2025 Theses Doctoral

Contraints on Effective Field Theories Without Lorentz Invariance

Zhou, Shengjia

Effective Field Theory is a powerful tool to understand low-energy physics. Constraining effective field theories without Lorentz invariance is an open question. In this thesis, we study two different approaches to constrain effective field theories without Lorentz invariance.

The first approach is to study analytic structures of scattering amplitudes without Lorentz invariance. The second approach is to consider the implications of microcausality. In the study of the first approach, we study the scattering amplitude in a simple example: a superfluid described by a complex scalar field with quartic interactions. We compute the 2 → 2 scattering amplitude of gapless excitations at tree-level. In the center of mass configuration, we find that crossing symmetry is lost, and there is a branch cut on the complex ? plane at tree level. Furthermore, all the even derivatives of the forward scattering amplitude at ? = 0 are positive, while all the odd derivatives are negative.

This pattern of the derivatives of the scattering amplitude can be derived in a more general theory in the limit of weak Lorentz breaking effect.In the second approach, we derive implications of microcausality on two-point correlation functions. For the commutator Green’s function, microcausality implies that its Fourier transform is analytic for all complex momentum and satisfies an exponential boundedness condition. We derive a similar result for the retarded Green’s function.

We verify these properties in several examples, including Lorentz invariant theories, a free non-relativistic scalar field theory, a UV-complete model of a relativistic superfluid, and scalar fields in de Sitter space. In addition, we derive a constraint on the effective field theory of inflation. Finally, we discuss the possibility of constraining higher-point correlation functions from microcausality.