Is Jake Barnes from The Sun Also Rises a representation of Hemingway's life?
Yes, according to Enotes Hemingway bibliography:
In 1925 he began work on The Sun Also Rises which reflected his life in Paris among the “Lost Generation.”
In fact, Hemingway was inspired to write the novel on his 3rd visit to the San Fermin fiesta in Pamplona in the 1920s.
In terms of comparisons, both Hemingway and Jake Barnes are expatriate journalists, first in Paris and then Spain. Both suffered war wounds from the Great War (WWI), although Jake never mentions how he received the wound (Hemingway, in fact, was not a soldier but an ambulance driver). There, both Jake and Papa met other expatriates, namely Harole Leob (Cohn) and Lady Duff Twysden (Brett). It was Jake's (Hemingway's) affection for Tysden (Brett) and jealousy of Leob (Cohn) that drives the narrator.
One addition to the excellent answer above is that Hemingway had an extremely difficult time committing to a woman. He was married several times and reportedly had numerous affairs. Readers can see that same struggle in Jake Barnes. Jake seems to want to show love or affection to Brett but is unable to do so. This characteristic is typical of Hemingway's Lost Generation. They roamed around Europe looking for adventure but were seemingly afraid of committing to anything, anybody, or any country. Just as Jake is on a quest for endless adventure, Hemingway spent most of his life traveling the world literally and figuratively hunting for the his next "game."