Constraining low energy effective field theories via high energy axioms
File(s)
Author(s)
Melville, Scott Andrew
Type
Thesis
Abstract
Low energy effective field theories (EFTs) allow us to predict low energy (macroscopic)
observables without specifying the high energy (microscopic) details of a
system. This is useful across many areas in physics, and particularly in situations
where the high energy is unknown or difficult to measure. However, the EFT is
not blind to all aspects of the high energy microphysics—certain consistency conditions
on very small scales are inherited as conditions on the large scale dynamics.
Physically, the high energy consistency conditions we wish to impose correspond
to locality, causality, unitarity and crossing symmetry. By exploiting the resulting
analytic structure of scattering amplitudes (S matrix elements), these translate into
rigorous constraints on the EFT. Failure to satisfy these constraints indicates that
no local, causal, unitary, Lorentz-invariant high energy completion of the low energy
theory can ever exist—the microphysics must be inherently incompatible with this
kind of quantum field theory. Here, such constraints are derived at nearly every order
in the EFT expansion, for massive particles of any spin with any kinematics. To
illustrate the power of these techniques, specific applications to various cosmological
field theories are presented—including the scalar, vector and massive gravity theories
used in the early Universe for inflation and the late Universe for dark energy, as
well as non-singular bouncing cosmologies and gravitational waves. Exploiting relations
between high and low energy in order to better constrain effective field theories
with fewer experimental data therefore proves itself to be a useful tool in a variety
of applications, and will guide our future efforts to construct both fundamental and
phenomenological models of the Universe in which we live.
observables without specifying the high energy (microscopic) details of a
system. This is useful across many areas in physics, and particularly in situations
where the high energy is unknown or difficult to measure. However, the EFT is
not blind to all aspects of the high energy microphysics—certain consistency conditions
on very small scales are inherited as conditions on the large scale dynamics.
Physically, the high energy consistency conditions we wish to impose correspond
to locality, causality, unitarity and crossing symmetry. By exploiting the resulting
analytic structure of scattering amplitudes (S matrix elements), these translate into
rigorous constraints on the EFT. Failure to satisfy these constraints indicates that
no local, causal, unitary, Lorentz-invariant high energy completion of the low energy
theory can ever exist—the microphysics must be inherently incompatible with this
kind of quantum field theory. Here, such constraints are derived at nearly every order
in the EFT expansion, for massive particles of any spin with any kinematics. To
illustrate the power of these techniques, specific applications to various cosmological
field theories are presented—including the scalar, vector and massive gravity theories
used in the early Universe for inflation and the late Universe for dark energy, as
well as non-singular bouncing cosmologies and gravitational waves. Exploiting relations
between high and low energy in order to better constrain effective field theories
with fewer experimental data therefore proves itself to be a useful tool in a variety
of applications, and will guide our future efforts to construct both fundamental and
phenomenological models of the Universe in which we live.
Version
Open Access
Date Issued
2019-01
Date Awarded
2019-04
Copyright Statement
Creative Commons Attribution NonCommercial ShareAlike Licence
Advisor
de Rham, Claudia
Publisher Department
Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)