Noncommutative Harmonic Oscillator at Finite Temperature: A Path Integral Approach

Recently, there has been an immense amount of challenge devoted to the subject of noncommutative space-time. Although, the idea of noncommutating space-time coordinates is an old proposal [1], the recent discoveries in string/M theories were the main source of renewed interests in the subject [2]. In particular, much work is dedicated to study the noncommutative version of the quantum field theory (see for example [3] and references there in). In noncommutative field theories one replaces the space-time coordinates xμ with operators x̂μ , which do not commute with each other, i.e.