Phase Diagram of a 3D, Gauge Fermion Scalar Model With Compact U(1) Gauge Symmetry

[摘要] One of the current concerns for particle physisists is to find out the origin of particle masses in the context of gauge field theories. Certain studies on the close connection that exists between mass generation and spontaneous symmetry breaking have led to an important breakthrough (the Higgs mechanism) but our understanding of the underlying phenomena still needs to be improved. Apparently the origin of particle mass lies outside the foundations of the standard model itself and therefore a satisfactory explanation has to be found beyond this framework. The development of lattice gauge theories in the last thirty years has permitted exploration of new situations that one could not consider before. It has been shown that at strong gauge coupling a spontaneous breakdown of chiral symmetry arises dynamically. This suggests that the process of fermion mass generation could in fact begin with an interaction between fermion and gauge fields. This thesis consists of a review of the different elements which compose this search and a presentation of a research performed on a viable alternative model for fermion mass generation. In the first part the basics of lattice gauge theory will be introduced. The second part outlines the elements of fermion mass generation process and reviews the results obtained so far. The research which is then presented in the third part is concerned with a lattice gauge theory which displays a so-called shielded gauge mechanism of dynamical fermion mass generation. This mechanism which assumes some scalar field in addition to the fermion and gauge fields might be retained in the continuum limit, as the lattice spacing shrinks to zero (it displays a second order phase transition). This raises the hope to elaborate a realistic theory with dynamically generated fermion mass in the continuum. The main purpose of the work presented here was to study the model, for a compact U(1) symmetry, on a three dimensional lattice and to draw its phase diagram. A method inspired by Lee and Yang has been used. It consisted of analysing the distribution of the zeros of the canonical partition function and their response to a change in the hopping parameter and/or the coupling constant. The partition function is expressed as a polynomial in the fermion mass and a Hybrid Monte-Carlo scheme is used to generate thermalised configurations at various value of beta and kappa. The coefficients of the corresponding polynomial are extracted via a Lanczos algorithm and the zeros are then found by a standard root-finding routine. The theorem of Lee and Yang allows us to locate the phase transitions. In order to perform a finite size scaling analysis of the zeros several simulations were made on 4.

[发布机构] University:University of Glasgow

[关键词] High energy physics, Theoretical physics