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

수학노트
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==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</h5>
 
  
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==evolution of Pauli exclusion principle==
 
* originated from atomic spectroscopy
 
* originated from atomic spectroscopy
 
* Dirac-antisymmetrizing the wave function for an assembly of indistinguishable particles
 
* Dirac-antisymmetrizing the wave function for an assembly of indistinguishable particles
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* anti-commutation relations for particle creation and annihilation operators in quantum field theory
 
* anti-commutation relations for particle creation and annihilation operators in quantum field theory
  
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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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*  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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==representation theory==
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* concept from the representation of  <math>SU(2)</math>
 +
* half of highest weight is called the spin of the module
 +
** 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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==spin particle statstics</h5>
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* Bosons<br>
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==spin particle statstics==
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* Bosons
 
** photon
 
** photon
 
** vector boson
 
** vector boson
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** 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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** matter particles<br>
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** matter particles
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==Dirac wave equation==
  
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<h5 style="line-height: 2em; margin: 0px;">Dirac wave equation[[search?q=dirac&parent id=6452627|search?q=dirac&parent id=6452627]]</h5>
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* [[Dirac equation]]
  
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* [[Dirac equation]]<br>
 
  
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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 style="margin: 0px; line-height: 2em;">articles</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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* W. Pauli, [http://prola.aps.org/abstract/PR/v58/i8/p716_1 The Connection Between Spin and Statistics] Phys. Rev. 58, 716 - 722 (1940)
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==메타데이터==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q131594 Q131594]
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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) 02:24 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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