The use of test functions to help define quadratic Lagrangian on a causal set
arXiv:1807.07403
Abstract
In some other papers, the Lagrangians in the causal sets included coefficients that were to be computed by integrating over Alexandrov set. In those other papers, this integral was explicitly evaluated, which resulted in rather sophisticated expressions. On the other hand, in this paper, instead of evaluating this integral, it was left in an integral form where the actual fields were replaced with test functions (thus avoiding nonlinearities). The test functions get absorbed into equations in a very natural way, so the resulting formulas look elegant.
13 pages, no figures
References in corpus (7)
- Causal Sets: Discrete Gravity (Notes for the Valdivia Summer School)
- Spacelike distance from discrete causal order
- Dynamics for causal sets with matter fields: A Lagrangian-based approach
- Gauge Fields in Causal Set Theory
- Quantum Fields on Causal Sets
- Electromagnetic Lagrangian on a causal set that resides on edges rather than points
- Restoring locality of scalar fields on a causal set by avoiding the use of d'Alembertians