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

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Discussion Overview

The discussion revolves around the concept of path integral formalism in quantum field theory (QFT) and its classification as a "quantization" procedure. Participants explore the implications of this formalism in both QFT and Quantum Gravity, questioning the meaning of quantization and its relationship to classical and quantum theories.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant expresses confusion about why the functional integral procedure in QFT is termed a "quantization" procedure, suggesting that integration is a summing process rather than a division into quantum aspects.
  • Another participant notes that path integrals are also utilized in Quantum Gravity, implying their significance in quantization, but questions the meaning of "quantizing" in relation to integration.
  • A different participant clarifies that quantization refers to converting classical theories into quantum theories, asserting that path integral formalism achieves this transformation.
  • Concerns are raised about the nature of Quantum Mechanics, with one participant arguing that path integral formalism only exhibits wave features, leading to confusion about its role in transitioning from Classical to Quantum Mechanics.
  • Another participant emphasizes that Quantum Mechanics is fundamentally a theory of dynamical systems, which can describe matter as waves or particles, but this distinction is not relevant in the quantum context.
  • Discussion includes the idea that path integrals serve as a mathematical tool for computing probability amplitudes in quantum mechanics, although the applicability of path integrals in classical theories like General Relativity is questioned.
  • A participant raises a point about Quantum Gravity, suggesting that the theory does not require discrete space-time "atoms" but rather aims to construct a theory of space-time at very small scales, mentioning gravitons as a consideration.
  • Another participant asserts that quantization does not imply manual discretization, indicating that any discretization is an emergent property.

Areas of Agreement / Disagreement

Participants express differing views on the nature of quantization and the role of path integrals in both QFT and Quantum Gravity. There is no consensus on the implications of path integral formalism or its relationship to classical mechanics.

Contextual Notes

Participants highlight various assumptions about the nature of Quantum Mechanics and the interpretation of path integrals, which may depend on specific definitions and contexts. The discussion remains open-ended regarding the application of path integrals in nonperturbative QFT and Quantum Gravity.

ndung200790
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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.
 
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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''?
 
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?
 
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?
 
quantization never means to discretize something by hand; the discretization is always emergent
 

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