Feynman Propagator for a Free Scalar Field on a Causal Set

The Feynman propagator for a free bosonic scalar field on the discrete spacetime of a causal set is presented. The formalism includes scalar field operators and a vacuum state which define a scalar quantum field theory on a causal set. This work can be viewed as a novel regularization of quantum field theory based on a Lorentz invariant discretization of spacetime.

Figure 1

Plots of $\Im \mathbf{(}(K_F{)}_{xy}\mathbf{)}$ for pairs of sprinkled points $v_x$ and $v_y$ in a single 600 element causal set generated by sprinkling into a unit-volume causal interval in ${\mathbb{M}}^2$ and $\Im \mathbf{(}{G}_F^{(2)}(X)\mathbf{)}$ for $X\in {\mathbb{M}}^2$.