Are hand-held high energy weapons possible via known physics?

Well, matter conversion technology takes care of the directionality.
You can convert a fraction of a gram of of matter into many, many ergs (E=MC^2).
Trick is to arrange it so the energy comes out all more or less in the same direction.
Think of laser light, or perhaps a magnetron tube, as an analogy. Directed energy output at nearly 100% efficiency.

Obviously matter -> energy conversion is the only way to meet the constraints. But how. Antimatter releases extremely high energy gamma rays in all directions. Most nuclear reactions release neutrons and gamma rays, and need a critical mass.

Off hand, the only way I can think of that might meet the constraints is aneutronic fusion. This is a series of fusion reactions that release charged particles only, that can be converted directly to energy.

Of course, the proposed fusion reactors that do this are huge…but maybe, just maybe, the conditions necessary to make fusion work could be done at the nanoscale.

Cold fusion or sonofusion would be nice, if these were real things.

How about a flywheel gun? Might be a bit tricky to aim, because of gyroscopic effects, but a diamond flywheel could have as much energy density as the same weight of kerosine - good for a few shots.

Maybe if your gun has lots of little flywheels, all pointing in different directions.

Can you clarify your constraint? I still don’t see why chemical sources are out by these conditions. It sounds like you are defining “indefinitely” as “as long as it isn’t too hot”. Why can’t a chemical energy weapon fire just as well as anything else until it gets too hot? Do you mean something different by “indefinitely”?

I mean you could fire the weapon for weeks on end if you could dispose of the waste heat. Aka the only power source that can work has to involve conversion of matter to energy.

I used the word “indefinite” to mean that no combat situation you could ever plausibly get involved in would drain the power source.

Think those “infinite ammo” blasters they have in video games, or the power source on a lightsaber, etc.

Well, I can’t operate it for days. But I’ve got a straight sword I could use for hours and still manage the waste heat.
The weapon allows killing at a distance, rapid redeployment rate, reliability of design, and to some extent, the use of a backup hand.

So really, any sort of storage device needs to start there, matching or exceeding a human. Then we can worry about matter conversion.

It would seem very likely. Chemical energy in gun powder is converted in to lethal kinetic energy but transferring that to bullets. Tazers are currently designed to be less then lethal, but can they be made to be lethal?

The problem does not seem to be the energy source, but the method of delivery. If the energy can be delivered efficiently on target it seems very possible.