# Why is it path integral formalism being a ''quantization'' procedure?

## Main Question or Discussion Point

Please teach me this:
I do not understand why we call functional integral procedure in QFT being ''quantization'' procedure.Because the integration is the ''summing up'' procedure,but not ''dividing'' into ''quantum'' procedure.Or does this term(quantization) has a origin of being able to deduce Feynman diagrams from functional integral formalism?By the way,does it in the nonperturbative QFT we still use Feynman diagrams?
Thank you very much for your kind helping.

## Answers and Replies

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I hear that path integral is also used in Quantum Gravity,so it is a powerful tool for quantization
procedure.Then where is the quantizing meaning with the ''integral''?

DarMM
Gold Member
Quantising just means converting a classical theory into a quantum theory, nothing to do with dividing things up into pieces or anything like. So the path integral formalism quantises a theory because it turns it into a quantum theory.

In nonperturbative QFT you do not use Feynman diagrams.

Quantum Mechanics is a dual particle-wave theory,but path integral formalism has only wave feature.So I do not understand why Path Integral Formalism changes Classical Mechanics into Quantum Mechanics?

dextercioby
Homework Helper
Quantum Mechanics is not a theory of waves or particles, nor of a duality between them, it is a theory of dynamical systems which provides the correct description of matter behavior at length-scales of 1 nanometer or less, if gravity effects are excluded. Matter can be seen as waves (quantum mechanical theory of light, for example) and/or particles (electrons in atoms, for example), but this distinction is lost, because it effectively pertains to classical/non-quantum mechanics.

Path integrals are mathematical means to a quicker computation of probability amplitudes/densities, which are key ingredients in quantum mechanics. So path integrals are part of quantum mechanics, if one decides to use them (I don't know of a classical theory such as GR which uses path integrals.)

So,in Quantum Gravity Theory,we need not ''make'' the discrete space-time ''atoms'',but needing to build a theory of space-time at ''tiny'' scale?How about the trying in Gravitons?

tom.stoer