"Spin system and Pauli exclusion principle"의 두 판 사이의 차이

수학노트
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<h5>introduction</h5>
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==introduction==
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* {{수학노트|url=스핀과_파울리의_배타원리}}
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* the simplest example of quantum mechanical system
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* quantization of the angular momentum
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* measures as being some multiple of Planck's constant divided by <math>2\pi</math>
  
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*  the simplest example of quantum mechanical system<br>
 
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*  quantization of the angular momentum<br>
 
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*  measures as being some multiple of Planck's constant divided by 2pi<br>
 
  
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==evolution of Pauli exclusion principle==
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* originated from atomic spectroscopy
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* Dirac-antisymmetrizing the wave function for an assembly of indistinguishable particles
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* Pauli's spin matrices
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* anti-commutation relations for particle creation and annihilation operators in quantum field theory
  
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<h5>angular momentum</h5>
 
  
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==representation theory==
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* concept from the representation of  <math>SU(2)</math>
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* half of highest weight is called the spin of the module
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** Casimir operator can also detect this number.
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* spin <math>1/2</math> is the most important case since they are the matter particles
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* this is why we have half-integral spin although those representation are integral highest weight representations.
  
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<h5 style="margin: 0px; line-height: 2em;">representation theory</h5>
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*  concept from the representation of  <math>SU(2)</math><br>
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==spin particle statstics==
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* Bosons
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*  half of highest weight is called the spin of the module<br>
 
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**  Casimir operator can also detect this number.<br>
 
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*  spin <math>1/2</math> is the most important case since they are the matter particles<br>
 
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*  this is why we have half-integral spin although those representation are integral highest weight representations.<br>
 
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<h5>operator formulation</h5>
 
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*  파울리 행렬 ([http://pythagoras0.springnote.com/pages/3063330 해밀턴의 사원수] 참조)<br><math>\sigma_1 = \sigma_x = \begin{pmatrix} 0&1\\ 1&0 \end{pmatrix} </math><br><math>\sigma_2 = \sigma_y = \begin{pmatrix} 0&-i\\ i&0 \end{pmatrix}  </math><br><math>\sigma_3 = \sigma_z = \begin{pmatrix} 1&0\\ 0&-1 \end{pmatrix}</math><br>
 
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*  raising and lowering 연산자<br><math>\sigma_{\pm}=\frac{1}{2}(\sigma_{x}\pm i\sigma_{y})</math><br><math>\sigma_{+}=\frac{1}{2}(\sigma_{x}+ i\sigma_{y})=\begin{pmatrix} 0&1\\ 0&0 \end{pmatrix}</math><br><math>\sigma_{-}=\frac{1}{2}(\sigma_{x}- i\sigma_{y})=\begin{pmatrix} 0&0\\ 1&0 \end{pmatrix}</math><br><math>[\sigma_{z},\sigma_{\pm}]=\pm 2\sigma_{\pm}</math><br>
 
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<h5 style="line-height: 2em; margin: 0px;">sl(2)</h5>
 
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*  commutator<br><math>[E,F]=H</math><br><math>[H,E]=2E</math><br><math>[H,F]=-2F</math><br>
 
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<h5>spin particle statstics</h5>
 
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* Bosons<br>
 
 
** photon
 
** photon
 
** vector boson
 
** vector boson
53번째 줄: 32번째 줄:
 
** follows Bose-Einstein statistics
 
** follows Bose-Einstein statistics
 
** force-transmitting particles
 
** force-transmitting particles
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* Fermions = spin- <math>1/2</math> particles<br>
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* Fermions = spin- <math>1/2</math> particles
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** quarks and leptons<br>
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** quarks and leptons
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** follows Fermi-Dirac statistics<br>
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** follows Fermi-Dirac statistics
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**  <br> matter particles<br>
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** matter particles
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<h5>history</h5>
 
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* http://www.google.com/search?hl=en&tbs=tl:1&q=
 
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<h5>related items</h5>
 
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<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">encyclopedia</h5>
 
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* http://en.wikipedia.org/wiki/
 
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* http://www.scholarpedia.org/
 
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* http://www.proofwiki.org/wiki/
 
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* Princeton companion to mathematics([[2910610/attachments/2250873|Companion_to_Mathematics.pdf]])
 
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<h5>books</h5>
 
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* [[2010년 books and articles]]<br>
 
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* http://gigapedia.info/1/
 
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* http://gigapedia.info/1/
 
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* http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
 
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<h5>expositions</h5>
 
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<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">articles</h5>
 
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* http://www.ams.org/mathscinet
 
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* http://www.zentralblatt-math.org/zmath/en/
 
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* http://arxiv.org/
 
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* http://www.pdf-search.org/
 
