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Bosonic Fields in Causal Set Theory

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Abstract

In this paper we will define a Lagrangian for scalar and gauge fields on causal sets, based on the selection of an Alexandrov set in which the variations of appropriate expressions in terms of either the scalar field or the gauge field holonomies around suitable loops take on the least value. For these fields, we will find that the values of the variations of these expressions define Lagrangians in covariant form.

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Data Availability

It is available on arXiv:0807.4709. Also, one of the older versions of this was posted on Proceedings for “Workshop on Continuous and Lattice Approaches to Quantum Gravity 17-19 September 2008” However, the Proceeding paper is a lot shorter: it is only 8 pages. So it is abbreviated in a lot of ways. For example, it doesn’t do a lot of the explicit calculations that are being done here. It also focuses exclusively on real scalar field and electromagnetic field, but it doesn’t do complex scalar fields, spin 0 multiplets and non-commutative gauge fields.

Code Availability

I used latex. While I submitted the PDF file, I still have the TeX version of it at the computer at home.

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Funding

I am currently a graduate student at the University of New Mexico and, as such, I am a Teaching Assistant, so I get paid for teaching.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM, USA

    Roman Sverdlov

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  1. Roman Sverdlov
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The current paper is single author, although the Proceeding (cited above) was joint work with Luca Bombelli.

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Correspondence to Roman Sverdlov.

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Conflict of Interests

While the current paper is single author, the Proceeding (cited below) was joint work with Luca Bombelli. However, seeing that the Proceedings below is a lot shorter than the current paper, and the presentation is different, I regard it as a separate paper, so I don’t see any conflict of interest.

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Sverdlov, R. Bosonic Fields in Causal Set Theory. Int J Theor Phys 60, 1481–1506 (2021). https://doi.org/10.1007/s10773-021-04772-6

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