690 research outputs found
A Perturbative Approach to the Tunneling Phenomena
The double-well potential is a good example, where we can compute the
splitting in the bound state energy of the system due to the tunneling effect
with various methods, namely WKB or instanton calculations. All these methods
are non-perturbative and there is a common belief that it is difficult to find
the splitting in the energy due to the barrier penetration from a perturbative
analysis. However, we will illustrate by explicit examples containing singular
potentials (e.g., Dirac delta potentials supported by points and curves and
their relativistic extensions)that it is possible to find the splitting in the
bound state energies by developing some kind of perturbation method.Comment: 24 pages, 4 figure
Poisson Algebra of Wilson Loops in Four-Dimensional Yang-Mills Theory
We formulate the canonical structure of Yang--Mills theory in terms of
Poisson brackets of gauge invariant observables analogous to Wilson loops. This
algebra is non--trivial and tractable in a light--cone formulation. For U(N)
gauge theories the result is a Lie algebra while for SU(N) gauge theories it is
a quadratic algebra. We also study the identities satsfied by the gauge
invariant observables. We suggest that the phase space of a Yang--Mills theory
is a co--adjoint orbit of our Poisson algebra; some partial results in this
direction are obtained.Comment: 32 Pages, 7 figures upon reques
Geometric Quantization and Two Dimensional QCD
In this article, we will discuss geometric quantization of 2d QCD with
fermionic and bosonic matter fields. We identify the respective large-N_c phase
spaces as the infinite dimensional Grassmannian and the infinite dimensional
Disc. The Hamiltonians are quadratic functions, and the resulting equations of
motion for these classical systems are nonlinear. In a previous publication,
the first author has shown that the linearization of the equations of motion
for the Grassmannian gave the `t Hooft equation. We will see that the
linearization in the bosonic case leads to the scalar analog of the `t Hooft
equation found by Tomaras.Comment: 46 pages, Latex, no figure
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