The Legend of Spinor
Fermions like protons,electrons,and quarks comprise(構成) all the ordinary matter in universe.
They do not obey the behavior typical of scalar,vector and tensor,but that of spinors.
So,what is a spinor?
It's essentially a two-component,vector-like quantity with special transformation property,in which rotations and Lorentz boosts are built into the overall formalism.
Spinors were originally introduced by Elie Cartan in 1913，and subsequently greatly expanded upon by Hermann Weyl，Richard Brauer and Oswald Veblen。
Spinors were found to be absolutely indispensible(不可或缺的)in describing the behavior of fermions:electrons,protons,neutrons and the like.
No one fully understands spinors. Their algebra is formally understood,but their geometrical signuficance is mysterious.
In some sense they describe the "square root" of geometry and,just as uderstanding the concept of sqr(-1) took centuries,
the same might be true of spinors.----Sir Michael Atiyah
The simplest approach to explain spinors is Lorentz group theory.Lorentz transformations of rotations and boosts.
William O. Straub :A Child's Guide to Spinors
這裡有些有趣的東西 例如 Differential Forms for Physics Students
The
notion of electron spin was first surmised(推測) in 1922 by Stern and Gerlach,
and confirmed by Uhlenbeck and Goudsmit three years latter.
Otto Stern 1888-1969
Walther Gerlach 1889-1979
George Uhlenbeck 1900-1988 Samus Goudsmit 1902-1978
薛丁格 狄拉克 Dirac relativistic electron equation :
1927年 年僅25歲的狄拉克意識到 質量極小的電子極易加速到接近光速,而對於這種高速電子的完整描述
應該考慮將相對論方程式與量子力學方程式相結合.
他把狹義相對論引進薛丁格方程式 創立了相對論性質的波動方程式---狄拉克方程式 p.164
於是,真空不是一無所有,而是像負能量電子組成的汪洋大海...
1931年 狄拉克提出正電子的概念 ,1932年 Carl David Anderson發現[反物質](1936年 諾貝爾獎)
粒子的自旋與特點 p.182
Anthony Zee(徐一鴻) [Quantum field theory in a nutshell]
二十世紀物理最重要的計算，指的是什麼？
[表現(representation) 隨處可見] 席南華教授
把一個對象的代數結構再現於一個由線性變換或矩陣構成的具體對象上
費米 (Enrico
Fermi
1901-1954)
玻色 (Satyendra Nath Bose 1894-1974)
所有粒子都能以自旋分類為費米子與玻色子
玻色-愛因斯坦凝態(condensed state)
An Introduction Theory of Spinors Moshe
Carmeli 1933-2007 [The First
Six Days of The Universe] [ResearchGate]
Shimon Malin 1937-2017 [ResearchGate]