ITS HARD TO BE a statesman in a world where unemployment is high and hopes for rapid improvement are vanishing. Today President Carter flies off to London where, like most visitors, he will discover that current anxieties run much deeper than in the United States. In this country, the only real question is the rate at which things will improve. But in Western Europe there is an undercurrent of concern about the political effects of prolonged stagnation.

The men who head Europe's governments are under rising pressure to defend the narrowest versions of national interests. The great visions of common purpose, worked out during the long boom of the 1960s, have been put away in mothballs. Hard times, now as always, are divisive.

Mr. Carter is the newcomer in this tight little group of seven - two North Americans, an Asian, four Europeans - who speak for the world's great industrial powers. The other six are likely to regard him a bit quizzically. When the planning for this meeting began, he was firmly on the side of the countries with big deficits who were urging the West Germans to speed up their economy and help everyone else's exports. Since then, Mr. Carter has changed his mind. He has embraced the German position, which regards inflation as the great menace. That leaves the other Europeans, particularly Italians and Britons, feeling more exposed than ever. It also leaves them more inclined to murmur audibly about the regrettable possibilities of having to discriminate against imports from their neighbors.

Mr. Carter evidently didn't realize it when he abandoned the symbolic $50 rebate, but he was marking an interesting turning point.He was backing off the American commitment to speed up business activity here and around the world. He was joining the Germans in acknowledging the great probability of low economic growth for the indefinite future. In the London talks this weekend, the other six will doubtless invite him, tactfully, to explore that somber prospect further. If the United States doesn't want to follow its customary methods of expanding the economy with devices like tax cuts and rebates, there is the German alternative. The Germans have more or less made up their minds to keep doggedly lending their surpluses back to their deficit-ridden customers in France, Britain and Italy, to keep their markets open and to avoid political collapses. Will the Americans also keep lending?

The seven men in London will have a firm grip on one central truth: It isn't the technical details that count, but rather the ultimate effects on standards of living. As Mr. Carter talks with the four Europeans, it will doubtless occur to him that all of them have two things in common. All of them are losing status at home. But none of them is under much challenge from new and interesting political figures in either his own party or the opposition. All the them have opposition, of course, but it's always the same old opposition, devoid of new ideas. It's hard to be brilliant in a stagnant economy, where everything keeps coming back to the grocery bill. Even the strongest of the four, West Germany's Helmut Schmidt, is seeing his strength nibbled away by tedious quarrels over things like the funding of pensions.

The current atmosphere throughout most of the industrial world these days is bad for political reputations. Most of the major governments are suffering a steady erosion of their status and public standing. President Carter will have achieved a good deal on this trip if he can only get the other six governments to believe that he and his administration are going to be the exception to this ominous rule. But exception or not, he will learn that much of his success now depends on theirs, and vice versa. Mr. Carter occupies a prominet place in the same boat as his six new friends.