Again a highly loaded question to answer because it depends on what "you mean". I need to be clear what you are asking.
Please read:
http://profmattstrassler.com/articles-an...alse-dichotomy/Ok so lets give you my version of a formal science answer:
Energy is just some currency that an observer creates relative to them. It is the same as if you live in the USA you use dollars, if you live in Europe you use Euros. All observers ultimately agree on the conservation of their own energy currency, so there exists a conversion calculation between any two observers energy currency but it may not be a trivial calculation.
To ask me whether you can create or destroy energy is an error to me, because you are assigning "existence" to energy. In it's broadest form energy equals information which is the approach QM takes. The problem is information exists only when there is an observer and now we have a problem to discuss.
For me energy doesn't exist to be created or destroyed, it is actually the observer that is created and destroyed
Can you create or destroy matter. Well yes you can we do it all the time and it occurs naturally in radioactive decay processes. However that probably isn't what you meant, what you were really asking is can matter be built from nothing or perhaps pure energy or go back to those things, depending on what lead you to the question in classical physics.
From our discussion above on energy it could not build anything as it doesn't exist except as an accounting concept to some observer. So you certainly can't build matter from energy. So can you build it from nothing or make it go to nothing, well that is going to depend how you define nothing.
From my previous post the only theory that can describe matter creation and annihilation is QFT and a field is neither energy nor matter, it is something else and Matt nicely summed it up
What do “fields and particles” have to do with “matter and energy”? Not much. Some fields and particles are what you would call “matter”, but which ones are matter, and which ones aren’t, depends on which definition of “matter” you are using. Meanwhile, all fields and particles can have energy; but none of them are energy.
When you had gone thru QFT, I tried to get look at the concept of the field and what the hell it is.
Matt stated it this way
The stuff of the universe is all made from fields (the basic ingredients of the universe) and their particles. At least this is the post-1973 viewpoint.
So if the universe is built of fields what I really need from you is how you define what I call fields. Given that I can possibly give you an answer we will both see as logical.
I have a religious friend who whenever anyone says they created something from nothing says, "GOD asks that you bring you own fields please, and stop using his".
Sorry I can't give a shorter answer but I need to be very clear what you are asking.