Treatment of Dirac Fields in Light—Front Coordinates by Dirac‘s Method for Constrained Hamiltonian Systems

Dirac‘s method which itself is for constrained Boson fields and particle systems is followed and developed to treat Dirac fields in light-front coordinates.     

The Proof of the Dirac Conjecture for a Class of Finite-Dimensional Dirac Hamiltonian Systems

Mathematical Notes -     

The parametric orbits and the form invariance of three-body in one-dimension

In this paper, the differential equations of motion of a three-body interacting pairwise by inverse cubic forces(“centrifugal potential”) in addition to linear forces (“harmonical potential”) are expressed in Ermakov formalism in two-dimension polar coordinates, and the Ermakov invariant is obtained. By rescaling of the time variable and the space coordinates, the parametric orbits of the three bodies are expressed in terms of relative energy H1 and Ermakov invariant. The form invariance of the transformations of two conserved quantities are also studied.     

Phase transition in a class of Hamiltonians

We consider a class of Hamiltonians for a system of one localized spin-1/2 particle per lattice site with the total spin as a good quantum number. We introduce a set of conditions in the form of a hypothesis relating the subpartition function, which is the partition function defined by the subset of energies with a specific value of spin. If the equality in the hypothesis is satisfied, then the system undergoes a phase transition as a consequence of Yang-Lee theorem. As an application, we estimate the bounds on the spectrum of the Heisenberg Hamiltonian. Supported by the National Science Foundation, Washington D.C. and the Robert A. Welch Foundation, Houston, Texas and partly supported by the United States Atomic Energy Commission, Contract Grant AT (40-1) 3992.     

Hamiltonian图和弱Ore条件

本文用弱 Ore条件和 NC2去研究 Hamiltonian图 ,得到深刻的结果 ,它们改进和统一文献 [1 ]至 [5 ]中熟知的一些著名结果 .     

Infinitely many solutions for Hamiltonian systems

We consider two classes of the second-order Hamiltonian systems with symmetry. If the systems are asymptotically linear with resonance, we obtain infinitely many small-energy solutions by minimax technique. If the systems possess sign-changing potential, we also establish an existence theorem of infinitely many solutions by Morse theory.     

Induced subgraphs with large degrees at end-vertices for hamiltonicity of claw-free graphs

A graph is called claw-free if it contains no induced subgraph isomorphic to K1,3. Matthews and Sumner proved that a 2-connected claw-free graph G is Hamiltonian if every vertex of it has degree at least (|V(G)|-2)/3. At the workshop C&C (Novy Smokovec, 1993), Broersma conjectured the degree condition of this result can be restricted only to end-vertices of induced copies of N (the graph obtained from a triangle by adding three disjoint pendant edges). Fujisawa and Yamashita showed that the degree condition of Matthews and Sumner can be restricted only to end-vertices of induced copies of Z₁ (the graph obtained from a triangle by adding one pendant edge). Our main result in this paper is a characterization of all graphs H such that a 2-connected claw-free graph G is Hamiltonian if each end-vertex of every induced copy of H in G has degree at least |V(G)|/3+1. This gives an affirmative solution of the conjecture of Broersma up to an additive constant.