GroupMath: A Mathematica package for group theory calculations

@article{Fonseca2021GroupMathAM,
  title={GroupMath: A Mathematica package for group theory calculations},
  author={Renato M. Fonseca},
  journal={Comput. Phys. Commun.},
  year={2021},
  volume={267},
  pages={108085}
}
  • R. Fonseca
  • Published 28 October 2020
  • Mathematics
  • Comput. Phys. Commun.
Phenomenological cornucopia of SU(3) exotica
We introduce an effort to catalog the gauge-invariant interactions of Standard Model (SM) particles and new fields in a variety of representations of the SM color gauge group SU(3)c. In this first
Decomposition of d = 9 short-range 0νββ decay operators at one-loop level
Abstract We perform a systematical study of the dimension-9 short-range 0νββ decay operators at one-loop level. There are only six genuine topologies which generate eight diagrams, and the recipe to
Pseudo-Nambu-Goldstone dark matter model inspired by grand unification
A pseudo-Nambu-Goldstone boson (pNGB) is an attractive candidate for dark matter (DM) due to the simple evasion of the current severe limits of DM direct detection experiments. One of the pNGB DM
Grand unification and the Planck scale: An $\mathit{SO}(10)$ example of radiative symmetry breaking
: Grand unification of gauge couplings and fermionic representations remains an appealing proposal to explain the seemingly coincidental structure of the Standard Model. However, to realise the
Gravitational vector Dark Matter
A new dark sector consisting of a pure non-abelian gauge theory has no renormalizable interaction with SM particles, and can thereby realise gravitational Dark Matter (DM). Gauge interactions confine

References

SHOWING 1-10 OF 29 REFERENCES
Semi-Simple Lie Algebras and Their Representations
This paper presents an overview of the representations of Lie algebras, particularly semi-simple Lie algebras, with a view towards theoretical physics. We proceed from the relationship between Lie
The Sym2Int program: going from symmetries to interactions
Model builders often need to find the most general Lagrangian which can be constructed from a given list of fields. These fields are actually representations of the Lorentz and gauge groups (and
Group Characters and Algebra
It has been known for some time* that the elements of a matrix of degree n may be arranged in sets which correspond to cycles of the symmetric group of order n !, and that there are relations
Finite-Dimensional Lie Algebras and Their Representations for Unified Model Building
We give information about finite-dimensional Lie algebras and their representations for model building in 4 and 5 dimensions; e.g., conjugacy classes, types of representations, Weyl dimensional
Computing tensor product decompositions
TLDR
An algorithm is presented for computing the decomposition of a tensor product of two irreducible representations of a semisimple complex Lie group into its irreduced components using techniques developed previously for efficiently computing Weyl group orbits.
Group theory for unified model building
LieART - A Mathematica application for Lie algebras and representation theory
PyR@TE: Renormalization group equations for general gauge theories
Weyl group orbits
TLDR
This new technique allows large orbits to be computed using only a small fraction of the computer memory required when using standard techniques, and the memory requirements can be reduced by a factor of 30,000.
...
1
2
3
...