A traffic policeman put a parking ticket on a car on Hamra Street, West Beirut's main thoroughfare, one day last week, and nobody shot at him or even argued.

That simple scene of everyday city life elsewhere in the world has not been witnessed here for years, because the few traffic police who did walk the streets did not dare risk their lives to give a ticket.

Policemen back to work was just one sign of the return of government authority and normalcy to this war-weary capital, where until only a few weeks ago militia gangs executed their own law in the tradition of the Old West.

Battered by three months of steady Israeli bombings and seven years of civil war, West Beirut has made a startling recovery in just the past two weeks, as the Israelis have withdrawn and the multinational peace-keeping force has established its presence.

Streets have been cleared of war rubble and mountains of uncollected garbage with amazing rapidity. Water and electricity are back in most West Beirut quarters now for 24 hours a day. The international airport is bustling anew, restaurants and nightclubs are coming back to life, and the Ferris wheel on the oceanfront corniche is turning once again.

The Green Line marking the division between the Moslem western and Christian eastern sectors may still exist psychologically, but more and more Beirut residents are crossing to visit each other's sector.

A West Beirut reporter who visited the restaurant Le Retro, favorite haunt of the Christian eastern sector's beautiful people, was amazed to see many of her friends there last night. Later, she told of crossing the old Green Line at midnight without the slightest problem, a trip once so certain to draw sniper fire that none dared brave it.

Now, the only way a newcomer to this city would know where the Green Line once ran is by the abandoned and shell-gutted buildings across the capital's old downtown center.

At the very center loom the ruins of Martyrs Square, whose sandbagged storefronts on each side served as gun emplacements for Moslem and Christian militiamen striving to blast each other out for seven years.

Today, residents from both sides wander through the square on outings, taking pictures of the horrendous sight to keep as mementos of the civil war in family photo albums.

Credit for the city's rapid return to normalcy must go partly to the multinational peace-keeping force, which has provided an umbrella under which the government and Army have begun a massive clean-up operation to rid the capital of arms depots, unwanted aliens and slums.

If in the process thousands of Lebanese war refugees and squatters are being made homeless and hundreds of Palestinians and other aliens deported or mistreated, most middle- and upper-class Beirut residents, Moslem and Christian alike, could not care less. In their minds, the Palestinians and squatters were the cause of much of the city's woes and degradation over the past seven years, and there is no love lost on them today.

The presence of American, French and Italian troops is only part of the story of this resilient city's surprising recovery, however.

Another part is due to the activities of the multi-millionaire Lebanese businessman Rafik Hariri, who has donated more than $7 million to clean up the city. Hariri's company, Oger-Liban, has provided 300 trucks and bulldozers and 700 workers to haul away the rubble and garbage, repave torn-up streets and spruce up West Beirut.

Hariri, a tycoon and philanthropist from Sidon who made his fortune in Saudi Arabia, has also let it be known that he plans to buy 450 street-corner containers for garbage to get the municipal sanitation service, out of order for seven years, working again. Right now, West Beirut residents simply toss garbage bags into the streets where eventually they are burned, scattered or picked up.

However, clearing the city's streets of war rubble is just part of the problem. West Beirut is dotted with tall apartment buildings whose sides have been sheared off by bombs and rockets or have gaping holes. Even so, residents or squatters are often living in them, walls or no walls.

There are reported to be 128 buildings of four or more stories that are in need of demolition in central Beirut as a result of the Israeli bombings. In addition, there are hundreds of others along the Green Line totally ravaged by seven years of sectarian warfare, leaving a monumental housing problem in the western sector, with thousands of Lebanese needing new homes. Even so, the government has decided to raze hundreds of dwellings belonging to squatters in the area around the airport, thereby adding thousands to the list of homeless.

Another reason for the city's rapid recovery from a summer of war, perhaps the main one, is the apparently undying industrious spirit of the Lebanese, who began putting their homes and shops back together the minute bullets stopped flying.

In some instances, shops whose fronts were blown away, are already back in business on West Beirut's Corniche Mazraa and along the Green Line. The Armenian jewelers and Hamra Street money changers -- bellwethers in good and bad times here -- are flourishing once again.

The country's vital economic life signs seem to be beating strongly again, too. The value of the Lebanese pound is already back to its pre-June level against the dollar and even somewhat stronger. Beirut banks are said to be bulging with liquid assets, amounting to more than $9 billion in deposits.

There is much discussion now about war rehabilitation and reconstruction but no clear estimate of the needs or cost so far nor any indication of where the money will come from.

Mohammed Atallah, chairman of the State Council for Development and reconstruction, has said $12 billion will be needed just to cover war damages, $9 billion of which will have to come from Arab and other international aid donors.

Peter McPherson, the administrator of the U.S. Agency for International Development, said at a press conference here today that he thought this was far too high an estimate. "Several hundreds of millions of dollars are needed, not billions, to get the infrastructure functioning again," he remarked, but, he added," if you include everyone's home, it quickly becomes billions of dollars." He said AID was providing $110 million in emergency war relief and rehabilitation aid.

Local press reports say the European Community has pledged more than $100 million as well and that the government will try to raise $500 million more in loans from Western European banks.

At the same time, they are pointing out that only $300 million of a total $4 billion pledged in aid during five years by the Arab countries in 1979 actually has been handed over to the government.

Thus, Lebanon seems to have the potential domestic resources and foreign assistance to get back on its feet, provided the peace and prosperity this capital has begun to taste these past two weeks continue-- but many Lebanese are holding their breath, as if the present good times are not for real.