As far as I understand it, the non-zero vacuum energy attributed to a quantum field (at each point in space-time) is precisely due to the Heisenberg uncertainty principle (and the fact that the energy of the quantum field at each space-time point is quantised). Accordingly (in order to satisfy the Heisenberg uncertainty principle) the value of a given quantum field will fluctuate at each space-time point such that its value is not precisely determined. In this sense, the fluctuations of the quantum field (due to the uncertainty principle) can be interpreted as the source of its vacuum energy. What particularly confuses me, if this is the case, is how a fluctuating value of the field results in a constant vacuum energy (or is the point that the average, i.e. expectation value of the energy due to these fluctuations a constant?) My question is, is this what people mean when they speak of quantum fluctuations and vacuum energy? Are the two intrinsically related (a result of the Heisenberg uncertainty principle and quantisation), or have I completely misunderstood things?