# Where can I find visualizations of quantum field theory equations? [closed]

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?

• Which equations? – innisfree Apr 10 '17 at 21:20
• There's a Royal Institution lecture with a visualisation at about 23mins of empty space according to QFT that may be of interest? – JohnP Apr 17 '17 at 16:16
• 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 ;) – BjornW Aug 6 '17 at 10:38

## 1 Answer

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

• Link-only answers are not really good. Could you summarize the main points here? – Chris Feb 7 '18 at 8:33