United Nations, N.Y. — The United States will play the odd man out when the controversial Law of the Sea talks resume here this week.
As one US delegate puts it only half in jest paraphrasing Hamlet: ''We are facing a sea of troubles.''
A United Nations treaty governing the world seas is expected to be concluded some time in April, but the US is unlikely to put its signature to it.
The nations of the world have been working for several years now on a form of world government for the oceans, which comprise nearly three-quarters of the earth's surface.
The proposed Law of the Sea treaty, which would attempt to settle the question of who owns the oceans, would also determine such things as the territorial and fishing limits of a country's coastline. It would also give the ships of the world the right to pass through important international waterways like canals and straits.
Leading experts consider the impasse now existing between the US and the so-called ''Group of 77'' (now numbering 120 developing nations) to be unbridgeable.
The US wants to reopen the negotiations on a number of major points, including seabed mining. It will present a 43-page list of demands including:
* A demand for a seat on the 36-member Council, the decisionmaking body which governs seabed mining.
* An objection to the ''review conference'' to take place 20 years from now. It could rewrite the treaty.
* A refusal to accept the clause governing the transfer of technology. It calls on ocean mining companies to furnish the international community with the same technology that companies use, thus providing third world countries with means to do their own mining.
* An objection to the quantitative limits placed by the draft on ocean mining production in order to protect the economies of countries who are dependent on producing similar minerals on land (Zaire, Chile, Canada, Peru, Colombia, Zambia , Gabon).
On the first two points the US may get its way, according to informed sources. But the ''Group of 77'' is not about to concede the other, more substantive points.
''The present transfer of technology clause represents the bare minimum of what is acceptable,'' says one key third world delegate.
Others declare that many developing countries feel insufficiently protected as it is under the present production limitation clause. Furthermore, almost to a single man the ''77'' agree that there is no reason for them to hand back to the US concessions obtained from it in exchange of concessions of their own. ''The US got what it wanted at a price and now refuses to pay,'' says one West European delegate.
Some of the principles involved in the treaty do not fit in with the US heritage of free enterprise. Furthermore, US officials fear that a Government of the Sea would set a precedent and open the door to similar devices for other commodities. Finally, they fear that the US Senate would not adopt a treaty containing provisions obliging private companies to give away their technological know-how.
Some highly placed US officials favored dropping out of the treaty talks altogether. But despite a major diplomatic effort by the Reagan administration to line up the support of other industrial nations behind the US position, Japan , France, Canada, Britain, West Germany have remained aloof and have refused to join the US. These countries have made it clear that while they also favor some changes in the draft, they basically remain committed to the Conference. France, West Germany, Great Britain have not agreed, as the US had hoped, to sign a Reciprocating States Agreement on seabed miningn with the US which would have amounted to a separate treaty.
This has forced the US to reenter negotiations. Furthermore, the ''77'' claim to have called the US's bluff regarding the possibility that US mining companies , after having received exploration licenses under existing US laws, would by themselves mine the potato-sized nodules of minerals which lie on the ocean bed. Indeed it has become clear that investors will not finance seabed mining operations without a treaty or with an treaty which the US would not have signed.
The US delegation led by Assistant Secretary of State James L. Malone reportedly has no negotiating instructions and no flexibility. Many delegates are convinced that the Reagan administration does not seek to negotiate seriously but simply hopes to drag the talks on. The ''77'' are in a testy mood. The president of the Conference, Singapore's Tommy Koh will not allow the negotiations between the US and the ''77'' to go beyond a period of three weeks. ''After that,'' he says, ''with or without the US on board, the officers of the Conference are determined to adopt a treaty in April.''
Other industrial nations which have the money and the technology to engage in seabed mining will work hard to bring about a compromise. ''We don't want to have to choose between turning our back on the US or on the '77' '' says a European representative. Ultimately however, one by one, they are expected by informed observers to join the world community and sign a treaty even without the US. The US could, of course, sign the treaty in a few years. Without the US, a Law of the Sea Treaty would be meaningless in the sense that the ''77'' would not get the benefits from ocean bed mining. But US metal-hungry companies could not explore the nodules either. ''It would be a stalemate but one that would make the US more uncomfortable than the '77' '' says one Latin American ambassador. He adds: ''The treaty is needed now, in order to fill a juridical void.''