On the first day of the new year. Jimmy Carter finally got to see some of the ordinary people of the world as he arrived in India on his grueling journey halfway around the globe.

They were stretched out before him today across 19 acres of a green city mall, thousands of Indians huddled together under a brilliant sun to hear the President of the United States.

Earlier, thousands more had lined the road leading from the airport to wave at Carter, who stood in his limousine to acknowledge their cheers.

The contrast between New Delhi's openness and the tightly controlled visits to Warsaw and Tehran last week could not have been greater.

Carter arrived here at mid-afternoon from Tehran, Iran, briefly leaving the Middle East, which has come to deminate his activities and the attention of those around him during this trip.

In Tehran, the President met with King Hussein of Jordan, whose help he is trying to enlist in building momentum behind the peace negotiations between Egyptian President Anwar Sadat and Israeli Prime Minister Menahem Begin.

Following the meeting, American officials sounded generally optimistie, although they conceded that there is little immediate prospect that Hussein will become a participant in the peace talks.

"Under certain principles" Carter told reporters, "King Hussein would be ready to join the talks either directly with the Israelis or jointly with Egypt and Israel. But at the moment I think President Sadat is strongly representing the Arab position and for the moment I see no reason - I think the king agrees - for Jordan to join the talks directly."

The principles the President referred to were not clearly spelled out. One senior administration official said it is unlikely that Jordan will join the peace talks until there is an "adequate definition of the principles to govern how the Palestinian question is to be handled . . ."

After two days in India, Carter is to return to the Middle East, first for an overnight stay Tuesday in Saudia Arabia and the next day for a meeting with Sadat in Aswan, Egypt.

The President came to India - the farthest point from home during his nine-day trip to seven nations - to lend symbolic support to the restoration of democracy here under Prime Minister Maorarji Desai and to encourage what U.S. officials believe is a new Indian policy of "genuine nonalignment" between the United States and the Soviet Union.

Desai and President N. Sanjave Reddy were at the airport to greet the Carters on their arrival. Following a joint appearance at the mall, Carter invited Desai into his suite for an unscheduled meeting. An aide to Desai said later that the conversation was essentially to help the two men get to know each other and did not go into policy questions.

Carter and Desai are to meet again Monday and discuss nuclear technology issues among others. India set off a nuclear explosion in 1974 and some of its critics charged that it had violated international agreements in diverting nuclear materials supposedly acquired for peaceful use. President Carter has frequently spoken out against the proliferation of nuclear weapons.

The President will also address the Indian Parliament on the issue of human rights in a developing country. The speech, one of two major addresses planned during this trip, is being given special attention by White House officials.

The reception given Carter by the Indian was a warm and friendly greeting to country with which the President claims special ties of affection. It was by no means tumultuous or equal to the greetings some other American Presidents have enjoyed here but satisfying nonetheless, and it contrasted sharply with his first two stops on this trip.

In Poland, he met government officials and Communist Party functionaries, and in Iran, his companions were the high and mighty of the state and military and the cream of Iranian society.

The President has sought to identify his foreign policy with people like those gathered on the mall here, struggling for a better life against the weight of centuries of poverty. This made it all the more suprising that he appeared to make such little effort to inspire or move them today.

Speaking for 13 minutes (more than half of the time taken up with translation), Carter drew the most enthusiastic response from the crowd when he referred to his mother, Lillian Carter, who served as a Peace Corps volunteer in a remote region of India in the late 1960s.

The President also pushed his human rights campaign, telling the silent audience that "every human being is entitled to certain basic human rights," among them "a right to choose one's own government, a right to worship one's own God, a right to think and speak one's own mind freely . . ."

A number of small bands lined the route from the airport to the mall, and the appearance of this city showed the extent to which Indian officials went in trying to impress the President.

The crowds were by far the largest Carter has encountered on this trip, but while they were friendly, they were not particularly enthusiastic or demonstrative. The size of the crowd also fell far short of the number of Indians who turned out to greet President Eisenhower in 1959 and President Nixon in 1969.

By the end of the motorcade, in fact, there was a general impression that Carter, as a leader and personality has yet to make a significant impact on this country.

Only one small group along the motorcade route was protesting the presidential visit. When the buses carrying the press, far behind Carter's limousine in the motorcade, reached the group all that could be heard were shouts of "go back, go back."

Indian officials estimated the size of the crowd at Carter's speech at 300,000 although it appeared to be closer to 50,000 to several American reporters.

An administration official said that, if asked to the President would meet with former Indian Prime Minister Indira Gandhi, whose opposition Congress Party is in the midst of a severe rupture that is the dominant political topic here at the moment. The official said he knew of no such request from Mrs. Gandhi.