Is it possible (not practical) to create a liquid nitrogen jet? Would it be possible (though not practical) to create a jet that runs on liquid nitrogen that is heated, creating the expansion effect? I believe nitrogen takes up 674 (about) times as much space in gaseous form as in liquid, but if it were somehow evenly heated, could it provide a similar effect to combustion without the carbon emissions?
At best, the mechanical energy you can release by evaporating liquid nitrogen would be about its heat of vaporization, which is 5.56 kJ/mol or roughly 200 kJ/kg. (Converting this energy to useful thrust probably requires you to use the expanding nitrogen to drive a turbine that drives a fan or propeller, but that's a Simple Matter of Engineering, at least comparatively).

The chemical energy density of jet fuel is about 46 MJ/kg.

Even if we suppose the efficiency of your nitrogen engine could be a bit better than that of hydrocarbon-burning engines, this still mean that you would need to carry about a hundred times more nitrogen (by weight) than jet fuel for the same result.