ABSTRACT
The introduction of a cutoff is called a regularisation. The field theory is called renormalisable if the limit can be defined in a suitable way, often by varying the parameters in a suitable way with the cutoff. The class of r ory is relatively small. For a finite momentum cutoff, the path integral is nothing but a simple generalisation of the one we defined for quantum mechanics in n dimensions, or in the absence of interactions. In principle a path integral should be independent of the discretisation used in order to define it. For the Euclidean path integral, one particular way that is used quite often is the lattice discretisation, where instead of a momentum cutoff one makes not only time but also space discrete.
