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Art Weldon

Professor Emeritus


304-293-5106 White Hall, Room 335

Plasma & Space Physics


  • Ph.D., Massachusetts Institute of Technology, 1974
  • B.S., Massachusetts Institute of Technology, 1969


Quantum Field Theory

The fundamental interactions found in nature are described mathematically by quantum field theory. Quantization of the classical electromagnetic field produced by charged particles requires photons as the quantum carrier of electromagnetic energy and allows for the creation photons (known as emission) and the destruction of photons (known as absorption). When the electron field is quantized it requires the existence of positrons as the antiparticle of electrons and allows charges to be created and destroyed. For example the collision of two electrons at high energy can yield four particles: three electrons plus a positron. During the past decade specific quantum field theories were developed to describe the two basic interactions that occur within nuclei: the weak interactions responsible for beta decay processes in which a neutron decays into one proton, one electron, and one neutrino; and the strong interactions which bind neutrons and protons together to form nuclei. Both the weak and the strong interactions are understood in terms of quantum fields carried by quarks and gluons. Quarks are the elementary constituents of protons and neutrons and obey Fermi statistics; gluons are the carriers of the strong force between quarks and obey Bose Research statistics.

Most research on the strong, weak, and electromagnetic interactions is concerned with processes in which only a few particles participate. Typically two particles collide at high energy (electron-electron, or electron-proton, or proton-proton) and although many more particles are produced, each of them has only a few significant interactions with the others.

Finite-Temperature Field Theory

A small subgroup of elementary particle physicists is concerned with collective behavior among elementary particles. If the particles reach equilibrium, they will have a temperature.

The study of such systems often involves applying kinetic theory, fluid mechanics, and statistical mechanics to quantum field theory.

It is rather surprising that at ultra-relativistic temperatures, particle behavior is highly quantum mechanical and not classical. The reason for this is simple. At nonrelativistic temperature a further increase in temperature will increase the separation between particles and make the behavior more classical. However, when then temperature is already ultra-relativistic, a further increase will produce very many particle-antiparticle pairs and the inter-particle spacing will decrease. The closer spacing makes the system more quantum mechanical.

The early universe began at an extremely high temperature and has since cooled. When the temperature cooled to about 200 GeV the universe underwent a phase transition as the electroweak symmetry was broken. After the phase transition most particles had a mass.

As the universe cooled to about 200 MeV there was a second phase transition produced as a symmetry of the strong chromodynamic forces was broken. Before this transition the colored quarks and gluons were able to propagate over large distances in a phase called the quark-gluon plasma. After the phase transition the quarks and gluons were dynamically confined inside protons, neutrons, and mesons.

Quark-Gluon Plasma Experiments

It is experimentally possible to achieve a temperature of 200 MeV by concentrating a large energy in a small volume. This is done by colliding two heavy nuclei that have been highly accelerated. When the temperature at the center of the collision is high enough, the nucleons will melt briefly into a plasma of quarks and gluons. The plasma will quickly cool back into protons, neutrons, and mesons. Learning about the quarks and gluons from these measurements is similar to the following problem. Suppose that we lived on a very cold planet where H 2O is always frozen in ice crystals. And suppose that the only way to learn about the liquid phase of H 2O would be to collide ice crystals together. In both cases, learning about the simpler phase (water or the quark-gluon fluid) would require difficult experiments with the complicated phase (ice or the heavy nuclei). For information about the quark-gluon plasma and the RHIC accelerator at Brookhaven National Laboratory (BNL) built to produce it, visit the BNL website.

Some of my research concerns the phenomenology of the collisions, i.e. what can be learned about the quark-gluon plasma from the experimentally measured particle distributions. Other parts of my research concern more basic problems of quantum field theory at high temperature such as the behavior of quarks and gluons in the plasma, resummations of perturbation theory, and the treatment of infrared divergences. A fundamental difficulty is that because of scattering in the plasma each quark and gluon behaves as a quasiparticle in the sense that the energy is temperature-dependent and has a line width from the energy’s imaginary part.

Selected Publications

  • “Fermions without Vierbeins in Curved Space-Time,” Physical Review D 63, 104010 p. 1-11 (2001).
  • “Thermal Green Functions in Coordinate Space for Massless Particles of any Spin,” Physical Review D 62, 056010 p. 1-9 (2000).
  • “Green Functions in Coordinate-Space for Gauge Bosons at Finite-Temperature,” Physical Review D 62, 056003 p. 1-10 (2000).
  • “Structure of the Quark Propagator at High Temperature,” Physical Review D 61, 036003 p. 1-8 (2000).
  • “Mass-Shell Behavior of Electron Propagator at Low Temperature,” Physical Review D 59, 065002 (1999).
  • Energy and Momentum Density of Thermal Gluon Oscillations,” Annals of Physics (N.Y.) 272, 177-195 (1999).
  • Structure of the Gluon Propagator at Finite Temperature,” Annals of Physics (N.Y.) 270, page (1998).
  • “Branch Cuts due to Finite-Temperature Quasiparticles,” Physical Review D 58, 105002, p. 1-13 (1998).
  • “Finite-Temperature Retarded and Advanced Fields,” Nuclear Physics B534, 467-490 (1998).
  • “Finite Temperature Field Theory,” in First Latin American Symposium on High Energy Physics and VII Mexican School of Particles and Fields ed. J.C. D’Olivo, M. Klein-Kreisler, and H. Mendez (AIP Conference Proceedings 400, Woodbury, NY, 1997) p 409-436.
  • “New Mesons in the Chirally Symmetric Plasma,” in RHIC Summer Study ‘96: Theory Workshop on Relativistic Heavy Ion Collisions (BNL-52514), ed. D.E. Kahana and Y. Pang, p. 279-285.
  • “Finite-Temperature Feynman Propagator in Operator Form,” Physical Review D 53, 7265-7269 (1996).
  • Exponential Growth of Space-like Gluon Distribution Functions?, Nuclear Physics A590, 593c-596c (1995).
  • “Cancellation of Infrared Divergences in QED at Nonzero Temperature,” Proceedings of the Third Workshop on Thermal Field Theories and Their Applications, Banff Canada (World Scientific, Singapore, 1994), p. 450-455.
  • “Cancellation of Infrared Divergences in Thermal QED,” Nuclear Physics A566, 581c-584c (1994).
  • “Suppression of Bremsstrahlung at Non-zero Temperature,” Physical Review D 49, 1579-1584 (1994).
  • “Generalization of the Breit-Wigner Formula to Finite Temperature and Density,” Annals Physics (N.Y.) 228, 43-51 (1993).
  • “Hard Thermal Loops and their Noether Currents,” Workshop on Perturbative Methods in Hot Gauge Theories, Winnipeg, Canada, Canadian Journal of Physics 71, 300-305 (1993).
  • “Mishaps with Feynman Parametrization at Finite Temperature,” Physical Review D 47, 594-600 (1993).

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