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| Author(s): |
Petrus Henrique Ribeiro dos Anjos
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | São Carlos. |
| Institution: | Universidade de São Paulo (USP). Instituto de Física de São Carlos (IFSC/BT) |
| Defense date: | 2004-10-22 |
| Examining board members: |
Paulo Afonso Faria da Veiga;
Liderio Citrangulo Ioriatti Junior;
Emmanuel Araújo Pereira
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| Advisor: | Paulo Afonso Faria da Veiga |
| Abstract | |
In this work, we consider the low-lying energy-momentum spectrum for the imaginary-time lattice quantum field model associated with d-dimensional lattice ferromagnetic classical N-component vector spin systems: The O(N) Spin Model. Each system is characterized by a single site 'a priori' spin probability distribution. We work only at high temperature region (0<β<=1). The energy-momentum spectrum exhibits isolated dispersion curves which are identified as single particles and multi-particle bands. In particular, we study states of one and two-particles. For the single particle spectrum, we obtain the dispersion curve and the particle mass. This result show the existence of the so called 'low spectral gap'. Still working with the single particle spectrum, e show the existence of a continuum spectra band, associated to states of two free partciles, and we obtain the band width. Our two-particle bound state analysis is restricted to a ladder approximation of the Bethe-Salpeter equation, and the existence of bound states depend on whether or not Gaussian domination for the four-point function is verified. It is known that two-particle bound states appear below the two-particle band if Gaussian domination does not hold. Here, we show that two two-particle bound states appear above the two-particle band if Gaussian domination is verified. We also show how the complete two-particle spectral pattern for these models can be understood by making a correspondence between the Bethe-Salpeter equation and a two-particle lattice Schrödinger Hamiltonian operator with attractive or repulsive spin-dependent delta potentials at the origin. A staggering transformation is used to relate the attractive and repulsive potential cases, as well as their associated Hamiltonians spectrum and eigenfunctions. (AU) | |