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We study the effects of many-body interactions on the interference in aMach-Zehnder interferometer for matter waves of ultracold Bose atoms. Afterswitching off an axial trapping potential, the thermal initial wavepacketexpands, and subsequently interference fringes may be observed in a circular 1Dtrap. These are computed for axial harmonic or $\delta$-function traps, and forinteraction strengths from the Thomas-Fermi regime to the Tonks-Girardeaulimit. It is shown that many-body correlations in a realistic setup destroyinterference to a large degree. Analytical expressions allowing to infer theobservability of phase coherence and interference are provided.Comment: 7 pages, 4 eps figures, final version, to be published in PR

Destruction of interference by many-body interactions in cold atomic Bose gases