We initiate a program to study the relationship between the target space, the spectrum and the scattering amplitudes in string theory. We consider scattering amplitudes following from string theory and quantum field theory on a curved target space, which is taken to be the SU(2) group manifold, with special attention given to the duality between contributions from different channels. We give a simple example of the equivalence between amplitudes coming from string theory and quantum field theory, and compute the general form of a four-scalar field-theoretical amplitude. The corresponding string theory calculation is performed for a special case, and we discuss how more general string theory amplitudes could be evaluated.
The introduction of spinor fields and the problem of the positivity of the energy. Need for anti-commutators. Calculus in a Grassmannian manifold, the Berezin integral. Clifford algebras. Quantum mechanics and quantum field theory with fermions. The use of path integrals.
This chapter covers the new on-shell methods that have been developed over the past twenty years for computing scattering amplitudes in quantum field theory. These methods break free from the traditional approach of Feynman diagrams. The chapter covers a subset of topics, setting up the basic kinematics, spinor helicities, spinor products, and the calculation of tree amplitudes.
Abstract
We obtain a first order post-Minkowskian two-body effective potential whose post-Newtonian expansion directly reproduces the Einstein-Infeld-Hoffmann potential. Post-Minkowskian potentials can be extracted from on-shell scattering amplitudes in a quantum field theory of scalar matter coupled to gravity. Previously, such potentials did not reproduce the Einstein-Infeld-Hoffmann potential without employing a suitable canonical transformation. In this work, we resolve this issue by obtaining a new expression for the first-order post-Minkowskian potential. This is accomplished by exploiting the reference frame dependence that arises in the scattering amplitude computation. Finally, as a check on our result, we demonstrate that our new potential gives the correct scattering angle.
Hentschel: The Einstein Tower/Bull: Physik mit dem PC/Chawla: Composite Materials. Science and Engineering/Brennan: The Physics of Semiconductors/Huang: Quantum Field Theory. From Operators to Path Integrals/Quang/Pham: Elementary Particles and Their Inte
