It is possible to perform the simplest QFT calculations with second quantization, in Maple? Bosons in a box. See attached example. bosons_in_a_box.mw

Sure any general purpose programming language is capable of performing this task with enough effort. What I am interested in is if the physics tools has a standard way of dealing with these calculations. The general impedement when attempting the calculation is that integrations are perfomed by replacements with delta functions or kronecker delta functions, and its not clear how to force the Maple Physics package to recognize this or if that's possible. Part of the problem is that integrations in maple are defined in one dimension at a time where as in QFT the integration element is almost always atleast three dimensional, d^3x or dxdydzy, the later of which can get extremely cumbersome with even a small number of fields under consideration. I don't find much of what I am refering to mentioned in the help pages and I doubt these types of QFT calculations are possible to perform in Maple without addressing these issues.

bosons_in_a_box.mw

My goal is to export images of curves where the output image has no background or equivalently, a fully transparent background. Is there a standard way to perform this task? I know that I can do this with the help of external software but I want to do it at the export stage in maple and avoid increasing the number of tools needed to perform the job. Eventually, I may want to generate many thousdands of curves/images with transparent backgrounds. 

Below I show how to make a plot while choosing a background with the color blue. I have found no way to select a fully transparent background. I expect this background transparency will be applied at the export image stage. 

how_do_I_plot_with_no_background.mw

To give an explicit example of what a plot with no background looks like, I make a plot in an unrelated software of a curve with no background. It's impossible to differentiate a white background from a transparent background in this environment, so we also show the same image embedded in an unrelated colored background also generated in an unrelated software.

In the image below, we can see how a image of a curve with a transparent background can be embedded over top of any other image without the blue square shown the the first example.

How do I change the legend position so it doesn't cover the plot label?

Before entertaining non-standard solutions to this problem such as building my own from scratch, is the a standard method for changing the position of the default legend generated along with a standard plot? I couldn't find anything about custom legend positions in the help sheets.

I can't help but wonder why this observed behaviour occurs by default? In what kind of plot would I prefer the plot labels to be obscured by the plot legend?

legend_covers_plot_labels.mw

Can I open Maple 2025 files in Maple 2024? Further, what if the files don't use Maple 2025 features/packages? Does that change the outcome?

Does Maple 2025 have a dark theme or GUI color customization?