Undergrad The Power of QM and QFT

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Quantum Mechanics (QM) and Quantum Field Theory (QFT) are fundamental to understanding much of modern physics, particularly in deriving Maxwell's Equations from first principles through local gauge invariance applied to the Dirac Lagrangian. The discussion highlights the prevalence of infinities in both classical and quantum physics, emphasizing the logical connections between Classical Field Theories (CFT) and QFT. While some participants express humor about the complexities of these theories, the main focus is on educating those less familiar with these concepts. The shared resource aims to clarify these foundational ideas for undergraduate students and others at an introductory level. Understanding QM and QFT is essential for grasping the broader implications in physics.
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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).
 
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
 
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I am slowly going through the book 'What Is a Quantum Field Theory?' by Michel Talagrand. I came across the following quote: One does not" prove” the basic principles of Quantum Mechanics. The ultimate test for a model is the agreement of its predictions with experiments. Although it may seem trite, it does fit in with my modelling view of QM. The more I think about it, the more I believe it could be saying something quite profound. For example, precisely what is the justification of...

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