Hilbert Series for Constructing Lagrangians: expanding the phenomenologist's toolbox
By L. Lehman, Adam Martin. 2015
156 citations recorded by the source corpus.
This note 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.
Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/63dd649d166a257370208bdc72640bb335d23215
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In Nuclear and High Energy Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Operator bases, S-matrices, and their partition functions (2017, methodology): “They were adapted in the two papers [40, 43] to deal with the problem of finding Lorentz invariant operators involving multiple types of field, but only for the subset of the operator basis where no more than one derivative appears in an operator.”
- Hilbert series and operator bases with derivatives in effective field theories (2015, methodology): “f the Hilbert series for general N. This treatment makes reference to Molien’s formula and the Haar integration measure, a general discussion of which we refer the reader to, e.g., the physics papers [5, 6]. For the following analysis to apply, we restrict α to lie in the maximal compact subgroup of”