Hilbert series for constructing Lagrangians: Expanding the phenomenologist’s toolbox
Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D, Particles, fields, gravitation, and cosmology2015Vol. 91(10)
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Abstract
This paper presents the Hilbert series technique to a wider audience in the context of constructing group-invariant Lagrangians. This technique provides a fast way to calculate the number of operators of a specified mass dimension for a given field content and is a useful cross-check on more well-known group theoretical methods. In addition, at least when restricted to invariants without derivatives, the Hilbert series technique supplies a robust way of counting invariants in scenarios which, due to the large number of fields involved or to high-dimensional group representations, are intractable by traditional methods. We work out several practical examples.