Green function and scattering amplitudes in many-dimensional space

Methods for solving scattering are studied in many-dimensional space. Green function and scattering amplitudes are given in terms of the required asymptotic behaviour of the wave function. The Born approximation and the optical theorem are derived in many-dimensional space. Phase-shift analyses are performed for hypercentral potentials and for non-hypercentral potentials by use of the hyperspherical adiabatic approximation.     

Yangian-invariant scattering amplitudes in supersymmetric Chern-Simons theory

We propose a generating function for scattering amplitudes of N=6 supersymmetric-Chern-Simons theory, which parallels a recent work on N=4 supersymmetric-Yang-Mills theory by Arkani-Hamed et?al. Our result suggests that the scattering amplitudes of the supersymmetric-Chern-Simons theory exhibit Yangian invariance.     

Infinite-dimensional geometry and closed string-field theory

The Letter is deveted to the mathematical formulation of the closed string-field theory on a flat background.     

Torus amplitudes in minimal Liouville gravity and matrix models

We evaluate one-point correlation numbers on the torus in the Liouville theory coupled to the conformal matter M(2,2p+1)$M(2,2p+1)$. We find agreement with the recent results obtained in the matrix model approach.     

Signals of confinement in Green functions of SU(2) Yang-Mills theory

It has been well established that the removal of center vortices from SU(2) lattice configurations results in the loss of confinement. The running coupling constant, gluon form factor, and ghost form factor are studied in the Landau gauge for the full and the vortex removed theory. In the latter case, a strong suppression of the running coupling constant and the gluon form factor at low momenta is observed, and the IR singularity of the ghost form factor disappears. Hence, the removal of the vortices generates a theory for which Zwanziger's horizon condition for confinement is no longer satisfied.     

Coulomb integrals in Liouville theory and Liouville gravity

The four-point correlation function has been studied in Liouville field theory. If one of the fields is degenerate, such a function is described in terms of Coulomb integrals. Some nontrivial relations for these integrals have been found that can be used to obtain new exact results in conformal field theory. In particular, a four-point correlation function has been calculated in minimal quantum gravity. The result agrees with the results obtained recently by different methods [A. A. Belavin and A. B. Zamolodchikov, JETP Lett. 82, 7 (2005); Theor. Math. Phys. 147, 729 (2006); A. B. Zamolodchikov, Theor. Math. Phys. 142, 183 (2005); I. K. Kostov and V. B. Petkova, Theor. Math. Phys. 146, 108 (2006)]. The text was submitted by the authors in English.     

Green functions in stochastic field theory

Functional representations are reviewed for the generating function of Green functions of stochastic problems stated either with the use of the Fokker-Planck equation or the master equation. Both cases are treated in a unified manner based on the operator approach similar to quantum mechanics. Solution of a second-order stochastic differential equation in the framework of stochastic field theory is constructed. Ambiguities in the mathematical formulation of stochastic field theory are discussed. The Schwinger-Keldysh representation is constructed for the Green functions of the stochastic field theory which yields a functional-integral representation with local action but without the explicit functional Jacobi determinant or ghost fields.     

Unitarizing high-energy scattering amplitudes in field theories I: QED

Using a procedure which incorporates the s-channel unitarity and t-channel unitarity at every step, we calculate the scattering amplitudes of QED in the high-energy limit. We find that all scattering amplitudes, elastic and inelastic, are summarized by a single eikonal formula which is explicitly unitary.     

A generalized leading-term approximation of high-energy scattering amplitudes in Yang-Mills theory

In this paper, the high-energy vector meson-vector meson elastic scattering amplitudes of a Yang-Mills theory of an SU(2) model are calculated in a generalized leading-term approximation (s→∞ with t fixed). The resulting amplitude, through the 10th order, coincides with the expansion of an eikonal formula. The present method is generalizable to other non-Abelian gauge theories.     

Infinite-dimensional geometry and generally covariant quantum closed string-field theory

A version, based on infinite-dimensional geometry, of the generally covariant closed string-field theory is proposed.     

Bootstrap in supersymmetric Liouville field theory. I. NS sector

A four point function of basic Neveu–Schwarz exponential fields is constructed in the N=1$N=1$ supersymmetric Liouville field theory. Although the basic NS structure constants were known previously, we present a new derivation, based on a singular vector decoupling in the NS sector. This allows to stay completely inside the NS sector of the space of states, without referencing to the Ramond fields. The four-point construction involves also the NS blocks, for which we suggest a new recursion representation, the so-called elliptic one. The bootstrap conditions for this four point correlation function are verified numerically for different values of the parameters.     

Analytic properties of scattering amplitudes in two variables in general quantum field theory

It is shown that scattering amplitudes have analytic properties as functions of momentum transfer not only for physical, but also for complex energies. This follows from local relativistic field theory for all reactions for which an ordinary dispersion relation can be proved.It is further shown that such amplitudes are boundary values of analytic functions of the two variables energy and momentum transfer. A domain of holomorphy — which is however not best possible — is given explicitly. It follows then that partial waves can be analytically continued to complex energies.     

Renormalization group and relations between scattering amplitudes in a theory with different mass scales

In the Yukawa model with two different mass scales, the renormalization group equation is used to obtain relations between scattering amplitudes at low energies. By considering fermion-fermion scattering as an example, a basic one-loop renormalization group relation is derived which gives the possibility to reduce the problem to the scattering of light particles in the “external field” substituting a heavy virtual state. Applications of the results to problems of searches for new physics beyond the Standard Model are discussed.     

Field theory amplitudes in a space with SU(2) fuzziness

The structure of transition amplitudes in field theory in a three-dimensional space whose spatial coordinates are noncommutative and satisfy the SU(2) Lie algebra commutation relations is examined. In particular, the basic notions for constructing the observables of the theory as well as subtleties related to the proper treatment of δ distributions (corresponding to conservation laws) are introduced. Explicit examples are given for scalar field theory amplitudes in the lowest order of perturbation.     

Higher multipole polarizabilities of hadrons from compton scattering amplitudes (II)

A procedure to derive closed form-sum rules for the hadron generalized electric and magnetic polarizabilities of any multipolar order is presented and discussed. The obtained results complete our previous analysis and may prove useful for a better understanding of the polarizability properties of a spin 0 or $\text{1}\text{2}$ hadron in as far as these show themselves in low energy elastic photon-hadron interactions.