Spin system and Pauli exclusion principle

introduction

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

 

 

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

• Dirac equation
  

 

 

 

articles

• W. Pauli, The Connection Between Spin and Statistics Phys. Rev. 58, 716 - 722 (1940)