dimensional Lie groups
The unitary representations of the three dimensional simple Lie groups are reconsidered from the perspective of harmonic functions acting on certain manifolds related to differential realisations of the groups themselves. By means of contractions of Lie groups, the procedure is also applied to the group E2 of rotations-translations in two dimensions.Depto. de Álgebra, Geometría y TopologíaFac. de Ciencias MatemáticasTRUEpu
Doubly-charged particles at the Large Hadron Collider
In this work we investigate the production and signatures of doubly-charged
particles at the Large Hadron Collider. We start with the Standard Model
particle content and representations and add generic doubly-charged exotic
particles. We classify these doubly-charged states according to their spin,
considering scalar, fermionic and vectorial fields, and according to their
SU(2)L representation, being chosen to be either trivial, fundamental, or
adjoint. We write the most general interactions between them and the Standard
Model sector and study their production modes and possible decay channels. We
then probe how they can most likely be observed and how particles with
different spin and SU(2)L representations could be possibly distinguished.Comment: 18 pages, 8 figures, 1 table; version accepted by Phys.Rev.
Fermion realisations of generalised Kac--Moody and Virasoro algebras associated to the two-sphere and the two-torus
Using the notion of extension of Kac-Moody algebras for higher dimensional
compact manifolds recently introduced in [1], we show that for the two-torus
and the two-sphere , these
extensions, as well as extensions of the Virasoro algebra can be obtained
naturally from the usual Kac-Moody and Virasoro algebras. Explicit fermionic
realisations are proposed. In order to have well defined generators, beyond the
usual normal ordering prescription, we introduce a regulator and regularise
infinite sums by means of Riemann function.Comment: 10 page
Three-loop Euler-Heisenberg Lagrangian in 1+1 QED, part 1: single fermion-loop part
We study the three-loop Euler-Heisenberg Lagrangian in spinor quantum
electrodynamics in 1+1 dimensions. In this first part we calculate the
one-fermion-loop contribution, applying both standard Feynman diagrams and the
worldline formalism which leads to two different representations in terms of
fourfold Schwinger-parameter integrals. Unlike the diagram calculation, the
worldline approach allows one to combine the planar and the non-planar
contributions to the Lagrangian. Our main interest is in the asymptotic
behaviour of the weak-field expansion coefficients of this Lagrangian, for
which a non-perturbative prediction has been obtained in previous work using
worldline instantons and Borel analysis. We develop algorithms for the
calculation of the weak-field expansions coefficients that, in principle, allow
their calculation to arbitrary order. Here for the non-planar contribution we
make essential use of the polynomial invariants of the dihedral group D4 in
Schwinger parameter space to keep the expressions manageable. As expected on
general grounds, the coefficients are of the form r1+r2*zeta(3) with rational
numbers r1, r2. We compute the first two coefficients analytically, and four
more by numerical integration.Comment: 50 pages, 8 figure
Group invariants for Feynman diagrams
It is well-known that the symmetry group of a Feynman diagram can give
important information on possible strategies for its evaluation, and the
mathematical objects that will be involved. Motivated by ongoing work on
multi-loop multi-photon amplitudes in quantum electrodynamics, here I will
discuss the usefulness of introducing a polynomial basis of invariants of the
symmetry group of a diagram in Feynman-Schwinger parameter space.Comment: 9 pages, 8 figures, talk given by C. Schubert at 34th International
Colloquium on Group Theoretical Methods in Physics, Strasbourg, 18-22 July
202
Automated mass spectrum generation for new physics
We describe an extension of the FeynRules package dedicated to the automatic
generation of the mass spectrum associated with any Lagrangian-based quantum
field theory. After introducing a simplified way to implement particle mixings,
we present a new class of FeynRules functions allowing both for the analytical
computation of all the model mass matrices and for the generation of a C++
package, dubbed ASperGe. This program can then be further employed for a
numerical evaluation of the rotation matrices necessary to diagonalize the
field basis. We illustrate these features in the context of the
Two-Higgs-Doublet Model, the Minimal Left-Right Symmetric Standard Model and
the Minimal Supersymmetric Standard Model.Comment: 11 pages, 1 table; version accepted by EPJ
Unexpected Features of Supersymmetry with Central Charges
It is shown that N=2 supersymmetric theories with central charges present
some hidden quartic symmetry. This enables us to construct representations of
the quartic structure induced by superalgebra representations.Comment: 14 pages, more details have been given, to appear in J. Phys.