One-Loop Quantum Correction to the Kink Mass in a Lorentz-Violating Scalar Field Theory

Abstract

We study the radiative correction to the mass of the $(1+1)$-dimensional $λϕ^4$ kink in the presence of an irreducible, spacelike Lorentz-violating interaction. The Lorentz-violating operator is chosen as $-\frac12 cϕ^2(u\!\cdot\!\partialϕ)^2$ with $u^μ=(0,1)$, which is the lowest-order single-scalar operator considered in this class of models that produces effects that cannot be removed by a linear redefinition of coordinates or the field. We perform the one-loop renormalization of the underlying quantum field theory. In contrast with Lorentz-invariant $λϕ^4$ theory in two dimensions, the Lorentz-violating theory requires, at this order, both a modified mass counterterm and a nonzero field-strength counterterm. The corrected stability problem contains modified bound and continuum modes, while the continuum phase shift remains unchanged at $O(c)$ with the boundary-condition prescription adopted here. Finally, using the vacuum-subtracted zero-point energy and the counterterm Hamiltonian, we obtain the one-loop kink mass through first order in $c$. We give the finite coefficient in the subtraction prescription implemented in the accompanying thesis calculation, for which the Lorentz-violating contribution is numerically negative.