相关论文: Revisit of Weinberg's sum rules
The Ward identity in gauge theory constrains the behavior of the amplitudes. We discuss the Ward identity for amplitudes with a pair of shifted lines with complex momenta. This will induce a recursion relation identical to BCFW recursion…
A $U(2)_{L}\times U(2)_{R}$ chiral theory of pseudoscalar, vector, and axial-vector mesons has been proposed. VMD has been revealed from this theory. The physical processes of normal parity and abnormal parity have been studied by using the…
A doubly infinite set of series expansion for $1/\pi$ are reported. They follow trivially from a formal expansion for the quotient of the values taken by the gamma function for two (complex) arguments differing by an integer plus one half,…
We review some of the recent progress in the continuum formulation of two-dimensional string theory, i.e. two-dimensional quantum gravity coupled to $c=1$ matter. Special attention is devoted to the discrete states and to the $w_\infty$…
Recursion relations for integrals of amplitudes over the phase space, i.e. for partial wave amplitudes, are introduced. In their simplest form these integrals are proportional to the s-wave amplitudes and represent rigorous lower bounds on…
We show that a binomial identity arising in the context of the study of series expansions of $1/\pi$ can be seen as an incarnation of Whipples second theorem for hypergeometric series.
We compare the low-energy partial wave analyses $\pi N$ scattering with a high-energy data via finite energy sum rules. We construct a new set of amplitudes by matching the imaginary part from the low-energy analysis with the high-energy,…
We derive new amplitudes relations revealing a hidden unity among wide-ranging theories in arbitrary spacetime dimensions. Our results rely on a set of Lorentz invariant differential operators which transmute physical tree-level scattering…
We derive weighted summation identities involving the second order recurrence sequence $\{w_n\} =\{ w_n(a,b; p, q)\}$ defined by $w_0 = a,\,w_1 = b;\,w_n = pw_{n - 1} - qw_{n - 2}\, (n \ge 2)$, where $a$, $b$, $p$ and $q$ are arbitrary…
Several combinatorial identities are presented, involving Stirling functions of the second kind with a complex variable. The identities involve also Stirling numbers of the first kind, binomial coefficients and harmonic numbers.
The Ward identities for amplitudes at the tree level are derived from symmetries of the corresponding classical dynamical systems. The results are applied to some 2 into n amplitudes.
We report on the Hopf algebraic description of renormalization theory of quantum electrodynamics. The Ward-Takahashi identities are implemented as linear relations on the (commutative) Hopf algebra of Feynman graphs of QED. Compatibility of…
The near-threshold expansion of the $\pi \pi$ amplitude is developed using the crossing-covariant independent variables. The independent threshold parameters entering the real part of the amplitude in an explicitly Lorentz-invariant way are…
Once and twice subtracted crossing symmetric dispersion relations applied to $\pi\pi \to \pi\pi$ scattering data are analyzed and compared. Both sets of dispersion relations can be used to test the $\pi\pi$ amplitudes in low partial waves…
We consider binomial and inverse binomial sums at infinity and rewrite them in terms of a small set of constants, such as powers of $\pi$ or $\log(2)$. In order to perform these simplifications, we view the series as specializations of…
We derive two new identities involving the Bernoulli numbers, the Euler numbers, and the Stirling numbers of the first kind using analytic continuation of a well known identity for the Stirling numbers of the first kind.
The Ward identities of the $W_{\infty}$ symmetry in two dimensional string theory in the tachyon background are studied in the continuum approach. We consider amplitudes different from 2D string ones by the external leg factor and derive…
Weinberg's theorem for \pi-\pi scattering, including the Adler zero at threshold in the chiral limit, is analytically proved for microscopic quark models that preserve chiral symmetry. Implementing Ward-Takahashi identities, the isospin 0…
Using a simple Vi\`ete-like formula for $\pi$ based on the nested radicals $a_k = \sqrt{2 + a_{k-1}}$ and $a_1 = \sqrt{2}$, we derive a set of the recurrence relations for the constant $1$. Computational test shows that application of this…
The generalized Weinberg sum rules containing the difference of isovector vector and axial-vector spectral functions saturated by both finite and infinite number of narrow resonances are considered. We summarize the status of these sum…