First off, let's make one thing completely clear:
Star Wars if fantasy. It has nothing to do with science.
Now that we've got that out of the way, I was sitting around, thinking, when I started thinking about lightsabers. Obviously there are a lot of problems with them. They just can't work. However, I did think of a way to make something that looks almost identical, works the same, and actually has some science fiction BS behind it.
The saber itself has two main parts: The hilt, and the blade. The blade is a device which exudes gelatinous metal antimatter at a constant rate as long as it is turned on. The blade also contains a magnetic strip down the middle, which controls the density of the jelly. As we know, when matter and antimatter collide, it creates energy. This energy then gives off the light and buzzing sound that we know from the lightsabers.
On top of that, the creation of energy likely has an electric discharge. This would travel down the jelly and into the hilt, where it would be received and recycled.
The hilt itself would contain a tiny fusion reactor/battery, creating the necessary power to generate the antimatter. The antimatter would be generated by converting the waste from the fusion reaction as it is piped up to the blade. There would be a slot around the core, in which the blade can retract while not in use.
There are a few downsides to doing this, though:
1. The user would probably be exposed to radiation while using the saber.
2. There is still a power limit, as you would eventually have no more energy inside the fusion batteries.
3. The blade is not instantly drawable. There would be about 1 to 2 seconds of delay at least before the saber would be out and usable.
4. If the hilt were to be cut, there would be a loss of containment and likely an explosion.
And the last, biggest problem with all this is:
5. It's still not possible.