标题： 倒格子空间中的波矢子群及其表示 显示英文标题

标题： Wave vector substar group in reciprocal lattice space and its representation

摘要： 在论文中，我们建立了波矢子星群及其表示的新概念，该概念在研究晶体平移对称性破缺时，只需考虑参与相变的特定波矢星臂，而不需要考虑波矢星的所有臂，这与传统的朗道理论不同。 我们表明，使用这一新概念，可以有效地研究与平移对称性破缺相关的晶体有趣物理性质。 我们可以看到，利用新概念，诸如钙钛矿型KMnF3多铁晶体和高温超导体La2/3Mg1/2W1/2O3（La4Mg3W3O18）化合物中的可约表示相关的复杂相变研究大大简化了，波矢子星群及其表示的理论成为一种能够积极促进固态晶体各种对称性破缺现象研究的强大数学工具。 显示英文摘要

摘要： In the paper we establish the new conception of the wave vector substar group and its representation that, in the study on translational symmetry breaking of crystal, can only consider the particular arms of wave vector star taking part in phase transition, but not all arms of wave vector star, unlike the traditional Landau theory. We show that using the new conception, we can effectively investigate the interesting physical properties of crystals associated with translational symmetry breaking. We can see that the studies on the complicated phase transitions related to reducible representations, such as phase transitions in perovskite KMnF3 multiferroics crystal and high temperature superconductor La2/3Mg1/2W1/2O3 (La4Mg3W3O18) compound, are much simplified by the new conception, and the theory of the wave vector substar group and its representation becomes a powerful mathematical tool being able to promote actively the study of various symmetry breaking phenomena of solid state crystals .