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.

15 pages, 6 figures; Plenary talk presented at the XXVI International Symposium on Lattice Field Theory, July 14 - 19, 2008, Williamsburg, Virginia, USA