Abstract
These lecture notes review the foundations and some applications of
light-cone quantization. First I explain how to choose a time in special
relativity. Inclusion of Poincare invariance naturally leads to Dirac's forms
of relativistic dynamics. Among these, the front form, being the basis for
light-cone quantization, is my main focus. I explain a few of its peculiar
features such as boost and Galilei invariance or separation of relative and
center-of-mass motion. Combining light-cone dynamics and field quantization
results in light-cone quantum field theory. As the latter represents a
first-order system, quantization is somewhat nonstandard. I address this issue
using Schwinger's quantum action principle, the method of Faddeev and Jackiw,
and the functional Schroedinger picture. A finite-volume formulation,
discretized light-cone quantization, is analysed in detail. I point out some
problems with causality, which are absent in infinite volume. Finally, the
triviality of the light-cone vacuum is established. Coming to applications, I
introduce the notion of light-cone wave functions as the solutions of the
light-cone Schroedinger equation. I discuss some examples, among them
nonrelativistic Coulomb systems and model field theories in two dimensions.
Vacuum properties (like chiral condensates) are reconstructed from the particle
spectrum obtained by solving the light-cone Schroedinger equation. In a last
application, I make contact with phenomenology by calculating the pion wave
function within the Nambu and Jona-Lasinio model. I am thus able to predict a
number of observables like the pion charge and core radius, the r.m.s.
transverse momentum, the pion structure function and the pion distribution
amplitude. The latter turns out to be the asymptotic one.
Original language | English |
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Pages (from-to) | 55-142 |
Number of pages | 0 |
Journal | Lect.Notes Phys. |
Volume | 572 |
Issue number | 0 |
Publication status | Published - 11 Aug 2000 |
Keywords
- hep-th
- hep-ph