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Since 2003, Faculty member Freddy Cachazo has been a leader in

this effort, and has discovered much simpler methods for calculating

scattering amplitudes that have become widely adopted by theorists

and experimentalists.

Recently, Cachazo et al. found that the equations used to predict

the results of complex collisions were analogous to a much more

straightforward mathematical problem: ﬁnding the volume of a class

of geometric objects called polytopes. While calculating polytope

volumes is still complicated, it is far simpler than the usual methods

of modelling particle collisions. The discovery of this relationship

means that even very precise calculations can be greatly simpliﬁed.

The principles underlying this work are profound and hint at a new

understanding of the fundamental structure of the universe. Well beyond

their immediate utility to experimentalists, they are providing an entirely

new approach to understanding fundamental physical properties.

Cachazo is now pursuing this deeper theoretical understanding with

collaborators including Perimeter Distinguished Research Chair Nima

Arkani-Hamed of the Institute for Advanced Study.

Cachazo’s achievements in this area have been recognized with the

2009 Gribov Medal of the European Physical Society and the 2011

Rutherford Medal of the Royal Society of Canada.

Senior Postdoctoral Fellow David Skinner and collaborators have

taken another geometric approach to simplifying calculations

of scattering amplitudes. Several years ago, Luis Alday and

Juan Maladacena conjectured a relationship between scattering

amplitudes for strongly coupled interactions and complex objects

known as Wilson Loops, but it remained unproven. (Wilson loops

represent the ﬂux of the strong nuclear force ﬁelds through various

geometrical areas.) Soon after, the conjecture was extended to all

ranges of coupling but it remained a conjecture. Now, using ideas

from an area of mathematics called twistor theory, Skinner and

colleagues have proven the conjecture precisely.

In the same way a major snarl can be untangled by breaking it down

into several smaller knots, Skinner’s equations can break a complex

several-particle collision into collisions of fewer particles that can

be modeled more easily. It is a crucial new technique with wide

implications for the work of other Perimeter researchers, such as

Faculty member Pedro Vieira, and well beyond.

These recent discoveries are likely to be of enormous signiﬁcance.

Not only do they allow physicists to calculate complex physical

processes relevant to real experiments, but they also enable them to

tackle fundamental questions about the structure of spacetime itself.

References:

N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo, A. Hodges, and J. Trnka, “A Note on Polytopes for

Scattering Amplitudes,” arXiv:1012.6030.

M. Bullimore and D. Skinner, “Holomorphic Linking, Loop Equations and Scattering Amplitudes in

Twistor Space,” arXiv:1101.1329.

PROFILE: WILLIAM UNRUH

In these days of economic crisis, many governments

around the world are losing sight of the importance of

fundamental, curiosity-driven research. They are much

more likely to support research if it promises to solve

immediate problems – not recognizing that addressing

short-term issues often requires thinking about long-term

problems.

Perimeter, by contrast, acts as a refuge, a supportive

environment where people can carry out long-term

fundamental research. For example, I do research on the

relationship between gravity and quantum mechanics,

asking questions such as, “Why do black holes evaporate

by emitting quantum radiation?” When Stephen Hawking

discovered this phenomenon, it was treated as highly

mysterious and believed to be unique to black holes. In

1981, I argued that this phenomenon is far from unique

and that black holes in fact behave analogously to water

waves at a river mouth. In both cases, incoming waves

become ampliﬁed when they interact with outﬂowing

energy. We can use similar equations to describe both

situations.

Identifying analogues between seemingly unrelated

systems like these can help explain the physical properties

of one system in terms of the other. Not only do waves in

a ﬂowing ﬂuid help us understand black holes, but black

holes also help us understand the behaviour of waves in

the ocean.

Perimeter resists doing only immediately relevant research,

which makes it an island of sanity. It gives researchers like

me the freedom to solve problems for the knowledge they

give of how our world operates, whether in the far reaches

of space or understanding our immediate world from a

totally different direction.

− William Unruh

Distinguished Research Chair William Unruh is a Professor of

Physics at the University of British Columbia who has made

seminal contributions, including the discovery of the Unruh

effect. He is the recipient of many honours and awards, including

the Canadian Association of Physicists Medal of Achievement

and the Canada Council Killam Prize.