Of course you can do a integral over time for example, but you logically understand in the process that its only a virtual dimension in this case, not a real eu

Of course you can do a integral over time for example, but you logically understand in the process that its only a virtual dimension in this case, not a real euclidean one. Your spin 'dimensions' still reside in 3 euclidean dimensions but for technical reasons you implement those vectors as an axis. Don't get me wrong, sometimes its useful to add a virtual dimension in the mathematical sense to get a shortcut in calculation, but it should be clear that those are not real ones. One the level of physical implementation, everything requiring more then 3 looks unlikely.