Fermions, Bosons and their Statistics Peter Hertel Fundamental Fermions, Bosons and their Statistics particles Spin and statistics Many particles Peter Hertel Gibbs state Fermions University of Osnabr¨uck,Germany Zero temperature Lecture presented at APS, Nankai University, China White dwarfs and neutron stars http://www.home.uni-osnabrueck.de/phertel Bosons Black body radiation March/April 2011 Bose-Einstein condensation • proton p=(uud) and neutron n=(udd) • both have spin 1/2 • excited states ∆++=(uuu)∗, ∆+=(uud)∗ etc. • they have spin 3/2 • p is stable, n ! p+e−+¯ν is allowed Fermions, Bosons and their Statistics Structure fermions Peter Hertel Fundamental particles charge -1 -2/3 -1/3 0 +1/3 +2/3 +1 Spin and − + statistics generation 1 e u¯ d νe ; ν¯e d¯ u e Many particles − + generation 2 µ c¯ s νµ; ν¯µ ¯s c µ Gibbs state − ¯ + Fermions generation 3 τ ¯t b ντ ; ν¯τ b t τ Zero temperature White dwarfs • all structure particles have spin 1/2 and neutron stars Bosons Black body radiation Bose-Einstein condensation • both have spin 1/2 • excited states ∆++=(uuu)∗, ∆+=(uud)∗ etc. • they have spin 3/2 • p is stable, n ! p+e−+¯ν is allowed Fermions, Bosons and their Statistics Structure fermions Peter Hertel Fundamental particles charge -1 -2/3 -1/3 0 +1/3 +2/3 +1 Spin and − + statistics generation 1 e u¯ d νe ; ν¯e d¯ u e Many particles − + generation 2 µ c¯ s νµ; ν¯µ ¯s c µ Gibbs state − ¯ + Fermions generation 3 τ ¯t b ντ ; ν¯τ b t τ Zero temperature White dwarfs • all structure particles have spin 1/2 and neutron stars • proton p=(uud) and neutron n=(udd) Bosons Black body radiation Bose-Einstein condensation • excited states ∆++=(uuu)∗, ∆+=(uud)∗ etc. • they have spin 3/2 • p is stable, n ! p+e−+¯ν is allowed Fermions, Bosons and their Statistics Structure fermions Peter Hertel Fundamental particles charge -1 -2/3 -1/3 0 +1/3 +2/3 +1 Spin and − + statistics generation 1 e u¯ d νe ; ν¯e d¯ u e Many particles − + generation 2 µ c¯ s νµ; ν¯µ ¯s c µ Gibbs state − ¯ + Fermions generation 3 τ ¯t b ντ ; ν¯τ b t τ Zero temperature White dwarfs • all structure particles have spin 1/2 and neutron stars • proton p=(uud) and neutron n=(udd) Bosons • both have spin 1/2 Black body radiation Bose-Einstein condensation • they have spin 3/2 • p is stable, n ! p+e−+¯ν is allowed Fermions, Bosons and their Statistics Structure fermions Peter Hertel Fundamental particles charge -1 -2/3 -1/3 0 +1/3 +2/3 +1 Spin and − + statistics generation 1 e u¯ d νe ; ν¯e d¯ u e Many particles − + generation 2 µ c¯ s νµ; ν¯µ ¯s c µ Gibbs state − ¯ + Fermions generation 3 τ ¯t b ντ ; ν¯τ b t τ Zero temperature White dwarfs • all structure particles have spin 1/2 and neutron stars • proton p=(uud) and neutron n=(udd) Bosons • both have spin 1/2 Black body radiation • excited states ∆++=(uuu)∗, ∆+=(uud)∗ etc. Bose-Einstein condensation • p is stable, n ! p+e−+¯ν is allowed Fermions, Bosons and their Statistics Structure fermions Peter Hertel Fundamental particles charge -1 -2/3 -1/3 0 +1/3 +2/3 +1 Spin and − + statistics generation 1 e u¯ d νe ; ν¯e d¯ u e Many particles − + generation 2 µ c¯ s νµ; ν¯µ ¯s c µ Gibbs state − ¯ + Fermions generation 3 τ ¯t b ντ ; ν¯τ b t τ Zero