We will describe the diagonalization of the Hamiltonian of $\lambda\phi^4$ theory. We will focus on scattering states far above the vacuum and will consider the inner product between these scattering states as the first step towards the calculation of the scattering amplitudes. We will show some of our preliminary results along with their comparison with perturbation theory.

We study 1+1 dimensional $\phi^4$ theory using the recently proposed method of conformal truncation. Starting in the UV CFT of free field theory, we construct a complete basis of states with definite conformal Casimir, $\mathcal{C}$. We use these states to express the Hamiltonian of the full interacting theory in lightcone quantization. After truncating to states with $\mathcal{C} \leq...

A Non-Local quantum field theory extension of QED is considered. Gauge invariance is checked to 1-loop order and the gauge coupling running is shown to be UV-Insensitive. In the future, extending this model to incorporate other fields could provide an avenue for remedying the Higgs vacuum instability problem.

Astrophysical black hole candidates, although long thought to have a horizon, could be horizonless ultra-compact objects. This intriguing possibility is motivated by the black hole information paradox and a plausible fundamental connection with quantum gravity. Asymptotically free quadratic gravity is considered here as the UV completion of general relativity. We find that sufficiently dense...