Finite Temperature
Field Theory
(Physics 880.20, Spring 2010,
course web page)
Course objective: Finite
temperature or thermal field theory refers to the formulation of
relativistic quantum field theory in a dense media. This is somewhat
different from the usual vacuum field theory which mostly deals with
the outcome of the scattering of asymptotically prepared states in
vacuum. Most of this course will deal with the path integral approach
to describe the various static properties and response to
external currents of extended systems of scalars, spinors and vector
gauge
fields held at a fixed high temperature. This will include both the
imaginary time and the real time formalisms. This will be followed by
an extended study of
finite temperature QCD and the set up of the gauge invariant theory of
hard
thermal loops. This will be followed by extensions of the theory to
mildly
non-equilibrium phenomena and a set of applications to high energy
heavy-ion
collisions.
Classes will be from 2:30 to 4:18, Tuesdays
and Thursdays in M2015.
Course
Textbook: Finite Temperature Field Theory, Principles and
Applications by J. Kapusta & C. Gale,
textbook web page@
Cambridge university press
Note: this is the most recent
textbook on the subject and contains a
large amount of the topics
that I intend to cover. However, it does not cover everything and so
this will be supplemented
by at least two other texts and a handful of research papers. I will
provide a list of papers
soon and a set of notes as the course progresses along.
Other books: Thermal Field Theory by M.
Le Bellac @
Cambridge university press
Finite temperature field theory by A. Das. @ World
Scientific
then there are the classics: Fetter and
Walecka, Baym and Kadanoff and Abrikosov, Gorkov and Dzyaloshinskii
(these are all non-relativistic but still useful for many basic
techniques).
Lecture
Notes and Home Work
Relevant
papers: (note these are only those papers whose content is not
completely included in the textbooks but will be used in the course)
Real and Imaginary Time Field Theory at Finite Temperature and
Density.
N.P. Landsman,
C.G.
van Weert,
(Amsterdam
U.)
. ITFA-86-12, Sep 16, 1986. (Received Sep 1986). 205pp. Published
in Phys.Rept.145:141,1987.
Determination of Thermodynamic Green's
Functions Gordon Baym and N. David Mermin.
J. Math. Phys. 2, 232 (1961)
Simple Rules for Discontinuities in Finite Temperature Field Theory.
H.Arthur
Weldon,
(Pennsylvania
U.)
. PRINT-83-0452 (PENN), Jun 1983. (Received Jun 1983). 30pp. Published
in Phys.Rev.D28:2007,1983.
Vector dominance model at finite temperature.
Charles Gale,
(McGill
U.)
,
Joseph
I. Kapusta,
(Minnesota
U.)
. MCGILL-90-57, Nov 1990. 27pp. Published in Nucl.Phys.B357:65-89,1991.
Reformulation of finite temperature dilepton production.
H.A. Weldon,
(West
Virginia U.)
. 1990. Published in Phys.Rev.D42:2384-2387,1990.
Production Of Soft Dileptons In The Quark - Gluon Plasma. Eric
Braaten,
(Northwestern
U.)
,
Robert
D. Pisarski,
(Brookhaven)
,
Tzu-Chiang
Yuan,
(Northwestern
U.)
. BNL-43941, NUHEP-TH-90-1, Jan 1990. 16pp. Published in Phys.Rev.Lett.64:2242,1990.
High-energy photons from quark - gluon plasma versus hot
hadronic gas.
Joseph
I. Kapusta,
P.
Lichard,
D.
Seibert,
(Minnesota
U.)
. 1991. Published in Phys.Rev.D44:2774-2788,1991,
Erratum-ibid.D47:4171,1993.
Two loop selfenergy and multiple scattering at finite temperature. Joseph
I. Kapusta,
(Minnesota
U.)
,
S.M.H.
Wong,
(Ohio
State U.)
. NUC-MINN-2001-4-T, Feb 2001. 13pp. Published in Phys.Rev.D64:045008,2001.
e-Print: hep-th/0103065
On the imaginary parts and infrared divergences of two loop vector
boson selfenergies in thermal QCD.
A. Majumder,
Charles
Gale,
(McGill
U.)
. Nov 2001. 34pp.
Published in Phys.Rev.C65:055203,2002.
e-Print: hep-ph/0111181
Energy loss of a heavy quark in the quark - gluon plasma.
