Quantum field theory with varying couplings

Understand

A quantum scalar field theory with spacetime-dependent coupling is studied.

• Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific choice of the coupling's profile for any finite-order perturbative expansion.
• For one of these cases, some tree and one-loop diagrams are calculated.
• This is an example of a theory where violation of Lorentz symmetry is not enhanced at the quantum level.