This may be a very basic question, but I've had now some background on the quantum theory, and I think I am missing something. Roughly speaking, I feel like the main difference is that quantizing involves going from field amplitudes to counting operators, implying that a quantum process involves exciting discrete lumps of energy. What I don't understand is how this is reflected on, say, the canonical quantization procedure. Take for example non relativistic theory:(adsbygoogle = window.adsbygoogle || []).push({});

[tex][q_{i},p_{j}]=i\hbar \delta_{ij}[/tex]

I don't see how that adds any restriction in a classical field theory. If you make the transition from a point particle to a field, then p is still the infinitesimal generator of translations, leading naturally to [tex]p_{i}=-i\hbar \partial_{i}[/tex], so for the field the relation is satisfied trivially. The transition to creator/anihilator operators can be done from the position/momentum ones, so they contain the same information. Why then counting operators lead to a different field theory?

Moreover, why are canonical quantization and path integral formalism equivalent?

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Difference between a classical and quantum field theory?

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

Similar Threads - Difference between classical | Date |
---|---|

I Difference between statistical and dynamical properties | Feb 25, 2017 |

I Difference between atomic behavior in QM and classical physics | Mar 3, 2016 |

The difference between classical and quantum correlations | Feb 8, 2016 |

Fundamental difference between quantum physics and classical physics | Dec 10, 2013 |

Difference between classical wave function and quantum wave function | May 27, 2012 |

**Physics Forums - The Fusion of Science and Community**