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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.
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.
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
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
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.