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  A new algebraic structure in the standard model of particle physics

Boyle, L., & Farnsworth, S. (2018). A new algebraic structure in the standard model of particle physics. Journal of high energy physics: JHEP, 2018(06): 071. doi:10.1007/JHEP06(2018)071.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-002A-C181-9 Version Permalink: http://hdl.handle.net/21.11116/0000-0002-E8B8-9
Genre: Journal Article

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 Creators:
Boyle, Latham, Author
Farnsworth, Shane1, Author
Affiliations:
1AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, ou_24008              

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Free keywords: High Energy Physics - Theory, hep-th,High Energy Physics - Phenomenology, hep-ph,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
 Abstract: We introduce a new formulation of non-commutative geometry (NCG): we explain its mathematical advantages and its success in capturing the structure of the standard model of particle physics. The idea, in brief, is to represent $A$ (the algebra of differential forms on some possibly-noncommutative space) on $H$ (the Hilbert space of spinors on that space); and to reinterpret this representation as a simple super-algebra $B=A\oplus H$ with even part $A$ and odd part $H$. $B$ is the fundamental object in our approach: we show that (nearly) all of the basic axioms and assumptions of the traditional ("spectral triple") formulation of NCG are elegantly recovered from the simple requirement that $B$ should be a differential graded $\ast$-algebra (or "$\ast$-DGA"). But this requirement also yields other, new, geometrical constraints. When we apply our formalism to the NCG traditionally used to describe the standard model of particle physics, we find that these new constraints are physically meaningful and phenomenologically correct. This formalism is more restrictive than effective field theory, and so explains more about the observed structure of the standard model, and offers more guidance about physics beyond the standard model.

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 Dates: 2016-04-042018
 Publication Status: Published in print
 Pages: 30 pages, no figures
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 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1604.00847
URI: http://arxiv.org/abs/1604.00847
DOI: 10.1007/JHEP06(2018)071
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Title: Journal of high energy physics : JHEP
Source Genre: Journal
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Publ. Info: Bologna, Italy : Società italiana di fisica
Pages: - Volume / Issue: 2018 (06) Sequence Number: 071 Start / End Page: - Identifier: ISSN: 1126-6708
CoNE: /journals/resource/111021927548002