There is substantial evidence that in his daring veto of the defense bill. President Carter was guided chiefly by a desire to reestablish his presidential authority rather than by fervent opposition to a costly, fifth nuclear aircraft carrier.

"The president was looking for a peg to hand his veto on," one usually pro-Carter Democrat on the House Armed Services committee told us. "The carrier was his best bet."

By asserting presidential mastery and muscling Congress to sustain his veto after Labor Day. Carter is following public-relations adviser Gerald Rafshoon's get-tough formula. But in getting tough, he has risked losing major defense items obtained as trade-offs for the carrier in the intricate congressional log-rolling process.

None of the president's military advisers, uniformed or civilian, recommended the veto. There was mirthless laughter in the Pentagon when Carter told his press conference that he had "not had a single adviser who told me that we ought to go ahead with the nuclear aircraft carrier."

By law, the president's "principal naval adviser" is the chief of naval operations. Both the present chief, Adm. Thomas B. Hayward, and Adm. James L. Holloway III, who was replaced by Hayward July 1, have been strong proponents of the nuclear carrier.

Apart from the president himself, the moving force behind the veto was White House political adviser Hamilton Jordan, along with Rafshoon - not Secretary of Defense Harold Brown.

That came out in Brown's private talks with congressional military specialists, sounding out sentiment before the veto. The defense secretary made clear he had not proposed such drastic action, but that Carter seemed determined on it.

Talking to one friendly congressman, Brown showed this was politics, not defense. He speculated whether the best way to defend the veto would be opposition to the nuclear carrier or opposition to cuts in research and development and in readiness funds. As it turned out, Carter used both arguments, emphasizing the carrier.

Politics showed irself when one congressman warned Rafshoon the veto might make the president look anti-defense. Rafshoon's answer revealed how clearly the political tactics had been developed: Don't worry; the president can deal with that in the veto message. Deal with it he did by calling Congress anti-defense.

Ignored by Rafshoon and Jordan was the effect of the veto on the delicate log-rolling needed to produce a defense bill. Although the veto probably will be sustained, writing a new defense bill will be no easy task.

A case in point is liberal Democratic Sen. Gary Hart of Colorado, an Armed Services Committee member highly skeptical of big nuclear carriers. Hart agreed in a trade-off with conservative Republican Sen. Jesse Helms of North Carolina to support the nuclear carriers in return for Helms's backing of a new generation of small carriers favored by Hart.

One day after the veto, Hart wrote all senators urging an override of the veto with this argument: "The Congress produced a carefully crafted, logical and progressive conceptual approach to the question of the future of the carrier. The veto destroys this achievement and puts us back on the treadmill of the carrier question - with no solution in sight."

Routine trade-offs, spun into a seamless web, are at the heart of the congressional defense-budget process. That explains why vetoing a major defense bill is so rare that it has not been tried in this century. In his dramatic effort to show himself a commander-in-chief who truly commands, th president ignored that record for the gamble of large political gain.

For now, however, the president is less concerned with putting the defense bill back together than with mobilizing public opinion behind his argument that he, not Congress, is the staunch fighter for national defense. That was the message Aug. 23 when 200 prominent businessmen were summoned to the White House for enlistment in the anti-carrier crusade led by Vice President Walter Mondale.

Results were mixed. One executive was puzzled that the White House expected hin to accept Mondale's word on faith against that of Sen. John Stennis (D-Miss.), veteran chairman of the Senate Armed Services committee. "They're crazy if they think I'm going to tell Sen. Stennis he's wrong," the executive told us.

No such national campaign was started against the carrier until after the defense bill was sent to the Oval Office. That only reinforces suspicions about the president's veto motives.