Per the second amendment: A lot of people really want to be able to declare that they can own any weapon they want but then the argument absurd is always, "Well that means you could own a nuke too."
Is there any legal academic literature that supports owning any weapon except nukes?
Sure: No Constitutional rights are totally unencumbered. Even natural rights like the "right to life" are legally "infringed" through various theories (e.g., self-defense, capital punishment, warfare).
The Second Amendment has been interpreted as a right to keep and bear weapons that would reasonably be used in self-defense or in military service. You don't have to go to strategic weapons like nukes to find "reasonable infringement" of that right. For example, even though the military and even police routinely use explosives, individuals are absolutely subject to the whims of a federal regulatory agency (the BATFE) as well as state restrictions if they want to keep and bear detonators.
Also, I'm not aware of an absolute prohibition on the possession of nuclear devices by non-government entities. E.g., various government regulators oversee private entities that operate commercial and research nuclear reactors and other activities that put them all-but in possession of nuclear arms. If an individual really wanted to legally keep and bear a nuclear weapon it could probably be done with enough money and oversight. (Amendment: Except, as cpast points out in the comments, that there is a law against private possession of nuclear weapons in the U.S. Which just goes back to the broad answer to your general question: In practice there are no unencumbered rights. Constitutional "rights" might better be called things that require "strict scrutiny" and "narrow tailoring" of government infringement.)
The authority you are looking for is District of Columbia v. Heller, 554 U.S. 570 (2008).
In this judgement, SCOTUS explained limitations of the second amendment. There is extensive historical analysis, but for your purpose, this is the important clause:
[T]he right to keep arms involves, necessarily, the right to use such arms for all the ordinary purposes, and in all the ordinary modes usual in the country, and to which arms are adapted, limited by the duties of a good citizen in times of peace.
To put it short: Since nuclear weapons are unlikely to be useful for ordinary purpose usual in the US by a good citizen in times of peace, they are not covered by the second amendment.
For reasons I don't want to get into, leaning on supreme court decisions to answer this question is just a little bit off kilter.
If we use the language as used around 1792, we end up with "arms" are weapons carried and used by one individual and "cannons" for larger weapons, and "arms" are protected but there is no mention of "cannons".
Most people cannot possibly hope to carry and use a nuke without assistance, so they would fall under "cannons" ergo no constitutional protection.
