Code and explanation:
Cute but the models are not very robust
Do you know of any libraries for doing 'backend' physical simulations, such as calculating scattering amplitudes, making projections of spacetime models onto either space-like or time-like slices, and, especially, using tensor networks for modelling condensed matter interactions?
Complicated dynamical systems usually involve solving PDEs and for that you need to discretize your domain. How you choose to do so will drastically affect the numerical properties of your simulation. Most "real-physics" simulators tend to be specialized to a given task or even a given domain (for example simulating heat diffusion in an engine part). There's a whole literature on finite element methods to simulate various physical phenomena though it can be quite dense.
The generic game physics engines use very simple models of mechanics and allow for numerical issues (e.g. by using finite differences) in exchange for being real-time. If you're looking to simulate more advanced physical phenomena for a game, you're going to have to make similar trade-offs and will have to choose which ones make for the best gameplay.
Most modern game physics engines aren't actually discretizing an ODE or a PDE, at this point. The current standard techniques (see Nvidia's PhysX, for example) are instead solving something that look like a constraint satisfaction problem but gives force-like effects. You don't even get consistency under refinement with these methods, but they are cheap, and importantly, stable when terminated early (to remain under strict time budgets required of game based physics).
PhysX is position based dynamics. The Mueller guy who wrote that paper was a Co-founder of PhysX (back when it was NovodeX, then purchased by Ageia, then purchased by Nvidia) and is now a lead researcher at Nvidia. 
> The common method in open source engines is a projected gauss Seidel  which is used in bullet physics.
PGS is just the numerical method that Bullet uses to solve for the collision impulses between the rigid bodies (there are tons of other possible methods, Nvidia again had a cool paper a few years back, there are also global approaches with better convergence, etc). This is solving a so-called 'Contact Dynamics' contact model , which originates in the work of French mechanicians in the 70s and 80s.
Actually, if op is interested in PDEs in games, check out 'Digital Molecular Matter' . It was used in some Star Wars games, iirc. It is a pretty straightforward Lagrangian discretization (linear shape functions on tets) of a linearized hyperelastic energy density. They added a simple fracture model on top which allowed for cool destruction effects in games.
Can you recommend any general-purpose libraries (preferably with python bindings) for tensor calculus?
My understanding is the numerical GR community is moving in this direction. The theory people tend to roll their own inside of Mathematica or Maple. Some Maple users use GRTensorIII (https://github.com/grtensor/grtensor)
Disclaimer: I am a co-creator of GRTensorIII
It may be worth saying that numerical relativity played a key part in the last Nobel prize for the detection of gravitational waves.
Nevertheless it's nice to refer to this analogy.