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advanced_notions:symmetry_breaking [2019/01/18 00:13]
68.112.101.198 Typos only.
advanced_notions:symmetry_breaking [2019/01/18 00:15] (current)
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 <tabbox History> ​ <tabbox History> ​
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-Nambu appears to have been the first to recognize that gauge invariance does hold true in the BCS Theory but has become hidden. He had identified a profound truth: When the temperature gets cold enough, the fundamental patterns of electromagnetism—gauge invariance—may be hid-den, as a result of which strange things happen, such as the appearance of the boson-like Cooper Pairs. .... In a superconductor,​ the ground state contains Cooper Pairs. It costs energy to break up any pair, liberating individual electrons. Once liberated,​the electrons have higher energy, the difference from their original bonding in pairs being called the “energy gap.” The freed electrons receive this energy, which via E=mc2 makes them appear to have gained mass. This gave Nambu an idea: If the universe itself was like a superconductor,​ could the masses of particles arise by some analogous mechanism? ... The way that Nambu investigated this possibility was to suppose that the mass of a proton or neutron is fundamentally zero and that they ac-quire their masses through the spontaneous violation of some symmetry.To implement this he focused on “chiral symmetry.” Chiral comes fromthe Greek for “hand,” and chirality is a word that refers to the distinction between left- and right-handedness. This is how chiral symmetry relatesto mass.+Nambu appears to have been the first to recognize that gauge invariance does hold true in the BCS Theory but has become hidden. He had identified a profound truth: When the temperature gets cold enough, the fundamental patterns of electromagnetism—gauge invariance—may be hidden, as a result of which strange things happen, such as the appearance of the boson-like Cooper Pairs. .... In a superconductor,​ the ground state contains Cooper Pairs. It costs energy to break up any pair, liberating individual electrons. Once liberated,​the electrons have higher energy, the difference from their original bonding in pairs being called the “energy gap.” The freed electrons receive this energy, which via E=mc2 makes them appear to have gained mass. This gave Nambu an idea: If the universe itself was like a superconductor,​ could the masses of particles arise by some analogous mechanism? ... The way that Nambu investigated this possibility was to suppose that the mass of a proton or neutron is fundamentally zero and that they ac-quire their masses through the spontaneous violation of some symmetry.To implement this he focused on “chiral symmetry.” Chiral comes fromthe Greek for “hand,” and chirality is a word that refers to the distinction between left- and right-handedness. This is how chiral symmetry relatesto mass.
  
-A proton can spin clockwise or anticlockwise,​ which we may think ofas right- or left-handed,​ like the two possibilities for a corkscrew. Now imagine how that spin appears as you catch up and then overtake it. If it was clockwise as you approached, it will appear to be spinning backward or anticlockwise when you look back after having passed: Its chirality will change. This is fine for a massive proton, but for a massless particle, there is a profound difference. Any massless particle always travels at the speed of light, which is nature’s speed limit. Nothing can move faster than this,so if you see a massless particle spinning left- or right-handed,​ you cannotovertake ​it and look back: Its chirality stays fixed.+A proton can spin clockwise or anticlockwise,​ which we may think ofas right- or left-handed,​ like the two possibilities for a corkscrew. Now imagine how that spin appears as you catch up and then overtake it. If it was clockwise as you approached, it will appear to be spinning backward or anticlockwise when you look back after having passed: Its chirality will change. This is fine for a massive proton, but for a massless particle, there is a profound difference. Any massless particle always travels at the speed of light, which is nature’s speed limit. Nothing can move faster than this,so if you see a massless particle spinning left- or right-handed,​ you cannot overtake ​it and look back: Its chirality stays fixed.
  
 The fundamental rule is that chirality can be conserved for massless particles but not massive ones.are chirally symmetric, and then he investigated what happens if this symmetry is spontaneously broken. The fundamental rule is that chirality can be conserved for massless particles but not massive ones.are chirally symmetric, and then he investigated what happens if this symmetry is spontaneously broken.
advanced_notions/symmetry_breaking.txt · Last modified: 2019/01/18 00:15 by 68.112.101.198