122 research outputs found
Scattering Equations and Feynman Diagrams
We show a direct matching between individual Feynman diagrams and integration
measures in the scattering equation formalism of Cachazo, He and Yuan. The
connection is most easily explained in terms of triangular graphs associated
with planar Feynman diagrams in -theory. We also discuss the
generalization to general scalar field theories with interactions,
corresponding to polygonal graphs involving vertices of order . Finally, we
describe how the same graph-theoretic language can be used to provide the
precise link between individual Feynman diagrams and string theory integrands.Comment: 18 pages, 57 figure
Integration Rules for Loop Scattering Equations
We formulate new integration rules for one-loop scattering equations
analogous to those at tree-level, and test them in a number of non-trivial
cases for amplitudes in scalar -theory. This formalism greatly
facilitates the evaluation of amplitudes in the CHY representation at one-loop
order, without the need to explicitly sum over the solutions to the loop-level
scattering equations.Comment: 22 pages, 17 figure
Integration Rules for Scattering Equations
As described by Cachazo, He and Yuan, scattering amplitudes in many quantum
field theories can be represented as integrals that are fully localized on
solutions to the so-called scattering equations. Because the number of
solutions to the scattering equations grows quite rapidly, the contour of
integration involves contributions from many isolated components. In this
paper, we provide a simple, combinatorial rule that immediately provides the
result of integration against the scattering equation constraints for any
M\"obius-invariant integrand involving only simple poles. These rules have a
simple diagrammatic interpretation that makes the evaluation of any such
integrand immediate. Finally, we explain how these rules are related to the
computation of amplitudes in the field theory limit of string theory.Comment: 30 pages, 29 figure
New Representations of the Perturbative S-Matrix
We propose a new framework to represent the perturbative S-matrix which is
well-defined for all quantum field theories of massless particles, constructed
from tree-level amplitudes and integrable term-by-term. This representation is
derived from the Feynman expansion through a series of partial fraction
identities, discarding terms that vanish upon integration. Loop integrands are
expressed in terms of "Q-cuts" that involve both off-shell and on-shell
loop-momenta, defined with a precise contour prescription that can be evaluated
by ordinary methods. This framework implies recent results found in the
scattering equation formalism at one-loop, and it has a natural extension to
all orders---even non-planar theories without well-defined forward limits or
good ultraviolet behavior.Comment: 4+1 pages, 4 figure
The Spared Nerve Injury (SNI) Model of Induced Mechanical Allodynia in Mice
Peripheral neuropathic pain is a severe chronic pain condition which may result from trauma to sensory nerves in the peripheral nervous system. The spared nerve injury (SNI) model induces symptoms of neuropathic pain such as mechanical allodynia i.e. pain due to tactile stimuli that do not normally provoke a painful response [1]
Paleoredox chemistry of Cenomanian–Coniacian black shales at high paleolatitudes: Implications for the extent of anoxia during OAE2
Geochemical and biologic constraints on the Archaean atmosphere and climate – A possible solution to the faint early Sun paradox
String-like dual models for scalar theories
We show that all tree-level amplitudes in scalar field theory can
be represented as the limit of an -invariant,
string-theory-like dual model integral. These dual models are constructed
according to constraints that admit families of solutions. We derive these dual
models, and give closed formulae for all tree-level amplitudes of any
scalar field theory.Comment: 15 pages, 0 figure
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