July 29, 1984

The Government began carrying out the second stage of its peace plan today, sending bulldozers and earthmovers to rip out the remaining earth and sandbag barricades of the so-called Green Line between the Moslem and Christian sectors of the capital. The immediate purpose was to neutralize the line, a 10-mile stretch of shattered buildings, barricades, wrecked cars and snipers' nests that separated Moslem West Beirut from Christian East Beirut. Units from the Third Brigade, made up of Moslems and Christians, are to take up positions along the line. The Moslem Sixth Brigade is to remain in West Beirut and the mostly Christian Fifth Brigade is to stay in East Beirut. Now a United Lebanon' ''There is no longer East nor West Beirut,'' the army commander, Brig. Gen. Mohammed al-Hajj said early this morning. ''It's now a united Lebanon with a united capital.''

Frank Corsaro has been staging operas of all kinds since 1958, but he was long reluctant to tackle ''Carmen.'' Not only did he find its form and story problematic, but its accumulated production traditions seemed to have created an impenetrable carapace around the work. ''Talk about warhorses!'' exclaimed the director recently. ''This is The Warhorse . It's an opera and it isn't an opera - it's sort of a French opera-comique and a zarzuela. It's story line is so tired, with the gypsy vamp and the garrisons, and with all those hit tunes it really seemed to belong in the old 'Vagabond King' operetta tradition.'' Mr. Corsaro is fascinated by the recent resurgence of interest in ''Carmen.'' But the rash of films and the much-discussed Peter Brook adaptation that played last season at the Vivian Beaumont Theater haven't addressed his problems with the work.

IF the James River Corporation has X number of 14-ounce soda cups in its warehouses, how long will they stay there before being transported to a Wendy's restaurant? Joe Hajla, an algebra teacher at New Canaan High School, spends the school year posing such questions to his students. This summer, Mr. Hajla himself has been assigned the problem. The question is part of a data base project he has undertaken in an experimental program to find useful summer work for Connecticut public school teachers, who often resort to such jobs as construction or house painting to supplement their salaries.

The Summer Games of the XXIII Olympiad, the first Olympics produced by private enterprise, began today under a brilliant afternoon sky with lavish opening ceremonies and a cast of thousands. Culminating the emotional ceremonies, Gina Hemphill, granddaughter of Jesse Owens, who won of four gold medals in the 1936 Olympics, ran out of a tunnel in the Los Angeles Memorial Coliseum, holding aloft a flame brought from Greece. 6 Years' Work for 16 Days Miss Hemphill ran one lap around the Coliseum track and handed the torch to Rafer Johnson, the American gold medal winner in the 1960 Olympic decathlon. He carried it up a staircase at the opposite end of the Coliseum and lighted a flame above it that is to burn throughout the 16 days of the Summer Games. After almost six years of preparation, this city, bedecked with bunting and finally gripped by Olympic fever, seemed ready for the Games, which have drawn more than 7,000 athletes from 140 countries. The number of countries competing is the largest in Olympic history, despite the decision by the Soviet Union and most other Communist countries to withdraw.

White Plains is a boom town by anyone's standards, with both commercial and residential development currently at its peak. According to David Ornstein, commissioner of the city's Planning Department, some developers have put their efforts into high-rise residential, hotel and office projects in the bustling downtown area, but new construction has also spread out into other neighborhoods.