Hidden Conformal Invariance of Scalar Effective Field Theories

We argue that conformal invariance is a common thread linking several scalar effective field theories that appear in the double copy and scattering equations. For a derivatively coupled scalar with a quartic ${\cal O}(p^4)$ 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 ${\cal O}(p^6)$ 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.Comment: 7 page

Learning through pictures : a study of cultural and cognitive aspects of visual images.

EducationDoctor of Education (EdD

Scattering Amplitudes and the Navier-Stokes Equation

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

Cahal Mor of the Wine-Red Hand : A Rhapsody for Baritone and Orchestra

https://digitalcommons.library.umaine.edu/mmb-me/1438/thumbnail.jp

Revealing the Landscape of Globally Color-Dual Multi-loop Integrands

We report on progress in understanding how to construct color-dual multi-loop amplitudes. First we identify a cubic theory, semi-abelian Yang-Mills, that unifies many of the color-dual theories studied in the literature, and provides a prescriptive approach for constructing $D$-dimensional color-dual numerators through one-loop directly from Feynman rules. By a simple weight counting argument, this approach does not further generalize to two-loops. As a first step in understanding the two-loop challenge, we use a $D$-dimensional color-dual bootstrap to successfully construct globally color-dual local two-loop four-point nonlinear sigma model (NLSM) numerators. The double-copy of these NLSM numerators with themselves, pure Yang-Mills, and $\mathcal{N}=4$ super-Yang-Mills correctly reproduce the known unitarity constructed integrands of special Galileons, Born-Infeld theory, and Dirac-Born-Infeld-Volkov-Akulov theory, respectively. Applying our bootstrap to two-loop four-point pure Yang-Mills, we exhaustively search the space of local numerators and find that it fails to satisfy global color-kinematics duality, completing a search previously initiated in the literature. We pinpoint the failure to the bowtie unitarity cut, and discuss a path forward towards non-local construction of color-dual integrands at generic loop order.Comment: 42 pages, 4 figures, ancillary fil

Generating 'good enough' evidence for co-production

Co-production is not a new concept but it is one with renewed prominence and reach in contemporary policy discourse. It refers to joint working between people or groups who have traditionally been separated into categories of user and producer. The article focuses on the coproduction of public services, offering theory-based and knowledge-based routes to evidencing co-production. It cites a range of ‘good enough’ methodologies which community organisations and small-scale service providers experimenting with co-production can use to assess the potential contribution, including appreciative inquiry, peer-to-peer learning and data sharing. These approaches have the potential to foster innovation and scale-out experimentation

Multiyear Looping: Theoretical Perspectives and Empirical Evidence

Multiyear student-teacher assignments, also known as looping, are unique in their ability to engage a cohesive group of students and families in persistent relationships that extend beyond the traditional single-year model. However, the practice is uncommonly implemented and receives scant treatment in scholarly literature. In this dissertation, I take an expansive view of looping and explore the phenomenon from three diverse angels across separate but interconnected articles, each of which offers a distinctive contribution to the relatively undeveloped looping literature base. In the first article, entitled Looping: A Proposed Theory of Action, I introduce the practice and contextualize it within the historical landscape of education reform in U.S. schools. In doing so, I propose a logic model describing a theory of action for looping and explain why it may work to improve outcomes for both students and teachers. I also offer an explanation, grounded in the history of U.S. school reform, for why, despite brief popularity as an intervention in the latter half of the 20th century, looping has largely remained an unexplored policy lever. The second article, Multiyear Looping and Teacher Retention, turns from theoretical to empirical analysis and introduces to the literature a first thorough descriptive analysis of modern-day looping&rsquo;s prevalence and distribution in a large urban school district. In this study, I also employ a novel survival analysis approach to explore whether an association exists between looping and patterns of teacher retention, finding suggestive evidence that the practice may be associated with longer durations of employment for teachers at a given school. Finally, the third article investigates looping at the student level and introduces a new strategy for identifying instances of the phenomenon in large-scale administrative datasets. The main analysis finds a significant positive impact of between 2% and 6% of a standard deviation unit on student test scores. These effects also appear to increase in magnitude with greater proportions of students moving together across grades with a teacher. Taken together, these three articles introduce a comprehensive theoretical and empirical portrait of an educational practice that may represent a unique and transformative opportunity to improve outcomes for both students and teachers.&nbsp;</p

Effective Field Theory Topics in the Modern S-Matrix Program

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.</p