arXiv subjects
Publications and source records attributed to Chuan-Jie Zhu.
We provide a new proof of Cachazo-Svrcek-Witten rules for tree-level gluonic amplitudes. As a key step, we explicitly show the cancellation of spurious poles originating from the maximally helicity violating vertices in these rules. To achieve this, we introduce specially-defined two-off-shell-line sub-amplitudes and study their residues at spurious poles.
We study the norms of the Bloch vectors for arbitrary $n$-partite quantum states. A tight upper bound of the norms is derived for $n$-partite systems with different individual dimensions. These upper bounds are used to deal with the separability problems. Necessary conditions are presented for $\mathbf m$-separable states in $n$-partite quantum systems. Based on the upper bounds, classification of multipartite entanglement is illustrated with detailed examples.
We investigate monogamy relations and upper bounds for generalized $W$-class states related to the Rényi-$α$ entropy. First, we present an analytical formula on Rényi-$α$ entanglement (R$α$E) and Rényi-$α$ entanglement of assistance (REoA) of a reduced density matrix for a generalized $W$-class states. According to the analytical formula, we show monogamy and polygamy relations for generalized $W$-class states in terms of R$α$E and REoA. Then we give the upper bounds for generalized $W$-class states in terms of R$α$E. Next, we provide tighter monogamy relations for generalized $W$-class states in terms of concurrence and convex-roof extended negativity and obtain the monogamy relations for R$α$E by the analytical expression between R$α$E and concurrence. Finally, we apply our results into quantum games and present a new bound of the nonclassicality of quantum games restricting to generalized $W$-class states.
We study the distinguishability of a particular type of maximally entangled states -- the "lattice states" using a new approach of semidefinite program. With this, we successfully construct all sets of four ququad-ququad orthogonal maximally entangled states that are locally indistinguishable and find some curious sets of six states having interesting property of distinguishability. Also, some of the problems arose from \cite{CosentinoR14} about the PPT-distinguishability of "lattice" maximally entangled states can be answered.
We study separability problem using general symmetric informationally complete measurements and propose separability criteria in $\mathbb{C}^{d_{1}}\otimes\mathbb{C}^{d_{2}}$ and $\mathbb{C}^{d_{1}}\otimes\mathbb{C}^{d_{2}}\cdots\otimes\mathbb{C}^{d_{n}}$. Our criteria just require less local measurements and provide experimental implementation in detecting entanglement of unknown quantum states.
We investigate monogamy relations related to the Rényi-$α$ entanglement and polygamy relations related to the Rényi-$α$ entanglement of assistance. We present new entanglement monogamy relations satisfied by the $μ$-th power of Rényi-$α$ entanglement with $α\in[\sqrt{7}-1)/2,(\sqrt{13}-1)/2]$ for $μ\geqslant2$, and polygamy relations satisfied by the $μ$-th power of Rényi-$α$ entanglement of assistance with $α\in[\sqrt{7}-1)/2,(\sqrt{13}-1)/2]$ for $0\leqμ\leq1$. These relations are shown to be tighter than the existing ones.
In this paper, we generalize the integration rules for scattering equations to situations where higher-order poles are present. We describe the strategy to deduce the Feynman rules of higher-order poles from known analytic results of simple CHY-integrands, and propose the Feynman rules for single double pole and triple pole as well as duplex-double pole and triplex-double pole structures. We demonstrate the validation and strength of these rules by ample non-trivial examples.
The rational parts of 6-gluon one-loop amplitudes with scalars circulating in the loop are computed by using the newly developed method for computing the rational parts directly from Feynman integrals. We present the analytic results for the two MHV helicity configurations: $(1^-2^+3^+4^-5^+6^+)$ and $(1^-2^+3^-4^+5^+6^+)$, and the two NMHV helicity configurations: $(1^-2^-3^+4^-5^+6^+)$ and $(1^-2^+3^-4^+5^-6^+)$. Combined with the previously computed results for the cut-constructible part, our results are the last missing pieces for the complete partial helicity amplitudes of the 6-gluon one-loop QCD amplitude.
The rational parts of 5-gluon one-loop amplitudes are computed by using the newly developed method for computing the rational parts directly from Feynman integrals. We found complete agreement with the previously well-known results of Bern, Dixon and Kosower obtained by using the string theory method. Intermediate results for some combinations of Feynman diagrams are presented in order to show the efficiency of the method and the local cancellation between different contributions.
A general formalism for computing only the rational parts of oneloop QCD amplitudes is developed. Starting from the Feynman integral representation of the one-loop amplitude, we use tensor reduction and recursive relations to compute the rational parts directly. Explicit formulas for the rational parts are given for all bubble and triangle integrals. Formulas are also given for box integrals up to two-masshard boxes which are the needed ingredients to compute up to 6-gluon QCD amplitudes. We use this method to compute explicitly the rational parts of the 5- and 6-gluon QCD amplitudes in two accompanying papers.
The overall coefficient of the two-loop 4-particle amplitude in superstring theory is determined by making use of the factorization and unitarity. To accomplish this we computed in detail all the relevant tree and one-loop amplitudes involved and determined their overall coefficients in a consistent way.
We study in detail the factorization of the newly obtained two-loop four-particle amplitude in superstring theory. In particular some missing factors from the scalar correlators are obtained correctly, in comparing with a previous study of the factorization in two-loop superstring theory. Some details for the calculation of the factorization of the kinematic factor are also presented.
Based on the recent developments of explicit computations at 2 loops in superstring theory in the covariant RNS formalism, we propose an explicit formula for the arbitrary loop 4-particle amplitude in superstring theory. We prove that this formula passes two very difficult tests: modular invariance and factorization. If proved, this shows that superstring theory is not only finite order by order in perturbation theory but is also exceptionally simple.
The Cachazo-Svrcek-Witten approach to perturbative gauge theory is extended to gauge theories with quarks and gluinos. All googly amplitudes with quark-antiquark pairs and gluinos are computed and shown to agree with the previously known results. The computations of the non-MHV or non-googly amplitudes are also briefly discussed, in particular the purely fermionic amplitude with 3 quark-antiquark pairs.
The generic googly amplitudes in gauge theory are computed by using the Cachazo-Svrcek-Witten approach to perturbative calculation in gauge theory and the results are in agreement with the previously well-known ones. Within this approach we also discuss the parity transformation, charge conjugation and the dual Ward identity. We also extend this calculation to include fermions and the googly amplitudes with a single quark-anti-quark pair are obtained correctly from fermionic MHV vertices. At the end we briefly discuss the possible extension of this approach to gravity.
The googly amplitudes in gauge theory are computed by using the off shell MHV vertices with the newly proposed rules of Cachazo, Svrcek and Witten. The result is in agreement with the previously well-known results. In particular we also obtain a simple result for the all negative but one positive helicity amplitude when one of the external line is off shell.
It is shown that the four-particle amplitude of superstring theory at two loops obtained in [1,2] is equivalent to the previously obtained results in [3,4,5]. Here the ${\bf Z}_2$ symmetry in hyperelliptic Riemann surface plays an important role in the proof.
In this paper I review some old and new works on the computation of two-loop 4-particle amplitude in superstring theory. I also present the proof by Iengo, showing the vanishing of the term related to the two-loop correction to the $R^4$ term. Finally I will present some recent works on two-loop computation in hyperelliptic language following the new gauging fixing method of D'Hoker and Phong.