Effective Field Theory, Renormalizability and Extra Dimensions

We discuss in this paper two ways of defining the concept of "effective field theory": effective field theory defined by low energy effectiveness and effective field theory defined by 4D effectiveness out of higher dimensions. We argue that these two views are actually equivalent, that effective field theories at low energy can in fact be regarded as field theories of higher dimensions confined on a 4D spcaetime. We examine this idea through comparing two different regularization schemes: Momentum Cutoff and Dimensional Regularization, and through analyzing how fields can be localized on branes.