Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lectures on Bound states   Even a first approximation of bound states requires contributions of all
powers in the coupling. This means that the concept of "lowest order bound
state" needs to be defined. In these lectures I discuss the "Born" (no loop,
lowest order in $\hbar$) approximation. Born level states are bound by gauge
fields which satisfy the classical field equations.
  As a check of the method, Positronium states of any momentum are determined
as eigenstates of the QED Hamiltonian, quantized at equal time. Analogously,
states bound by a strong external field $A^\mu(\boldsymbol{x})$ are found as
eigenstates of the Dirac Hamiltonian. Their Fock states have dynamically
created $e^+e^-$ pairs, whose distribution is determined by the Dirac wave
function. The linear potential of $D=1+1$ dimensions confines electrons but
repels positrons. As a result, the mass spectrum is continuous and the wave
functions have features of both bound states and plane waves.
  The classical solutions of Gauss' law are explored for hadrons in QCD. A
non-vanishing boundary condition at spatial infinity generates a constant
\order{\alpha_s^0} color electric field between quarks of specific colors.
Poincar\'e invariance limits the spectrum to color singlet $q\bar q$ and $qqq$
states, which do not generate an external color field. This restricts the
\order{\alpha_s^0} interactions between hadrons to string breaking dynamics as
in dual diagrams. Light mesons lie on linear Regge and parallel daughter
trajectories. There are massless states which may be significant for chiral
symmetry breaking. Since the bound states are defined at equal time in all
frames they have a non-trivial Lorentz covariance.

36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
2
The categories of this paper are: math
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin