ACCORDING TO the "big bang" theory, modern jazz began with the explosion of be-bop in the early '40s. The sudden expansion of improvisation possibilities sent jazz hurtling in dozens of different dirctions. Everything happened so quickly that Charlie Parker and Dizzy Gillespie's be-bop was soon eclipsed by Miles Davis' cool and cool in turn by John Coltrane's free jazz.

Now, during jazz's greatest popularity in 20 years, there is also currently a movement back to the first cause, to be-bop itself.

The original records are being reissued (it seems as if every minute of music Charlie Parker ever put on tape has been released or rereleased in the past couple years). The original artists are returning from the obscurity of American bars of European exile. And a whole new generation of musicians has arrived playing the augmented chord changes of be-bop.

Undoubtedly, the leading figures of the be-bop renaissance are Dexter Gordon and Woody Shaw. They have been winning jazz poll after jazz poll and both have been rewarded with unusual support from a major label. Their latest records -- Gordon's Manhattan Symphonie (Columbia JC 35608) and Shaw's Stepping Stones (Columbia JC 35560) -- are the most conspicuous examples of be-bop's resurgence.

Be-bop is a player's music. It doesn't have the restrictive charts of big band jazz. It doesn't push instruments to their limits like much avant-garde jazz, nor does it transform their tonal qualities through electronics. Be-bop gives musicians the best chance to show what they can do at the heart of an instrument's sound.

Few can do as much on the tenor saxophone as Dexter Gordon. Each note has its own birth, growth, decay and death, and Gordon traces each stage with supreme control. His breath pours through his saxophone like sand into an hourglass, filling each note to its brim with a vibrating lushness.

On his triumphant tours since his 1976 return from European exile, Gordon has recaptured the rich playing of his European albums for Blue Note and Inner City. But for some strange reason, he hasn't yet conveyed it on his recent American albums.

Manhattan Symphonie is built around showcases for the saxophone: the lyrical romanticism of "As Time Goes By," one of Coltrane's best melodies, "Moment's Notice," Donald Byrd's "Tany" and "Body and Soul" -- the song Coleman Hawkins used to bring the tenor sax to prominece in jazz.

I've heard Gordon's quartet play all these songs live since he returned, and the numbers were often overwhelming. These studio recordings seem lackluster by comparison. Either Gordon is uninspired without an audience or the studio microphones aren't picking up the resonating edge of his playing.

The edge is certainly missing on the record. Gordon's solos are as quick and fluid as ever, but the sense of irresistible power is missing. His playing on "Body and Soul" is disappointingly straight. His version of "Tanya" on One Flight Up (Blue Note BLP-4176) was a classic because the catchy theme built to an impressive climax. On the new version, the payoff never comes.

By contrast, another European jazz exile, Johnny Griffin, is captured at his best on a double album, Live in Tokyo (Inner City IC 6042-2). Like Gordon, Griffin was well-respected be-bop tenor saxophonist who found his skills better appreciated in Europe than here. Now a resident of Holland, Griffin's September 23 Carnegie Hall concert with Gordon was the former's first American appearance in 15 year.

Live in Tokyo is from a 1976 concert and features four long numbers, averaging 18 minutes each, and one shorter piece. On the extended numbers, Griffin lets loose a shower of stunning solos. Even his whispered passages have a resonating power.

He slips without effort into crescendos that scrape against atonality before they are resolved into immensely satisfying harmonies. His sense of timing is undiminished since his days with Art Blakey's swing and Thelonius Monk's shifting rhythms.

But like Gordon's record, Griffin's album is built around performances rather than composition. Both albums rely on standards and loose original progressions to show off the glory of be-bop playing. But audiences will soon tire of the be-bop renaissance if it proves to be nothing more than a revival. The genre needs new music and new approaches if it's to stay alive.

There's lots of room. The original be-bop explosion happened so quickly that many possibilities were never fully explored. One of the motivations for returning to this style is to pick up on those unseized opportunities. Woody Shaw is doing just that.

Shaw (who has given up the trumpet to play the related cornet and fluegelhorn exclusively) may not have the sheer technique of a Gordon or Griffin, but he has brought a vitally fresh dimension to the be-bop tradition. The common impulse is to expand be-bop by giving each player more room and by extending the range of each instrument. Shaw has chosen instead to thicken the music by having his muscians play in close relationship to each other and by giving each piece a dramatic shape.

His latest album, Stepping Stones , is the best example yet of what he's doing. As a composer on three of the five numbers, his works are not simply a string of solo variations on a theme but a dramatic whole. An emotional momentum is established, complicated, and finally resolved.

As an arranger, he gives soloists enough room to stretch their imagination but also enough direction to keep them from digressing. And rather than lying back, the other musicians push each soloist with secondary solos. Shaw's arrangements are unusually dense because everyone in his quintet plays a significant role. Drummer Victor Lewis' superb cymbal work and subtle fills thicken the texture everywhere. Carter Jefferson follows Shaw's pinpointed brass themes with blustery reed responses.

As a bandleader, Shaw has guided his younger musicians into the tightest unit in jazz today. Their first album for Columbia, Rosewood , was recorded last December and was recently named album of the year in the Downbeat reader's poll. A May concert in Baltimore showed them much improved over Rosewood , and Stepping Stones -- recorded at New York's Village Vanguard in August -- is tighter and brighter still. On "Theme for Maxine," which appears on both albums, the ensemble transitions are much sharper and the back-and-forth responses more intuitive on the second version. If Shaw can keep pianist Onaje Allan Gumbs, bassist Clint Houston, Jefferson and Lewis with him for a couple more years, they'll not only return be-bop to its former heights but also take it places it's never been before.