Spin system and Pauli exclusion principle

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

• Dirac equation

related items

• The Story of Spin by Tomonaga

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