BFKL approach and 2->5 MHV amplitude

We study MHV amplitude for the 2 -> 5 scattering in the multi-Regge kinematics. The Mandelstam cut correction to the BDS amplitude is calculated in the leading logarithmic approximation (LLA) and the corresponding remainder function is given to any loop order in a closed integral form. We show that the LLA remainder function at two loops for 2 -> 5 amplitude can be written as a sum of two 2 -> 4 remainder functions due to recursive properties of the leading order impact factors. We also make some generalizations for the MHV amplitudes with more external particles. The results of the present study are in agreement with all leg two loop symbol derived by Caron-Huot as shown in a parallel paper of one of the authors with collaborators.Comment: 24 pages, 17 figure

Mandelstam cuts and light-like Wilson loops in N=4 SUSY

We perform an analytic continuation of the two-loop remainder function for the six-point planar MHV amplitude in N=4 SUSY, found by Goncharov, Spradlin, Vergu and Volovich from the light-like Wilson loop representation. The remainder function is continued into a physical region, where all but two energy invariants are negative. It turns out to be pure imaginary in the multi-Regge kinematics, which is in an agreement with the predictions based on the Steinmann relations for the Regge poles and Mandelstam cut contributions. The leading term reproduces correctly the expression calculated by one of the authors in the BFKL approach, while the subleading term presents a result, that was not yet found with the use of the unitarity techniques. This supports the applicability of the Wilson loop approach to the planar MHV amplitudes in N=4 SUSY.Comment: 11 pages, 4 figure

BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes

After a brief review of the BFKL approach to Regge processes in QCD and in supersymmetric (SUSY) gauge theories we propose a strategy for calculating the next-to-next-to-leading order corrections to the BFKL kernel. They can be obtained in terms of various cross-sections for Reggeized gluon interactions. The corresponding amplitudes can be calculated in the framework of the effective action for high energy scattering. In the case of N=4 SUSY it is also possible to use the Bern-Dixon-Smirnov (BDS) ansatz. For this purpose the analytic properties of the BDS amplitudes at high energies are investigated, in order to verify their self-consistency. It is found that, for the number of external particles being larger than five, these amplitudes, beyond one loop, are not in agreement with the BFKL approach which predicts the existence of Regge cuts in some physical channels.Comment: 41 pages, expanded version with many clarifications and new references, conclusions unchanged. Note adde

Equivalence of particle-particle random phase approximation correlation energy and ladder-coupled-cluster doubles

We present an analytical proof and numerical demonstrations of the equivalence of the correlation energy from particle-particle random phase approximation (pp-RPA) and ladder-couple-cluster-doubles (ladder-CCD). These two theories reduce to the identical algebraic matrix equation and correlation energy expressions, under the assumption that the pp-RPA equation is stable. The numerical examples illustrate that the correlation energy missed by pp-RPA in comparison with couple-cluster single and double is largely canceled out when considering reaction energies. This theoretical connection will be beneficial to future pp-RPA studies based on the well established couple cluster theory

Axiomatic formulations of nonlocal and noncommutative field theories

We analyze functional analytic aspects of axiomatic formulations of nonlocal and noncommutative quantum field theories. In particular, we completely clarify the relation between the asymptotic commutativity condition, which ensures the CPT symmetry and the standard spin-statistics relation for nonlocal fields, and the regularity properties of the retarded Green's functions in momentum space that are required for constructing a scattering theory and deriving reduction formulas. This result is based on a relevant Paley-Wiener-Schwartz-type theorem for analytic functionals. We also discuss the possibility of using analytic test functions to extend the Wightman axioms to noncommutative field theory, where the causal structure with the light cone is replaced by that with the light wedge. We explain some essential peculiarities of deriving the CPT and spin-statistics theorems in this enlarged framework.Comment: LaTeX, 13 pages, no figure

Integrable spin chains and scattering amplitudes

In this review we show that the multi-particle scattering amplitudes in N=4 SYM at large Nc and in the multi-Regge kinematics for some physical regions have the high energy behavior appearing from the contribution of the Mandelstam cuts in the complex angular momentum plane of the corresponding t-channel partial waves. These Mandelstam cuts or Regge cuts are resulting from gluon composite states in the adjoint representation of the gauge group SU(Nc). In the leading logarithmic approximation (LLA) their contribution to the six point amplitude is in full agreement with the known two-loop result. The Hamiltonian for the Mandelstam states constructed from n gluons in LLA coincides with the local Hamiltonian of an integrable open spin chain. We construct the corresponding wave functions using the integrals of motion and the Baxter-Sklyanin approach.Comment: Invited review for a special issue of Journal of Physics A devoted to "Scattering Amplitudes in Gauge Theories", R. Roiban(ed), M. Spradlin(ed), A. Volovich (ed

Are spurred cyathia a key innovation? Molecular systematics and trait evolution in the slipper spurges (Pedilanthus clade: Euphorbia, Euphorbiaceae)

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/141662/1/ajb20493.pd

Continuity of the four-point function of massive ϕ44\phi_4^4-theory above threshold

In this paper we prove that the four-point function of massive \vp_4^4-theory is continuous as a function of its independent external momenta when posing the renormalization condition for the (physical) mass on-shell. The proof is based on integral representations derived inductively from the perturbative flow equations of the renormalization group. It closes a longstanding loophole in rigorous renormalization theory in so far as it shows the feasibility of a physical definition of the renormalized coupling.Comment: 23 pages; to appear in Rev. Math. Physics few corrections, two explanatory paragraphs adde

Analytic properties of high energy production amplitudes in N=4 SUSY

We investigate analytic properties of the six point planar amplitude in N=4 SUSY at the multi-Regge kinematics for final state particles. For inelastic processes the Steinmann relations play an important role because they give a possibility to fix the phase structure of the Regge pole and Mandelstam cut contributions. These contributions have the Moebius invariant form in the transverse momentum subspace. The analyticity and factorization constraints allow us to reproduce the two-loop correction to the 6-point BDS amplitude in N=4 SUSY obtained earlier in the leading logarithmic approximation with the use of the s-channel unitarity. The exponentiation hypothesis for the remainder function in the multi-Regge kinematics is also investigated. The 6-point amplitude in LLA can be completely reproduced from the BDS ansatz with the use of the analyticity and Regge factorization.Comment: To appear in the proceedings of 16th International Seminar on High Energy Physics, QUARKS-2010, Kolomna, Russia, 6-12 June, 2010. 15 page

Infra-Red Asymptotic Dynamics of Gauge Invariant Charged Fields: QED versus QCD

The freedom one has in constructing locally gauge invariant charged fields in gauge theories is analyzed in full detail and exploited to construct, in QED, an electron field whose two-point function W(p), up to the fourth order in the coupling constant, is normalized with on-shell normalization conditions and is, nonetheless, infra-red finite; as a consequence the radiative corrections vanish on the mass shell $p^2=\mu^2$ and the free field singularity is dominant, although, in contrast to quantum field theories with mass gap, the eigenvalue $\mu^2$ of the mass operator is not isolated. The same construction, carried out for the quark in QCD, is not sufficient for cancellation of infra-red divergences to take place in the fourth order. The latter divergences, however, satisfy a simple factorization equation. We speculate on the scenario that could be drawn about infra-red asymptotic dynamics of QCD, should this factorization equation be true in any order of perturbation theory.Comment: 30 pages, RevTex, 8 figures included using graphic