temperature White dwarfs • all structure particles have spin 1/2 and neutron stars • proton p=(uud) and neutron n=(udd) Bosons • both have spin 1/2 Black body radiation • excited states ∆++=(uuu)∗, ∆+=(uud)∗ etc. Bose-Einstein condensation • they have spin 3/2 Fermions, Bosons and their Statistics Structure fermions Peter Hertel Fundamental particles charge -1 -2/3 -1/3 0 +1/3 +2/3 +1 Spin and − + statistics generation 1 e u¯ d νe ; ν¯e d¯ u e Many particles − + generation 2 µ c¯ s νµ; ν¯µ ¯s c µ Gibbs state − ¯ + Fermions generation 3 τ ¯t b ντ ; ν¯τ b t τ Zero temperature White dwarfs • all structure particles have spin 1/2 and neutron stars • proton p=(uud) and neutron n=(udd) Bosons • both have spin 1/2 Black body radiation • excited states ∆++=(uuu)∗, ∆+=(uud)∗ etc. Bose-Einstein condensation • they have spin 3/2 • p is stable, n ! p+e−+¯ν is allowed • the photon couples to charged particles only • there are also gluons which mediate strong interactions − − • e.g. n=(udd) ! (uud)+W ! p+¯νe +e • is there also a graviton G ? • is there also a Higgs boson H ? Fermions, Bosons and their Statistics Exchange bosons Peter Hertel Fundamental particles − − − − W ν¯e e ν¯µµ ν¯τ τ ud¯ cs¯ ¯tb Spin and statistics 0 + − + − + − γ; Z e e µ µ τ τ (¯νe νe ν¯µνµ ν¯τ ντ ) dd¯ uu¯ ¯ss cc¯ bb¯ ¯tt Many particles + + + + ¯ ¯ Gibbs state W e νe µ νµ τ ντ du ¯sc bt Fermions Zero + 0 − temperature • W , γ,Z ,W mediate electro-weak interaction White dwarfs and neutron stars Bosons Black body radiation Bose-Einstein condensation • there are also gluons which mediate strong interactions − − • e.g. n=(udd) ! (uud)+W ! p+¯νe +e • is there also a graviton G ? • is there also a Higgs boson H ? Fermions, Bosons and their Statistics Exchange bosons Peter Hertel Fundamental particles − − − − W ν¯e e ν¯µµ ν¯τ τ ud¯ cs¯ ¯tb Spin and statistics 0 + − + − + − γ; Z e e µ µ τ τ (¯νe νe ν¯µνµ ν¯τ ντ ) dd¯ uu¯ ¯ss cc¯ bb¯ ¯tt Many particles + + + + ¯ ¯ Gibbs state W e νe µ νµ τ ντ du ¯sc bt Fermions Zero + 0 − temperature • W , γ,Z ,W mediate electro-weak interaction White dwarfs and neutron • the photon couples to charged particles only stars Bosons Black body radiation Bose-Einstein condensation − − • e.g. n=(udd) ! (uud)+W ! p+¯νe +e • is there also a graviton G ? • is there also a Higgs boson H ? Fermions, Bosons and their Statistics Exchange bosons Peter Hertel Fundamental particles − − − − W ν¯e e ν¯µµ ν¯τ τ ud¯ cs¯ ¯tb Spin and statistics 0 + − + − + − γ; Z e e µ µ τ τ (¯νe νe ν¯µνµ ν¯τ ντ ) dd¯ uu¯ ¯ss cc¯ bb¯ ¯tt Many particles + + + + ¯ ¯ Gibbs state W e νe µ νµ τ ντ du ¯sc bt Fermions Zero + 0 − temperature • W , γ,Z ,W mediate electro-weak interaction White dwarfs and neutron • the photon couples to charged particles only stars • there are also gluons which mediate strong interactions Bosons Black body radiation Bose-Einstein condensation • is there also a graviton G ? • is there also a Higgs boson H ? Fermions, Bosons and their Statistics Exchange bosons Peter Hertel Fundamental particles − − − − W ν¯e e ν¯µµ ν¯τ τ ud¯ cs¯ ¯tb Spin and statistics 0 + − + − + − γ; Z e e µ µ τ τ (¯νe νe ν¯µνµ ν¯τ ντ ) dd¯ uu¯ ¯ss cc¯ bb¯ ¯tt Many particles + + + + ¯ ¯ Gibbs state W e νe