Eric Braaten,
(Northwestern
U.)
,
Markus
H. Thoma,
(LBL,
Berkeley)
. LBL-30998, NUHEP-TH-91-14, Jul 1991. 14pp. Published in Phys.Rev.D44:2625-2630,1991.
Elastic energy loss and longitudinal straggling of a hard jet. A.
Majumder,
(Duke
U. & Ohio
State U.)
. Oct 2008. (Received Sep 2009). 5pp. Published in Phys.Rev.C80:031902,2009.
e-Print: arXiv:0810.4967 [nucl-th]
Quark - Gluon Transport Theory. Part 1. the Classical Theory.
Ulrich W. Heinz,
(Frankfurt
U.)
. UFTP-135-1984, Jun 1984. (Received Jun 1984). 46pp. Published
in Annals Phys.161:48,1985.
Quark - Gluon Transport Theory. Part 2. Color Response And Color
Correlations In A Quark - Gluon Plasma. Ulrich
W. Heinz,
(Brookhaven)
. BNL-36721, Jul 1985. (Received Jul 1985). 55pp. Published in Annals
Phys.168:148,1986.
Classical transport theory and hard thermal loops in the quark -
gluon
plasma. P.F.
Kelly,
Q.
Liu,
C.
Lucchesi,
C.
Manuel,
(MIT,
LNS)
. MIT-CTP-2320, Jun 1994. 23pp. Published in Phys.Rev.D50:4209-4218,1994.
e-Print: hep-ph/9406285
Effective theories for real time correlations in hot plasmas.
Peter
Brockway Arnold,
(Virginia
U.)
,
Laurence
G. Yaffe,
(Washington
U., Seattle)
. UW-PT-97-22, Sep 1997. 28pp. Published in Phys.Rev.D57:1178-1192,1998.
e-Print: hep-ph/9709449
Transport coefficients in high temperature gauge theories. 1.
Leading
log results. Peter
Brockway Arnold,
(Virginia
U.)
,
Guy
D. Moore,
Laurence
G. Yaffe,
(Washington
U., Seattle)
. UW-PT-00-15, Oct 2000. 41pp.
Published in JHEP 0011:001,2000.
e-Print: hep-ph/0010177
Tentative
Course
outline (this could change depending on how things go):
1) Review of Thermodynamics and Statistical Mechanics.
2) Path integrals in vacuum for a free scalar field.
3) The partition function of a free scalar field as a path integral and
Matsubara frequencies.
4) Interactions in phi^4
theory and Feynman rules in imaginary time.
5) The imaginary time propagator, self-energy, Schwinger-Dyson equation.
6) Higher orders, resummation and breakdown of perturbation theory.
7) The partition function for free fermions, chemical potentials and
non-covariant propagators.
8) The partition function for free gauge bosons, gauge invariance and
ghosts.
9) Linear response, real time correlators and spectral density.
10) Subtleties in analytic continuation to real energies and Carlmann's
theorem.
11) Applications: in-medium dispersion relations, space-like and
time-like modes,
12) Imaginary parts of self-energies, cutting rules, physical
interpretation.
13) Real time formalism, propagators and self-energies.
14) QED at finite temperature, self-energies and hard thermal loops
(HTL).
15) Dispersion relations, dynamical mass generation, Debye screening,
Landau damping.
16) QCD at
finite temperature, HTL self-energies and vertices.
17) Gauge invariance of HTL QCD and the gluon damping rate.
18) Applications 1: Hard quark elastic energy loss.
19) Applications 2: Dilepton and real photon production from a Quark
Gluon Plasma.
20) Introduction to the Boltzmann-Vlasov equation,
rederivation of HTL theory from the Vlasov equation
Possible extra topics: If we get this far, the remaining topics will be
covered at a more colloquial level
21) Collision term at Leading log and transport
coefficients.
22) Outstanding issues: magnetic screening, Linde's problem.
23) Collision term at Leading order, the Arnold-Moore-Yaffe resummation.
24) Symmetry breaking at finite
temperature and density, and Anomalies.
25) Restoration of spontaneously broken symmetries at finite
temperatures.
26) Simple hadronic theories at
finite temperature,
vector dominance.
27) Renormalization at finite temperature.