Polyakov's spinning string from canonical point of view

We give a canonical formulation of Polyakov's modified spinning string theory. This means that we start with the lagrangian , where $\text{L}$₁ is a counter term derived from the general form of the trace anomaly. In the superconformal gauge $\text{L}$₁ reduces to the supersymmetric Liouville lagrangian. A general solution of the supersymmetric Liouville equation is derived as well as appropriate boundary condutions for the Neveu-Schwarz (NS) and Ramond models. Under the assumption that the exact quantization of the Liouville theory does not yield any additional anomalies. We show that relativistic invariance requires the constant C to be $\text{C=}\text{10?D}\text{8π}$, in agreement with Polyakov's result. For D<10 the string acquires longitudinal modes. A semiclassical quantization of the Liouville theory is then performed with the result that the mass spectrum starts with $\text{m}{}^2\text{?}\text{1}\text{2}\text{α′}\text{and}\text{m}{}^2\text{= 0}$ in the NS and Ramond models in any dimension D?10. The longitudinal excitations are determined by a simple harmonic oscillator expression. It is shown that a consistent exact quantization could remove the tachyon state in the NS model.     

Saddle point analysis of pomeron singularities in Polyakov's string theory

A saddle-point analysis of Polyakov's string theory is carried out where the Liouville action is defined on surfaces with two disjoint boundaries, (the cylinder topology). This topology is appropriate for probing the closed string excitations. In a saddle point approach, a family of pomeron singularities having a Regge slope half of the ordinary particle trajectories is identified. However, a difficulty with the factorization property arises.     

Infinite number of local conservation laws for the self-dual SU(2) Yang-Mills system within 't Hooft's ansatz

We derive infinite sets of local continuity equations for the four-dimensional classical self-dual SU(2) Yang-Mills fields subjected to 't Hooft's ansatz. In striking analogy to the two-dimensional CP(n) non-linear sigma model where local conservation laws obtain either from complex Cauchy-Riemann analyticity or from a matrix Riccati equation, our local sets derive from quaternionic Fueter analyticity or a Riccati equation associated with the geometric prolongation structure implied by the Belavin-Zakharov linear spectral problem for the self-dual Yang-Mills system. Our analysis underlines the close connection between local and non-local conservation laws and suggests that infinite sets of local continuity equations should be present in the general self-(antiself-)dual gauge field case.     

关于Birkhoff逆问题中Santilli方法的研究

研究构造Birkhoff动力学函数的Santilli方法.首先,基于Cauchy-Kovalevskaya型方程解的存在性定理,采用反证法证明自治系统总有自治Birkhoff表示;其次,给出更简洁的方法证明Santilli第二方法可以被简化;找到Santilli第三方法中所隐含的一种等量关系,提出改进的Santilli第三方法,并研究该方法的MATLAB程序化计算;最后,总结全文并对结果进行讨论.     

Bethe ansatz solution of the asymmetric exclusion process with open boundaries

We derive the Bethe ansatz equations describing the complete spectrum of the transition matrix of the partially asymmetric exclusion process with the most general open boundary conditions. For totally asymmetric diffusion we calculate the spectral gap, which characterizes the approach to stationarity at large times. We observe boundary induced crossovers in and between massive, diffusive, and Kardar-Parisi-Zhang scaling regimes.     

On the infrared singularities of Green's functions in quantum electrodynamics

We present a formal calculation of the infrared singularity structure of the fermion propagator in QED based on the Faddeev-Kulish asymptotic solution. The Renormalization program is reviewed in the context of the BPHZ subtraction scheme and a refinement of the Renormalization group methods is employed to study the infrared singularities in perturbation theory.