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\section{\usemenu{slacpub7056::context::slacpub7056001}{QCD on the Light Cone }}\label{section::slacpub7056001}
One of the central problems in particle physics is to determine the
structure of hadrons such as the proton and neutron in terms of
their fundamental QCD quark and gluon degrees of freedom. The bound
state structure of hadrons plays a critical role in virtually every
area of particle physics phenomenology. For example, in the case of
the nucleon form factors, pion electroproduction $ep \rightarrow e
\pi^+n$, and open charm photoproduction $\gamma p\rightarrow
D\Lambda_c$, processes which will be interesting to study at ELFE,
the cross sections depend not only on the nature of the quark
currents, but also on the coupling of the quarks to the initial and
final hadronic states. Exclusive decay amplitudes such as $B
\rightarrow K^*\gamma$, processes which will be studied intensively
at $B$ factories, depend not only on the underlying weak transitions
between the quark flavors, but also the wavefunctions which describe
how the $B$ and $K^*$ mesons are assembled in terms of their
fundamental quark and gluon constituents. Unlike the leading twist
structure functions measured in deep inelastic scattering, such
exclusive channels are sensitive to the structure of the hadrons at
the amplitude level and to the coherence between the contributions
of the various quark currents and multiparton amplitudes.
The analytic problem of describing QCD bound states is compounded
not only by the physics of confinement, but also by the fact that
the wavefunction of a composite of relativistic constituents has to
describe systems of an arbitrary number of quanta with arbitrary
momenta and helicities. The conventional Fock state expansion based
on equaltime quantization quickly becomes intractable because of
the complexity of the vacuum in a relativistic quantum field theory.
Furthermore, boosting such a wavefunction from the hadron's rest
frame to a moving frame is as complex a problem as solving the bound
state problem itself. The BetheSalpeter bound state formalism,
although manifestly covariant, requires an infinite number of
irreducible kernels to compute the matrix element of the
electromagnetic current even in the limit where one constituent is
heavy.
The description of relativistic composite systems using lightcone
quantization \cite{1} is in contrast remarkably simple. The
Heisenberg problem for QCD can be written in the form
\begin{equation}
H_{LC }\vert H\rangle = M_H^2 \vert H\rangle\; ,
\end{equation}
where $H_{LC}=P^+ P^  P_\perp^2$ is the mass operator. The
operator $P^=P^0P^3$ is the generator of translations in the
lightcone time $x^+=x^0+x^3.$ The quantities $P^+=P^0+P^3$ and
$P_\perp$ play the role of the conserved threemomentum. Each
hadronic eigenstate $\vert H\rangle$ of the QCD lightcone
Hamiltonian can be expanded on the complete set of eigenstates
$\{\vert n\rangle\} $ of the free Hamiltonian which have the same
global quantum numbers: $\vert H\rangle=\sum\psi^H_n(x_i, k_{\perp
i}, \lambda_i) \vert n\rangle.$ In the case of the proton, the Fock
expansion begins with the color singlet state $\vert u u d \rangle $
of free quarks, and continues with $\vert u u d g \rangle $ and the
other quark and gluon states that span the degrees of freedom of the
proton in QCD. The Fock states $\{\vert n\rangle \}$ are built on
the free vacuum by applying the free lightcone creation operators.
The summation is over all momenta $(x_i, k_{\perp i})$ and
helicities $\lambda_i$ satisfying momentum conservation $\sum^n_i
x_i = 1$ and $\sum^n_i k_{\perp i}=0$ and conservation of the
projection $J^3$ of angular momentum.
The simplicity of the lightcone Fock representation relative to
that in equaltime quantization arises from the fact that the
physical vacuum state has a much simpler structure on the light
cone. Indeed, kinematical arguments suggest that the lightcone
Fock vacuum is the physical vacuum state. This means that all
constituents in a physical eigenstate are directly related to that
state, and not disconnected vacuum fluctuations. In the lightcone
formalism the parton model is literally true. For example, as we
shall discuss in section 3, all of the structure functions measured
in deep inelastic lepton scattering are simple probabilistic
measures of the lightcone wavefunctions.
The wavefunction $\psi^p_n(x_i, k_{\perp i},\lambda_i)$ describes
the probability amplitude that a proton of momentum $P^+= P^0+P^3$
and transverse momentum $P_\perp$ consists of $n$ quarks and gluons
with helicities $\lambda_i$ and physical momenta $p^+_i= x_i P^+$
and $p_{\perp i} = x_i P_\perp + k_{\perp i}$. The wavefunctions
$\{\psi^p_n(x_i, k_{\perp i},\lambda_i)\},n=3,\dots$ thus describe
the proton in an arbitrary moving frame. The variables $(x_i,
k_{\perp i})$ are internal relative momentum coordinates. The
fractions $x_i = p^+_i/P^+ = (p^0_i+p^3_i)/(P^0+P^3)$, $0