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* http://pythagoras0.springnote.com/
 
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* [http://math.berkeley.edu/%7Ereb/papers/index.html http://math.berkeley.edu/~reb/papers/index.html]
 
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* http://dx.doi.org/
 
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<h5>question and answers(Math Overflow)</h5>
 
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* http://mathoverflow.net/search?q=
 
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* http://mathoverflow.net/search?q=
 
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<h5>blogs</h5>
 
  
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*  구글 블로그 검색<br>
 
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**  http://blogsearch.google.com/blogsearch?q=<br>
 
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** http://blogsearch.google.com/blogsearch?q=
 
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* http://ncatlab.org/nlab/show/HomePage
 
  
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==Dirac wave equation==
  
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* [[Dirac equation]]
  
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<h5>experts on the field</h5>
 
  
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* http://arxiv.org/
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==related items==
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* [[The Story of Spin by Tomonaga]]
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[[분류:개인노트]]
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[[분류:physics]]
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[[분류:math and physics]]
  
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== articles ==
  
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<h5>links</h5>
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* Enrico Santamato, Francesco De Martini, Weyl-gauge invariant proof of the Spin-Statistics Theorem, arXiv:1604.06253 [quant-ph], April 21 2016, http://arxiv.org/abs/1604.06253
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[[분류:migrate]]
  
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* [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier]
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==메타데이터==
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* [http://pythagoras0.springnote.com/pages/1947378 수식표현 안내]
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===위키데이터===
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* [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences]
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* ID :  [https://www.wikidata.org/wiki/Q131594 Q131594]
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* http://functions.wolfram.com/
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===Spacy 패턴 목록===
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* [{'LOWER': 'pauli'}, {'LOWER': 'exclusion'}, {'LEMMA': 'principle'}]
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* [{'LOWER': 'exclusion'}, {'LOWER': 'principle'}, {'OP': '*'}, {'LOWER': 'physics'}, {'LEMMA': ')'}]
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* [{'LOWER': 'principle'}, {'LOWER': 'of'}, {'LOWER': 'exclusion'}, {'OP': '*'}, {'LOWER': 'quantum'}, {'LOWER': 'mechanics'}, {'LEMMA': ')'}]
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* [{'LOWER': 'exclusion'}, {'LOWER': 'principle'}, {'OP': '*'}, {'LOWER': 'fermi'}, {'OP': '*'}, {'LOWER': 'dirac'}, {'LOWER': 'statistics'}, {'LEMMA': ')'}]

2021년 2월 17일 (수) 01:24 기준 최신판

introduction

  • 틀:수학노트
  • the simplest example of quantum mechanical system
  • quantization of the angular momentum
  • measures as being some multiple of Planck's constant divided by \(2\pi\)


evolution of Pauli exclusion principle

  • originated from atomic spectroscopy
  • Dirac-antisymmetrizing the wave function for an assembly of indistinguishable particles
  • Pauli's spin matrices
  • anti-commutation relations for particle creation and annihilation operators in quantum field theory


representation theory

  • concept from the representation of \(SU(2)\)
  • half of highest weight is called the spin of the module
    • Casimir operator can also detect this number.
  • spin \(1/2\) is the most important case since they are the matter particles
  • this is why we have half-integral spin although those representation are integral highest weight representations.



spin particle statstics

  • Bosons
    • photon
    • vector boson
    • Gluon
    • follows Bose-Einstein statistics
    • force-transmitting particles
  • Fermions = spin- \(1/2\) particles
    • quarks and leptons
    • follows Fermi-Dirac statistics
    • matter particles


Dirac wave equation


related items

articles

  • Enrico Santamato, Francesco De Martini, Weyl-gauge invariant proof of the Spin-Statistics Theorem, arXiv:1604.06253 [quant-ph], April 21 2016, http://arxiv.org/abs/1604.06253

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'pauli'}, {'LOWER': 'exclusion'}, {'LEMMA': 'principle'}]
  • [{'LOWER': 'exclusion'}, {'LOWER': 'principle'}, {'OP': '*'}, {'LOWER': 'physics'}, {'LEMMA': ')'}]
  • [{'LOWER': 'principle'}, {'LOWER': 'of'}, {'LOWER': 'exclusion'}, {'OP': '*'}, {'LOWER': 'quantum'}, {'LOWER': 'mechanics'}, {'LEMMA': ')'}]
  • [{'LOWER': 'exclusion'}, {'LOWER': 'principle'}, {'OP': '*'}, {'LOWER': 'fermi'}, {'OP': '*'}, {'LOWER': 'dirac'}, {'LOWER': 'statistics'}, {'LEMMA': ')'}]
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