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Effective Field Theory Topics in the Modern S-Matrix Program


Mangan, James Francis (2021) Effective Field Theory Topics in the Modern S-Matrix Program. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/qg7a-7n08.


Quantum field theory is the most predictive theory of nature ever tested, yet the scattering amplitudes produced from the standard application of Lagrangians and Feynman rules belie the simplicity of the underlying physics, obscuring the physical answers behind off-shell actions and gauge redundant descriptions. The aim of the modern S-matrix program (or the "amplitudes" subfield) is to reformulate specific field theories and manifest underlying structures in order to make high multiplicity and/or high loop scattering calculations tractable.

Many of the systems amenable to amplitudes techniques are actually intimately related to each other through the double-copy relations. We argue that conformal invariance is common thread linking several of the scalar effective field theories appearing in the double copy. For a derivatively coupled scalar with a quartic O(p⁴) vertex, classical conformal invariance dictates an infinite tower of additional interactions that coincide exactly with Dirac-Born-Infeld theory analytically continued to spacetime dimension D = 0. For the case of a quartic O(p⁶) vertex, classical conformal invariance constrains the theory to be the special Galileon in D = -2 dimensions. We also verify the conformal invariance of these theories by showing that their amplitudes are uniquely fixed by the conformal Ward identities. In these theories, conformal invariance is a much more stringent constraint than scale invariance.

Although many of the theories in the double-copy admit a high degree of space-time symmetry, amplitudes tools can be applied to non-relativistic theories as well. We explore the scattering amplitudes of fluid quanta described by the Navier-Stokes equation and its non-Abelian generalization. These amplitudes exhibit universal infrared structures analogous to the Weinberg soft theorem and the Adler zero. Furthermore, they satisfy on-shell recursion relations which together with the three-point scattering amplitude furnish a pure S-matrix formulation of incompressible fluid mechanics. Remarkably, the amplitudes of the non-Abelian Navier-Stokes equation also exhibit color-kinematics duality as an off-shell symmetry, for which the associated kinematic algebra is literally the algebra of spatial diffeomorphisms. Applying the double copy prescription, we then arrive at a new theory of a tensor bi-fluid. Finally, we present monopole solutions of the non-Abelian and tensor Navier-Stokes equations and observe a classical double copy structure.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Amplitudes, effective field theory, S-matrix
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Cheung, Clifford W.
Thesis Committee:
  • Wise, Mark B. (chair)
  • Bern, Zvi
  • Schwarz, John H.
  • Cheung, Clifford W.
Defense Date:21 May 2021
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Record Number:CaltechTHESIS:05262021-204932248
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for Chapter 2. adapted for Chapter 3.
Mangan, James Francis0000-0002-9713-7446
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:14177
Deposited By: James Mangan
Deposited On:04 Jun 2021 00:14
Last Modified:26 Oct 2021 16:35

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