  Developments in algorithms over the past decade suggest that there is a new
computational approach to a class of quantum field theories. This approach is
based on rewriting the partition function in a representation similar to the
world-line representation and hence we shall call it the "WL-approach". This
approach is likely to be more powerful than the conventional approach in some
regions of parameter space, especially in the presence of chemical potentials
or massless fermions. While world-line representations are natural in the
Hamiltonian formulation, they can also be constructed directly in Euclidean
space. We first describe the approach and its advantages by considering the
classical XY model in the presence of a chemical potential. We then argue that,
$CP^{N-1}$ models, models of pions on the lattice and the lattice massless
Thirring model, can all be formulated and solved using the WL-approach. In
particular, we discover that the WL-approach to the Thirring model leads to a
novel determinantal Monte-Carlo algorithm which we call the "dynamical-bag"
algorithm. Finally, we argue that a simple extension of the WL-approach to
gauge theories leads to a world-sheet, "WS-approach", in Abelian Lattice Gauge
theory.
