The Power of QM and QFT

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SUMMARY

This discussion emphasizes the fundamental role of Quantum Mechanics (QM) and Quantum Field Theory (QFT) in modern physics, particularly in deriving Maxwell's Equations from first principles through local gauge invariance applied to the Dirac Lagrangian. The conversation highlights the relationship between classical and quantum theories, specifically how Classical Field Theories (CFT) can be inferred from QFT. The discussion also addresses the common misconceptions and knowledge gaps among students at the introductory and undergraduate levels regarding these concepts.

PREREQUISITES
  • Understanding of Quantum Mechanics (QM)
  • Familiarity with Quantum Field Theory (QFT)
  • Knowledge of Dirac Lagrangian and its applications
  • Basic principles of gauge invariance
NEXT STEPS
  • Study the derivation of Maxwell's Equations from first principles
  • Explore the implications of local gauge invariance in quantum theories
  • Research the Standard Model Lagrangian and its components
  • Investigate the relationship between Classical Field Theories (CFT) and Quantum Field Theory (QFT)
USEFUL FOR

Students in physics, particularly those at the introductory and undergraduate levels, as well as educators and researchers looking to deepen their understanding of the foundational concepts of Quantum Mechanics and Quantum Field Theory.

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We often see discussions about what QM and QFT mean, but hardly anything on just how fundamental they are to much of physics. To rectify that, see the following;
https://www.cambridge.org/engage/ap...maxwell-s-equations-from-first-principles.pdf

'Somewhat magically, if one then applies local gauge invariance to the Dirac Lagrangian, a field appears, and from this field it is possible to derive Maxwell’s Equations (and therefore all of ElectroMagnetism).'


Thanks
Bill
 
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Well you have two options Quantum vs Classical. Now infinities are all over physics (classical and quantum), the self energy of an electron is known to diverge to infinity.

So from a classical logic stand it's obvious you can infer CFT (Classical Field Theories) from QFT, from logical contradiction you can infer whatever you like.... a dead and alive cats and kets that wear bras.
:oldbiggrin: (sorry, that's my sense of humour, not everyone get it).
 
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bhobba said:
We often see discussions about what QM and QFT mean, but hardly anything on just how fundamental they are to much of physics. To rectify that, see the following;
https://www.cambridge.org/engage/ap...maxwell-s-equations-from-first-principles.pdf

'Somewhat magically, if one then applies local gauge invariance to the Dirac Lagrangian, a field appears, and from this field it is possible to derive Maxwell’s Equations (and therefore all of ElectroMagnetism).'


Thanks
Bill
Isn’t that how we justify the whole Standard Model Lagrangian? What’s new here?
 
mad mathematician said:
a dead and alive cats and kets that wear bras.
:oldbiggrin: (sorry, that's my sense of humour, not everyone get it).

I get it.

Thanks
Bill
 
pines-demon said:
What’s new here?

Nothing,

It's for those that do not know about it, especially at the I level here or those in later undergraduate years.

Thanks
Bill
 
Last edited:
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