Complex scalar field (Klein-Gordon, Schrodinger, Higgs...)

Question

Hello! One of the simplest (if not the simplest) examples of classical field theory is the complex scalar Klein-Gordon field, the relativistic version of the classical Schrodinger field. Now, Cadabra seems great for General Relativity, the DIrac field, the elecgtromagnetic field... but I see no clear treatment of complex scalars. It would be amazing if the tutorial would include a simple example with the Klein-Gordon field (i.e. how to find the Klein-Gordon equation given the action). This is done in the tutorial for the free classical Maxwell field, having another example would be great.

Comments

Hi Mark.

I agree with you. Do you have a specific problem in mind? Have you tried to prepare a tutorial yourself?

If you have a specific idea I could help you to develop it (as long as it fits my capabilities).

Regards, Dox.

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Dear @doxdrum, thank you for your reply. I was thinking about somethign like this:

https://cadabra.science/notebooks/beginners.html

(this is the first tutorial on the official website: finding the equations of motion for the Faraday field $F_{\mu \nu}$ by varying the action).

How about adding a complementary turorial where one derived the equations of motion for the complex scalar Klein-Gordon field? In this way, one can learn how to deal with complex fields and (at the same time) scalars: in fact, I see quite good references for vectors (i.e. $A^\mu$), spinors and, of course, the metric and higher rank tensors (since Cadabra seems to be very General Relativity oriented).

To be specific, it would be amazing to have a tutorial on these lines:

https://en.wikipedia.org/wiki/Klein–Gordon_equation#Lagrangian_formulation

Since the compelx Klein-Gordon has a conserved U(1) charge, this tutorial would be extremely useful, a fort of first step for everyone interested in checking the conserved quantities of an action with the Noether theorem. Thank you again!

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Hi Mark.

We could try to write a notebook ourselves. If you're interested, send me an email d o x d r u m (at) p m . m e to schedule a meeting.

Cheers, Dox.