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Lattice Gauge Theory for the Quark-Gluon Plasma

Lattice Gauge Theory for the Quark-Gluon Plasma. Sourendu Gupta TIFR. Particles in the Standard Model (1990s). The Eightfold Way (variables). The Eightfold Way (variables). The Eightfold Way (variables). The Eightfold Way (variables). The basics of extreme matter.

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Lattice Gauge Theory for the Quark-Gluon Plasma

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  1. Lattice Gauge Theory for the Quark-Gluon Plasma Sourendu Gupta TIFR

  2. Particles in the Standard Model (1990s) Tuesday Talk: S. Gupta

  3. The Eightfold Way (variables) Tuesday Talk: S. Gupta

  4. The Eightfold Way (variables) Tuesday Talk: S. Gupta

  5. The Eightfold Way (variables) Tuesday Talk: S. Gupta

  6. The Eightfold Way (variables) Tuesday Talk: S. Gupta

  7. The basics of extreme matter • Normal matter made of baryons • Baryons contain 3 quarks and interact by exchanging mesons • Mesons contain 2 quarks • When you squeeze this matter by applying pressure (or heating it up) you get matter with large numbers of quarks • This is the quark gluon plasma Tuesday Talk: S. Gupta

  8. Quark matter factories • Create an universe through a big bang and let it cool • Create a supernova and let its core collapse into a really compressed star • Bang some (relatively) large chunks of matter together very hard • Think hard … you may get a patent Tuesday Talk: S. Gupta

  9. The RHIC at Brookhaven Tuesday Talk: S. Gupta

  10. Normal matter needs QED or its effective theories There are many phases of normal matter Normal matter may be neutral or a plasma Normal matter may be a solid, liquid or a gas Quark matter needs QCD or its effective theories There are many phases of quark matter Quark matter may be neutral or a plasma Quark matter is fluid: either gas or liquid On quark matter Tuesday Talk: S. Gupta

  11. Droplets from Colliders Tuesday Talk: S. Gupta

  12. Gas or Liquid? Difference is in flow Tuesday Talk: S. Gupta

  13. How to pro(b/v)e a liquid • Show that there is some matter • …count the number of particles coming out of the collision and compute density • Show that this generates pressure • …elliptic flow: Bhalerao’s talk • Does the pressure cause coherent velocities? • …detailed analysis of spectra and flow • Is the flow turbulent? Tuesday Talk: S. Gupta

  14. How to predict its properties • Need to use quantum field theory • Equation for fields due to Maxwell • Equation for matter due to Dirac • ∞ first found by Lorentz (self interaction of point particle) • ∞ in the quantum theory: Heisenberg, Bethe • Removed by Feynman, Schwinger, Tomonaga • Modern formulation by Wilson: unifying field theory and statistical mechanics Tuesday Talk: S. Gupta

  15. The bubbling vacuum Quantum fluctuations: t  h/2 Particles can be produced from vacuum for a short time … and disappear again (if no one is looking) Mobile charges  the vacuum screens No one measures the charge of an electron without the screening cloud: it is actually ∞ and cancels Lorentz’s ∞ This affects the mass: gauge symmetry Tuesday Talk: S. Gupta

  16. Charge renormalization: screening in QED Tuesday Talk: S. Gupta

  17. Anti-screening in QCD Asymptotic freedom is anti-screening: the opposite of electrodynamics Tuesday Talk: S. Gupta

  18. Numerical renormalization • Solve coupled differential equations: Maxwell + Dirac • Do it many times: quantum theory is a sum over possibilities (Feynman) • Do it on a lattice (spacing d): no infinities in solid state physics • e changes with d Can do large e ! Tuesday Talk: S. Gupta

  19. The phase diagram • Several phases • Several 1st order transitions • More than one critical point • More variables not shown: tri-critical points… Tuesday Talk: S. Gupta Rajarshi Ray

  20. Flow parameters • P(T) or P(T,): relativistic gas • Equation of state is either E(P) or E(P,N) • Speed of sound • Specific heat • Compressibility • Viscosity Swagato Mukherjee Tuesday Talk: S. Gupta

  21. Lots more to do… • Analogues of Debye screening for pions, strange and charmed particles, causing them to dissolve • Photon emission rates: is the plasma a black body? Are there plasmons? • Supersonic shock waves: jets of particles travel with speed of light through the plasma • Quantum coherence created as particles freeze out of the plasma • Anything else you can think of… Tuesday Talk: S. Gupta

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