17.1 Fermions and bosons

Particles in quantum mechanics are classified as fermions or bosons based on their spin and behavior. Fermions, like electrons, follow the Pauli exclusion principle, while bosons, such as photons, can occupy the same quantum state.

Understanding particle classification is crucial for grasping the structure of matter and fundamental forces. Fermions make up ordinary matter, while bosons act as force carriers, mediating interactions between particles and shaping the universe's behavior.

Particle Classification and Behavior

Fermions vs bosons

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• Fermions have half-integer spin (1/2, 3/2) follow Fermi-Dirac statistics obey the Pauli exclusion principle
• Bosons have integer spin (0, 1, 2) follow Bose-Einstein statistics can occupy the same quantum state

Pauli exclusion principle

• No two identical fermions can occupy the same quantum state simultaneously
• Each quantum state can be occupied by at most one fermion
  • Fermions must have different sets of quantum numbers (spin, orbital angular momentum)
• Leads to the structure of the periodic table and the stability of matter

Wave function symmetry

• Fermion wave functions are antisymmetric under the exchange of any two identical particles
  • Change sign when two identical fermions are exchanged: $\Psi(x_1, x_2) = -\Psi(x_2, x_1)$
• Boson wave functions are symmetric under the exchange of any two identical particles
  • Remain unchanged when two identical bosons are exchanged: $\Psi(x_1, x_2) = \Psi(x_2, x_1)$

Examples of particle classifications

• Fermions
  • Electrons, protons, neutrons fundamental building blocks of matter
  • Quarks fundamental particles that make up hadrons (protons, neutrons)
  • Neutrinos nearly massless particles that rarely interact with matter
• Bosons
  • Photons quanta of light electromagnetic force carriers
  • Gluons strong nuclear force carriers bind quarks together
  • W and Z bosons weak nuclear force carriers responsible for radioactive decay
  • Higgs boson gives particles their mass through interactions with the Higgs field
  • Mesons particles composed of an even number of quarks (pions, kaons)