Spinor fields in Causal Set Theory

Abstract

The goal of this paper is to define fermionic fields on causal set. This is done by the use of holonomies to define vierbines, and then defining spinor fields by taking advantage of the leftover degrees of freedom of holonomies plus additional scalar fields. Grassmann nature is being enforced by allowing measure to take both positive and negative values, and also by introducing a vector space to have both commutting dot product and anticommutting wedge product.

19 pages, no figures

References in corpus (4)

• The causal set approach to quantum gravity
• Bosonic Fields in Causal Set Theory
• Gauge Fields in Causal Set Theory
• Novel definition of Grassmann numbers and spinor fields

Cited by in corpus (6)

• Dynamics for causal sets with matter fields: A Lagrangian-based approach
• Gauge Fields in Causal Set Theory
• Quantum mechanics and gravity as preclusion principles of four dimensional geometries
• A Geometrical Description of Spinor Fields
• Ph.D. Thesis: Quantum Field Theory and Gravity in Causal Sets
• A note on discrete Holonomy through directed edges, with no lengths