The independence of this small Central American state last month has brought new security worries to Washington with the Reagan administration apparently fearing that the new nation could become another springboard for revolutionary activities in the convulsed region.

While informal conversations have already been held, in the coming weeks the U.S. and Belize are expected to begin formal talks about U.S. security assistance, involving both military training and equipment sales, sources from both governments said.

One U.S. official said he expected the U.S. commitment to Belize to be "significant, not perhaps in Washington terms, but by Belize standards, yes."

To security analysts looking at this tiny former British colony on the edge of Central America, Belize is being born in the eye of a storm.

The peaceful democracy of 145,000 people lies beneath part of the vast rain forest that covers much of northern Central America, and it could be easily turned into a guerrilla hideout and clandestine arms route. Revolutionary wars are going on in neighboring Guatemala and in El Salvador.

At the same time, Guatemala's rightist military regime continues to assert its longstanding claim over the territory. Even on independence day, Sept. 21, as five heads of state and government and dozens of other foreign envoys were attending the ceremonies here, Guatemala sent a military plane strafing the border. In response, one of Britain's jet fighters, stationed here to defend Belize, scrambled and showed its guns along the same route.

But from the point of view of Washington, which hopes to dissuade Guatemala from doing anything more than just snarl at Belize, the danger lies on the left. Both the U.S. and Guatemalan governments share the fear that a helpless Belize may, even unwillingly, be used as a haven for Guatemalan guerrillas and Cuban arms deliveries.

"You bet there is concern in Washington about security here," one U.S. analyst said. "Belize is vulnerable. It has unpatrollable jungle borders. The Guatemalan guerrillas are getting stronger, and Cuba wants to expand in Central America."

Quoting CIA sources, American press reports recently claimed that weapons were already passing through Belize for El Salvador's insurgency as a result of U.S. pressure to cut down the flow via Nicaragua. But a top British official here emphatically denied this, saying, "there is not a shred of evidence" to support such a claim.

But Belize, the size of Massachusetts, nonetheless presents Washington and London with a multifaceted policy dilemma for which there is no simple answer.

Britain wants to pull out its nearly 1,800 troops and equipment costing about $40 million per year. It has said it will stay for an "appropriate" time, but, beyond fulfilling its colonial responsibilities, London foresees no security interests in the area. British officers are presently training Belize's defense force of 700 men, half of whom are volunteers.

Yet the British wish to leave comes at a time when the United States perceives a heightened security interest in the Caribbean basin. "The irony is that the government most interested in having the British stay is the U.S. It cannot simply put troops here as a buffer the way London has," one Western analyst here said.

The policy quirk for Washington is that on the one hand it has supported Belize's desire for independence and pressed Guatemala to negotiate a treaty, which is still not final. But the same support speeds up the departure of the British troops.

On the other hand, Washington has wanted to bolster the Guatemalan Army, which is facing a growing leftist guerrilla threat. U.S. policy makers have said privately they are somewhat constrained as long as the British troops are theoretically up against Guatemala's largely U.S.-trained Army.

Washington refused a Guatemalan request three years ago for U.S. F5 fighters, which, while not suitable for guerrilla warfare, would be a match for the four British Harrier jets here.

More recently, according to a Belize Cabinet member, the United States has sought to make a deal with Guatemala. Last November, just after President Reagan's electoral victory, this Cabinet member said, a State Department official told Belizean Prime Minister George Price, "We have told the Guatemalans it will be easier for us to rearm them if only they would drop their claim over Belize's territory and settle for economic benefits."

Since then, Guatemala has entered negotiations for a treaty, and in June the Reagan administration sidestepped human-rights considerations in U.S. law and approved a $3.2 million consignment of U.S. military trucks and jeeps to Guatemala.

But there are indications that the United States is holding back further sales to retain leverage. One senior State Department official suggested Washington not only wants Guatemala to be more cooperative in reaching an early settlement with Belize but it also wants to press the repressive military regime into reforms much as Washington did in El Salvador.

Top British officials here declined to spell out how long their troops will remain in Belize. One option, Belize officials say, is a British-U.S. agreement to keep London's troops here until Guatemala emerges from its rapidly escalating civil war. Another would be to seek a joint defense force, against Guatemala's threat as well as against guerrilla incursions, put together by members of the Commonwealth.

The Belizeans say they are aware the turmoil around them could easily force them from London's arms into Washington's. "We would accept U.S. equipment and training abroad," said one senior official, "but the thinking in the government is that we don't want U.S. military advisers stationed here."

"We like to think of ourselves as a little Costa Rica or a little Switzerland without an army," said a Cabinet minister.

British officials here say there is no need for any great security flap in Belize. They argue the country is too much out of the way, the terrain is too difficult and Guatemala has enough jungle of its own to serve as guerrilla hideouts.

British helicopters regularly patrol the border and the one road that cuts across Belize to Guatemala. In the south, a company of Gurkhas covers the rivers and the five jungle trails between the two uneasy neighbors.

Their only reports, a British military spokesman said, are of a fair amount of traffic of Mayan Indians who flee the Guatemalan Army raids in the villages where guerrillas operate and where many civilians have been killed by Guatemalan military and rightist death squads.