Spontaneous Symmetry Breaking and Analogies to the Higgs-Mechanism Superconductivity and Ferromagnetism Spontaneous Symmetry Breaking and Analogies to the Higgs-Mechanism Robin Zech

Outline Review: Spontaneous Symmetry Breaking Ferromagnetism Superconductivity The BEH-Field as a Cosmic Superconductor Robin Zech

Spontaneous Symmetry Breaking breaking parameter (e.g. temperature) Robin Zech

Spontaneous Symmetry Breaking Symmetric physical laws but nonzero ground state (expectation value) “Breaking” with respect to a certain symmetry group Excitations around minimum  (gauge) particles Robin Zech

Spontaneous Symmetry Breaking Higgs-Mechanism Ferromagnetism Superconductivity Superfluidity Origin of hadron masses Robin Zech

Ferromagnetism Electrons have an angular momentum (spin)  microscopic magnetic field Over Curie temperature: no macroscopic magnetization can build up Lowering temperature  spontaneous aligning of microscopic dipoles creates macroscopic dipole field  broken rotational invariance Robin Zech

Ferromagnetism http://www.tulane.edu/~sanelson/images/curiet.gif Robin Zech

Superconductivity Electrical resistance exactly zero under critical temperature BCS theory (1972) Cooper pairs of electrons, which all have the same phase  Bose-Einstein-Condensate Breaking of U(1) phase symmetry (before: changing the phase via photon exchange of two electrons) http://www.slac.stanford.edu/pubs/beamline/26/1/26-1-dixon.pdf Robin Zech

Superconductivity Meissner effect: Virtual photon mass Superconductor is ideal diamagnetic  no electromagnetic fields Characteristic penetration depth (≈10…100 nm) Virtual photon mass Second length scale: coherence length https://upload.wikimedia.org/wikipedia/commons/2/22/EXPULSION.png Robin Zech

Superconductivity External magnetic field … Type I: breakdown of superconductivity at critical value Type II: formation of magnetic vortices Robin Zech

The BEH-Field as a Cosmic Superconductor Superconductivity BEH Field ‘Sea’ of electric charges (Bose-Einstein-Condensate) ‘Sea’ of weak charges Breaking of U(1) phase symmetry Breaking of SU(2) symmetry Condensation at ≈ 1…200K ≈ 1015 K Cancellation of electromagnetic fields or photons Cancellation of weak force or W/Z-Bosons Penetration depth (≈100 nm) Range of weak force (10-18 m) Coherence Length (≈100 nm) Mass of the Higgs Boson Robin Zech

The BEH-Field as a Cosmic Superconductor  Superconductivity for electromagnetic charge is analogue to Higgs mechanism for weak charge! BEH field 10 billion times more effective than superconductivity! Robin Zech

The BEH-Field as a Cosmic Superconductor Question: BEH-Field = elementary field? Superconductivity: ‘bosons made of fermions’  technicolor theory Robin Zech

Sources Coughlan, Dodd and Gripaios, 2006, “The Ideas of particle Physics, An Introduction for Scientists, Third Edition” Thomson, 2013, “Modern Particle Physics” Dixon, 1996, http://www.slac.stanford.edu/pubs/beamline/26/1/26-1-dixon.pdf Kobel, 2013, http://iktp.tu-dresden.de/IKTP/pub/13/higgs_cosmology-zeuthen.pdf Robin Zech