Just a few months after its stunning victory against Quebec separatists who threatened to split Canada down the middle, Prime Minister Pierre Trudeau's Liberal Party now faces another front in the battle for national unity -- the Canadian west.

The immediate issue between the central government and the four westernmost provinces is oil. For more than a year, central and provincial leaders have negotiated over which has the right to set prices for western Canada's petroleum resources.

The negotiations are expected to come to a head Thursday, when Trudeau meets in Ottawa with Alberta Premier Peter Lougheed, a tough adversary whose province produces the bulk of Canada's oil exports and who has shown no past hesitation in hoarding provincial resources for Alber tans.

Promised a hefty oil price increase by the Tories, before their government fell on a parliamentary budget vote last year, the oil-producing provinces want as good a deal from the Liberals now.

Oil prices within Canada are now less than half the average world price, running at about $12.90 a barrel, and Lougheed is a man who sees riches as fleeting -- particularly oil riches. Already, he has insisted upon establishment of a Heritage Fund, a rainy-day kitty for his province with assets from oil royalties and investments last reported at $6.5 billion.

Just before the 1979 provincial election, his party distributed $1 billion to Alberta's municipalities, which works out to something over $500 a head for every man, woman and child in Alberta.

The legal ground on who sets the prices is muddy. In Canada, the provinces clearly own their resources. But once the oil crosses a provincial or national boundary -- the Canadian equivalent of interstate commerce -- the federal government claims the right to set the price.

It is conceivable that the producing provinces, rather than sell at a lower price than they see as fair, might turn off the tap. Ottawa argues it could then invoke emergency powers to force the production of oil, a strategy that could lead to long court battles and political trouble for Trudeau.

Looming large over the oil tanks are Trudeau's hopes that, before finishing his political career, he can bring national unity and national identity to Canada with a new constitution. That will require the cooperation of all 10 provincial premiers -- something that may prove impossible for the west if Trudeau imposes an oil-pricing solution they find unacceptable.

Thus Trudeau's goals may be impossible to achieve, and his mission to truly unify Canada for the first time in its 113 years of existence could rip the country apart instead of binding it together.

Now 60, and having held power almost continuously since 1968, Trudeau's instinct has been to force the issues, while Canada's genius has been to avoid them with almost a congenital inability to agree.

Canada took until 1965 to adopt the maple-leaf flag and until this year to make "O Canada" the official anthem. In place of a constitution, Canada is ruled by the British North American Act of 1867, and Trudeau points out that no other independent nation has to go to another country's parliament to get its constitution amended.

While the oil issue is now the focus of the problems between the Liberals and the provinces, it is by no means the only conflict. Although Trudeau -- fluent in both official Canadian languages, English and French -- was well-equipped to take on separatists in Quebec, his home province, he is ill-equipped to do battle on the westernfront.

Here in the great sweep of land from the Ontario-Manitoba border, north of Minnesota and across the Rockies to the Pacific, Trudeau's bilingualism is a liability.

Canadian Frenchness is often seen as a petty annoyance -- as for westerners finding the wrong side of package labels facing them on supermarket shelves.

Trudeau's Liberal Party is widely mistrusted as favoring industrial central Canada, Ontario and Quebec over the interests of the west with its farming and ranching, forestry and hydrocarbon.

Here federally imposed freight rates, for example, are seen as propping up central Canada at the cost of the real producers, the west.

The Canada West Foundation, a Calgary-based think tank, recently reported results of a poll indicating that 71 percent of residents in the four western provinces of British Columbia, Alberta, Saskatchewan and Manitoba believe that the west "usually gets ignored in national politics because the political parties depend upon Quebec and Ontario for most of their votes."

About half of those polled believed that western Canada has more in common with the western United States than with the rest of Canada and that the western provinces have sufficient resources and industry without the rest of the country.

The population of the four provinces is not quite a third of Canada's 24 million people.

In the February election, only two Liberals were elected to Parliament from the four western provinces, and both of them were from the easternmost of the four -- Manitoba.

Other than in hostility toward Trudeau, the Liberals and the federal capital of Ottawa, the west is hardly monolithic. The provincial governments are run by three different parties with the Liberals conspicuously excluded.

Several weeks ago, the Liberals ventured to show the flag in the west by holding a national policy convention in Winnipeg, Manitoba, about 100 miles this side of the Ontario border. Rather than adopting a conciliatory stance, however Trudeau was combative, taking a tough line on both domestic prices for crude oil and the sorting out of provincial-federal responsibilities in a new constitution.

He also has been scornful of a suggestion put forward by the leader of the Progressive Conservative, or Tory, opposition, former prime minister Joe Clark, that Canada is a "community of communities."

"We believe in the necessity of a strong central government," Trudeau said in language likely to cause equal uneasiness in the west and in Quebec. "If you weaken the center, you weaken Canada.'

So far, separatist sentiment apparently has not taken root in the west despite the formation of a couple of small movements that advocate formation of a new country and establishment of a party that proposes union with the United States. Indeed, the western poll indicated that 88 percent of western respondents favored remaining part of Canada despite their negative feelings.