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result(s) for
"Goddard, Peter"
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Off-shell CHY amplitudes and Feynman graphs
A
bstract
A polynomial form is established for the off-shell CHY scattering equations proposed by Lam and Yao. Re-expressing this in terms of independent Mandelstam invariants provides a new expression for the polynomial scattering equations, immediately valid off shell, which makes it evident that they yield the off-shell amplitudes given by massless 𝜙
3
Feynman graphs. A CHY expression for individual Feynman graphs, valid even off shell, is established through a recurrence relation.
Journal Article
The Great Gould
\"Considered one of the most influential musicians and cultural figures of his time, Glenn Gould remains a fascinating figure. In the first book to be published in co-operation with Gould's estate, Peter Goddard draws on Gould's unpublished writings, interviews, and never-before-seen photographs to present a startling new portrait of Gould, the man and the musician. Drawing on never-before-seen material, it presents a deep and nuanced study of Gould's life with unmatched candour and clarity. Inside is a love letter Gould wrote but never sent (he later revised it again and again); the text of a speech that Gould gave to a group of children about life and childhood; and portions of Glenn Gould: hysteric return, a never-before-seen radio script in which Gould imagines his return to the concert stage and all it would have entailed. All of this and more makes The Great Gould the perfect gift for the Gould fan, or for anyone interested in Canadian music.\"-- Provided by publisher.
Book
Proof of the formula of Cachazo, He and Yuan for Yang-Mills tree amplitudes in arbitrary dimension
A
bstract
A proof is given of the formula, recently proposed by Cachazo, He and Yuan (CHY) for gluon tree amplitudes in pure Yang-Mills theory in arbitrary dimension. The approach is to first establish the corresponding result for massless
ϕ
3
theory using the BCFW recurrence relation and then to extend this to the gauge theory case. Additionally, it is shown that the scattering equations introduced by CHY can be generalized to massive particles, enabling the description of tree amplitudes for massive
ϕ
3
theory.
Journal Article
LEGO space : building the future
In LEGO Space, you'll explore an entire LEGO universe. Astounding spaceships, eye-popping aliens, and vast planets come to life in a series of truly impressive LEGO models. Step-by-step building instructions at the end of each chapter will have you recreating a piece of each LEGO world for your own collection. Marvel at page after page of out-of-this-world spaceships, rockets, astronauts, space-villains, and other amazing creations from a distant, future realm!
Book
The polynomial form of the scattering equations
A
bstract
The scattering equations, recently proposed by Cachazo, He and Yuan as providing a kinematic basis for describing tree amplitudes for massless particles in arbitrary space-time dimension (including scalars, gauge bosons and gravitons), are reformulated in polynomial form. The scattering equations for
N
particles are shown to be equivalent to a Möbius invariant system of
N
− 3 equations,
h
˜
m
= 0, 2 ≤
m
≤
N
− 2, in
N
variables, where
h
˜
m
is a homogeneous polynomial of degree
m
, with the exceptional property of being linear in each variable taken separately. Fixing the Möbius invariance appropriately, yields polynomial equations
h
m
= 0, 1 ≤
m
≤
N
− 3, in
N
− 3 variables, where
h
m
has degree
m
. The linearity of the equations in the individual variables facilitates computation, e.g. the elimination of variables to obtain single variable equations determining the solutions. Expressions are given for the tree amplitudes in terms of the
h
˜
m
and
h
m
. The extension to the massive case for scalar particles is described and the special case of four dimensional space-time is discussed.
Journal Article
General solution of the scattering equations
A
bstract
The scattering equations, originally introduced by Fairlie and Roberts in 1972 and more recently shown by Cachazo, He and Yuan to provide a kinematic basis for describing tree amplitudes for massless particles in arbitrary space-time dimension, have been reformulated in polynomial form. The scattering equations for
N
particles are equivalent to
N
− 3 polynomial equations
h
m
= 0, 1 ≤
m
≤
N
− 3, in
N
− 3 variables, where
h
m
has degree
m
and is linear in the individual variables. Facilitated by this linearity, elimination theory is used to construct a single variable polynomial equation, Δ
N
= 0, of degree (
N
− 3)! determining the solutions. Δ
N
is the sparse resultant of the system of polynomial scattering equations and it can be identified as the hyperdeterminant of a multidimensional matrix of border format within the terminology of Gel’fand, Kapranov and Zelevinsky. Macaulay’s Unmixedness Theorem is used to show that the polynomials of the scattering equations constitute a regular sequence, enabling the Hilbert series of the variety determined by the scattering equations to be calculated, independently showing that they have (
N
− 3)! solutions.
Journal Article
Pockets of resistance
The most detailed, sophisticated and theoretically grounded analysis of wartime media coverage written to date. Describes and explains how British news media variously supported, and dissented from, coalition propaganda campaigns during the 2003 invasion of Iraq.
eBook
Pockets of resistance
This book analyses British news media coverage of the 2003 invasion of Iraq. It describes the analytical framework that serves as the basis for theoretically informed and systematic analysis of wartime media performance. The book synthesises a range of models, hypotheses and explanatory variables to set out a framework composed of three models of news media performance: the elite-driven model, the independent model and the oppositional model. It provides three case studies which, in different ways, illuminate each model of news media performance in wartime. The three case studies include the case of Jessica Lynch, the case of Ali Abbas and the case of the anti-war movement. The book then presents an account of how the relationship between foreign policy, news media and war might be expected to operate, based on current theoretical understanding. In order to place British coverage of the invasion in context, the book offers brief summaries of the structure and character of Britain's television news services and its press. The book provides an analysis of the ways in which the news media's visual depictions of the war reinforced supportive coverage. It is devoted to documenting and analysing evidence for negotiated and oppositional coverage. The book also examines the representation of civilian casualties, military casualties and humanitarian operations across both television and press, three subject areas that generated a good deal of media criticism.
eBook
Current Algebra on the Torus
We derive the N-point one-loop correlation functions for the currents of an arbitrary affine Kac-Moody algebra. The one-loop amplitudes, which are elliptic functions defined on the torus Riemann surface, are specified by group invariant tensors and certain constant tau-dependent functions. We compute the elliptic functions via a generating function, and explicitly construct the invariant tensor functions recursively in terms of Young tableaux. The lowest tensors are related to the character formula of the representation of the affine algebra. These general current algebra loop amplitudes provide a building block for open twistor string theory, among other applications.
Journal Article