path integral quantization

I keep hearing, mostly in the areas of “expertise” of some uneducated quantum fundamentalists that “path integrals are not well defined”… my dears… this is so wrong! It would be better to say: path integrals can be so badly defined that they make no sense at all… this may be true but it is not the fault of the path integrals. The main “problem” with path integrals is the definition of their measures. Obviously, when integrating over a functional space the measure may not exist in a classical sense but then again, why should it? The equivalence classes or homology and cohomology classes could do a equally fine job in defining the results. Whenever you define your integral over cohomology classes the problems disappear (provided you define these last ones correctly, of course)… So, reminder: don’t tell me again “the path integral is ill defined” … it is so only when you make it so!  


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