µ νµ τ ντ du ¯sc bt Fermions Zero + 0 − temperature • W , γ,Z ,W mediate electro-weak interaction White dwarfs and neutron • the photon couples to charged particles only stars • there are also gluons which mediate strong interactions Bosons − − Black body • e.g. n=(udd) ! (uud)+W ! p+¯νe +e radiation Bose-Einstein condensation • is there also a Higgs boson H ? Fermions, Bosons and their Statistics Exchange bosons Peter Hertel Fundamental particles − − − − W ν¯e e ν¯µµ ν¯τ τ ud¯ cs¯ ¯tb Spin and statistics 0 + − + − + − γ; Z e e µ µ τ τ (¯νe νe ν¯µνµ ν¯τ ντ ) dd¯ uu¯ ¯ss cc¯ bb¯ ¯tt Many particles + + + + ¯ ¯ Gibbs state W e νe µ νµ τ ντ du ¯sc bt Fermions Zero + 0 − temperature • W , γ,Z ,W mediate electro-weak interaction White dwarfs and neutron • the photon couples to charged particles only stars • there are also gluons which mediate strong interactions Bosons − − Black body • e.g. n=(udd) ! (uud)+W ! p+¯νe +e radiation • is there also a graviton G ? Bose-Einstein condensation Fermions, Bosons and their Statistics Exchange bosons Peter Hertel Fundamental particles − − − − W ν¯e e ν¯µµ ν¯τ τ ud¯ cs¯ ¯tb Spin and statistics 0 + − + − + − γ; Z e e µ µ τ τ (¯νe νe ν¯µνµ ν¯τ ντ ) dd¯ uu¯ ¯ss cc¯ bb¯ ¯tt Many particles + + + + ¯ ¯ Gibbs state W e νe µ νµ τ ντ du ¯sc bt Fermions Zero + 0 − temperature • W , γ,Z ,W mediate electro-weak interaction White dwarfs and neutron • the photon couples to charged particles only stars • there are also gluons which mediate strong interactions Bosons − − Black body • e.g. n=(udd) ! (uud)+W ! p+¯νe +e radiation • is there also a graviton G ? Bose-Einstein condensation • is there also a Higgs boson H ? Fermions, Bosons and their Statistics Peter Hertel Fundamental particles Spin and statistics Many particles Gibbs state Fermions Zero temperature White dwarfs and neutron stars Bosons Black body radiation Bose-Einstein condensation The Aleph detector (opened) at Cern • or helicity 1/2 and -1/2 • massless structure fermions (neutrinos) have either helicity 1/2 or -1/2 • • this explains parity violation • spin and statistics are related Fermions, Bosons and their Statistics Spin 1/2 fermions Peter Hertel Fundamental particles • massive structure fermion (quarks, electrons) have spin Spin and 1/2 statistics Many particles Gibbs state Fermions Zero temperature White dwarfs and neutron stars Bosons Black body radiation Bose-Einstein condensation • massless structure fermions (neutrinos) have either helicity 1/2 or -1/2 • • this explains parity violation • spin and statistics are related Fermions, Bosons and their Statistics Spin 1/2 fermions Peter Hertel Fundamental particles • massive structure fermion (quarks, electrons) have spin Spin and 1/2 statistics Many particles • or helicity 1/2 and -1/2 Gibbs state Fermions Zero temperature White dwarfs and neutron stars Bosons Black body radiation Bose-Einstein condensation • • this explains parity violation • spin and statistics are related Fermions, Bosons and their Statistics Spin 1/2 fermions Peter Hertel Fundamental particles • massive structure fermion (quarks, electrons) have spin Spin and 1/2 statistics Many particles • or helicity 1/2 and -1/2 Gibbs state • massless