As I work through A. Zee's "Quantum Field Theory in a Nutshell," I'd love to be able to visualize the different equations so I can explore the effects of different terms. Any suggestions? Python script, Matlab, Mathematica, or are there any tools or videos already out there that cover this subject?
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1$\begingroup$ Which equations? $\endgroup$ – innisfree Apr 10 '17 at 21:20
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$\begingroup$ There's a Royal Institution lecture with a visualisation at about 23mins of empty space according to QFT that may be of interest? $\endgroup$ – JohnP Apr 17 '17 at 16:16
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$\begingroup$ I've been looking for visualisations as well, it's surprisingly hard to find. You can of course go through the work yourself with Mathematica or numerically in python with scipy/numpy (the latter being free software). If you do, please post nice graphs somewhere google can find them ;) $\endgroup$ – BjornW Aug 6 '17 at 10:38
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The difficulty of visualizing a quantum field comes from the large number of degrees of freedom it has: Even if you discretize the field to a 2-dimensional mattress of, e.g., $100\times100$ points each of which can only oscillate in one dimension (similar to how Zee does it in one of the entry examples of his book), you already need a state function $\Psi: \mathbb R^{10\,000} \to \mathbb C$ (i.e. from a 10 000 dimensional real space to the complex plane).
One way of visualizing such a high dimensional function is to use a parallel axes diagram and plot only a relatively small number of randomly chosen points.
You can see how the result looks like in this paper:
https://www.researchgate.net/publication/321684743_A_new_way_of_visualizing_quantum_fields
Best regards Helmut
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1$\begingroup$ Link-only answers are not really good. Could you summarize the main points here? $\endgroup$ – Chris♦ Feb 7 '18 at 8:33
