106,565 research outputs found
Scattering Amplitude Recursion Relations in BV Quantisable Theories
Tree-level scattering amplitudes in Yang-Mills theory satisfy a recursion
relation due to Berends and Giele which yields e.g. the famous Parke-Taylor
formula for MHV amplitudes. We show that the origin of this recursion relation
becomes clear in the BV formalism, which encodes a field theory in an
-algebra. The recursion relation is obtained in the transition to a
smallest representative in the quasi-isomorphism class of that
-algebra, known as a minimal model. In fact, the quasi-isomorphism
contains all the information about the scattering theory. As we explain, the
computation of such a minimal model is readily performed in any BV quantisable
theory, which, in turn, produces recursion relations for its tree-level
scattering amplitudes.Comment: 33 pages, minor improvements, typos corrected, references added,
published versio
Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
Recently, by using the known structure of one-loop scattering amplitudes for
gluons in Yang-Mills theory, a recursion relation for tree-level scattering
amplitudes has been deduced. Here, we give a short and direct proof of this
recursion relation based on properties of tree-level amplitudes only.Comment: 10 pp. Added section 4: Proof of MHV Recursion Relation
A Two-Parameter Recursion Formula For Scalar Field Theory
We present a two-parameter family of recursion formulas for scalar field
theory. The first parameter is the dimension . The second parameter
() allows one to continuously extrapolate between Wilson's approximate
recursion formula and the recursion formula of Dyson's hierarchical model. We
show numerically that at fixed , the critical exponent depends
continuously on . We suggest the use of the independence as a
guide to construct improved recursion formulas.Comment: 7 pages, uses Revtex, one Postcript figur
Nijenhuis operator in contact homology and descendant recursion in symplectic field theory
In this paper we investigate the algebraic structure related to a new type of
correlator associated to the moduli spaces of -parametrized curves in
contact homology and rational symplectic field theory. Such correlators are the
natural generalization of the non-equivariant linearized contact homology
differential (after Bourgeois-Oancea) and give rise to an invariant Nijenhuis
(or hereditary) operator (\`a la Magri-Fuchssteiner) in contact homology which
recovers the descendant theory from the primaries. We also sketch how such
structure generalizes to the full SFT Poisson homology algebra to a (graded
symmetric) bivector. The descendant hamiltonians satisfy to recursion
relations, analogous to bihamiltonian recursion, with respect to the pair
formed by the natural Poisson structure in SFT and such bivector. In case the
target manifold is the product stable Hamiltonian structure , with
a symplectic manifold, the recursion coincides with genus topological
recursion relations in the Gromov-Witten theory of .Comment: 30 pages, 3 figure
Tree amplitudes of noncommutative U(N) Yang-Mills Theory
Following the spirit of S-matrix program, we proposed a modified
Britto-Cachazo-Feng-Witten recursion relation for tree amplitudes of
noncommutative U(N) Yang-Mills theory. Starting from three-point amplitudes,
one can use this modified BCFW recursion relation to compute or analyze
color-ordered tree amplitudes without relying on any detail information of
noncommutative Yang-Mills theory. After clarifying the color structure of
noncommutative tree amplitudes, we wrote down the noncommutative analogies of
U(1)-decoupling, Kleiss-Kuijf and Bern-Carrasco-Johansson relations for
color-ordered tree amplitudes, and proved them using the modified BCFW
recursion relation.Comment: 24 pages, 3 figures. v2 References added. v3 some typos correcte
Simple Recursion Relations for General Field Theories
On-shell methods offer an alternative definition of quantum field theory at
tree-level, replacing Feynman diagrams with recursion relations and interaction
vertices with a handful of seed scattering amplitudes. In this paper we
determine the simplest recursion relations needed to construct a general
four-dimensional quantum field theory of massless particles. For this purpose
we define a covering space of recursion relations which naturally generalizes
all existing constructions, including those of BCFW and Risager. The validity
of each recursion relation hinges on the large momentum behavior of an n-point
scattering amplitude under an m-line momentum shift, which we determine solely
from dimensional analysis, Lorentz invariance, and locality. We show that all
amplitudes in a renormalizable theory are 5-line constructible. Amplitudes are
3-line constructible if an external particle carries spin or if the scalars in
the theory carry equal charge under a global or gauge symmetry. Remarkably,
this implies the 3-line constructibility of all gauge theories with fermions
and complex scalars in arbitrary representations, all supersymmetric theories,
and the standard model. Moreover, all amplitudes in non-renormalizable theories
without derivative interactions are constructible; with derivative
interactions, a subset of amplitudes is constructible. We illustrate our
results with examples from both renormalizable and non-renormalizable theories.
Our study demonstrates both the power and limitations of recursion relations as
a self-contained formulation of quantum field theory.Comment: 27 pages and 2 figures; v2: typos corrected to match journal versio
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