Symmetry breaking Department of Physics, Chungnam National University, Daejeon , Republic of Korea Taegeun Song

Symmetry What ? How ? When?

Physicists look for various types of symmetry in models that seek to explain the workings of the universe. Critical behavior (Phase transition) – spontaneous polarization ; brand new something, and interesting The symmetric physical quantity make a law mathematically simple or lead us to intuitive world. Let me allow to point out some more about ‘Symmetry’ Symmetric state has low energy relatively compare to anti-symmetric state in quantum mechanics Time reversal symmetry (TRS), Mirror symmetry (Parity), Translation symmetry, Charge symmetry etc. Broken symmetry In solid state physics, ^-^;; Ferroelectrics Wigner crystal

Winning Nobel prize in 2008 물리계 ( 혹은 라그랑지안 ) 는 큰 대칭성 에 대해 불변이나, 진공은 그 부분적인 대칭성 에 대해서만 불변인 경우 우리는 대칭성이 자발적으로 붕괴되었다고 한다. 출처 :2008 노벨 물리학상의 물리학 1 편 : 대칭성의 자발적 붕괴2008 노벨 물리학상의 물리학 1 편 : 대칭성의 자발적 붕괴

이론적으론 대칭적이지만 이론의 여러 해들 중 선택된 현실은 비 대칭적인 경우 그냥 제 생각일 뿐입니다.

J. Goldstone 1961 ‘Goldstone conjecture’ " 라그랑지안이 대칭군 G 에 대해 불변이고, 진공은 그 부분군인 H 에 대해 불변인 경우 D(G/H) 개의 스핀이 0 이고, 질량이 0 인 입자가 존재한다 " 남부 - 골드스톤 입자 혹은 남부 - 골드스톤 보존 대칭성의 자발적 붕괴와 동반해서 질량이 없는 스칼라 입자의 존재 가 반드시 수반된다는 이 가설의 질량이 없는 스칼라입자 1 년뒤에 골드스톤 - 살람 - 와인버그에 의해 3 가지 다른 방식으로 증명 - 오늘날 골드스톤 정리 (Goldstone Theorem) 스칼라 입자가 보즈 통계를 따름

Degenerate vacuum ! Consider two direction – radial direction and rotational direction - Wiki Mathematical example: the Mexican hat potential

CP violation – Winning Nobel prize in 1980 C – charge conjugation symmetry P – parity symmetry The strong interaction and electromagnetic interaction seem to be invariant under the combined CP transformation operation, but this symmetry is slightly violated during certain types of weak decay It plays an important role both in the attempts of cosmology to explain the dominance of matter over antimatter in the present Universe, and in the study of weak interaction in particle physics. - Wiki

Without spontaneous symmetry breaking, the Standard Model of elementary particle interactions predicts the existence of a number of particles. However, some particles (the W and Z bosons) would then be predicted to be massless, when, in reality, they are observed to have mass. (This would appear to be a major failing of the theory.) To overcome this, the combination of spontaneous symmetry breaking in conjunction with the Higgs mechanism gives these particles mass. It also suggests the presence of a new, as yet undetected particle, the Higgs boson. If the Higgs boson is not found, it will mean that the simplest implementation of the Higgs mechanism and spontaneous symmetry breaking as they are currently formulated are invalid, requiring an alternative model implementation of SSB and the Higgs mechanism operative in the accepted theory of Electroweak Interactions. - Wiki Importance of the spontaneous symmetry breaking within the standard model