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

17 May, 2005Tuesday Talk: S. Gupta2 Particles in the Standard Model (1990s)

17 May, 2005Tuesday Talk: S. Gupta3 The Eightfold Way (variables)

17 May, 2005Tuesday Talk: S. Gupta4 The Eightfold Way (variables)

17 May, 2005Tuesday Talk: S. Gupta5 The Eightfold Way (variables)

17 May, 2005Tuesday Talk: S. Gupta6 The Eightfold Way (variables)

17 May, 2005Tuesday Talk: S. Gupta7 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

17 May, 2005Tuesday Talk: S. Gupta8 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

17 May, 2005Tuesday Talk: S. Gupta9 The RHIC at Brookhaven

17 May, 2005Tuesday Talk: S. Gupta10 On quark matter 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

17 May, 2005Tuesday Talk: S. Gupta11 Droplets from Colliders

17 May, 2005Tuesday Talk: S. Gupta12 Gas or Liquid? Difference is in flow

17 May, 2005Tuesday Talk: S. Gupta13 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?

17 May, 2005Tuesday Talk: S. Gupta14 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

17 May, 2005Tuesday Talk: S. Gupta15 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

17 May, 2005Tuesday Talk: S. Gupta16 Charge renormalization: screening in QED

17 May, 2005Tuesday Talk: S. Gupta17 Anti-screening in QCD Asymptotic freedom is anti-screening: the opposite of electrodynamics

17 May, 2005Tuesday Talk: S. Gupta18 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 !

17 May, 2005Tuesday Talk: S. Gupta19 The phase diagram Several phases Several 1st order transitions More than one critical point More variables not shown: tri-critical points… Rajarshi Ray

17 May, 2005Tuesday Talk: S. Gupta20 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

17 May, 2005Tuesday Talk: S. Gupta21 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…