We analyze 7.3 years of ANTARES high-energy neutrino and Fermi LAT {gamma}-ray data in search of cosmic neutrino + {gamma}-ray ({ u}+{gamma}) transient sources or source populations. Our analysis has the potential to detect either individual { u}+{gamma} transient sources (durations {delta}t < 1000~s), if they exhibit sufficient {gamma}-ray or neutrino multiplicity, or a statistical excess of { u}+{gamma} transients of lower multiplicities. Treating ANTARES track and cascade event types separately, we establish detection thresholds by Monte Carlo scrambling of the neutrino data, and determine our analysis sensitivity by signal injection against scrambled datasets. We find our analysis is sensitive to { u}+{gamma} transient populations responsible for $>$5% of the observed gamma-coincident neutrinos in the track data at 90% confidence. Applying our analysis to the unscrambled data reveals no individual { u}+{gamma} events of high significance; two ANTARES track + Fermi {gamma}-ray events are identified that exceed a once per decade false alarm rate threshold ($p=17%$). No evidence for subthreshold { u}+{gamma} source populations is found among the track ($p=39%$) or cascade ($p=60%$) events. While TXS 0506+056, a blazar and variable (non-transient) Fermi {gamma}-ray source, has recently been identified as the first source of high-energy neutrinos, the challenges in reconciling observations of the Fermi {gamma}-ray sky, the IceCube high-energy cosmic neutrinos, and ultra-high energy cosmic rays using only blazars suggest a significant contribution by other source populations. Searches for transient sources of high-energy neutrinos remain interesting, with the potential for neutrino clustering or multimessenger coincidence searches to lead to discovery of the first { u}+{gamma} transients.
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