mmh.. you should consider the Unruh effect.

In relativistic regime the zero point energy appears increased.

Hope this has helped.

Classically one would expect that vacuum has a zero energy. It does not matter if it is a relativistic or a non relativistic description. Therefore yes, in a classical relativistic theory vacuum can be so chosen that vacuum energy is zero, but in a quantum field theory vacuum energy is the sum of an infinite number of  tiny harmonic oscillators which constitute a quantum field. Then vacuum energy in a QFT is non zero.

   Dear Rajan,

   In relativity energy doesn't exist as a separated quantity, it is just a component the tensor energy-momentum. For instance, for the electromagnetic field you cannot get a rest sytem where you can remain only with energy (or density of energy better). Thus it would be necessary to write your question in more accurate form for giving an answer.

   It is true that you can consider a rest system for a particle having a velocity lower than c, where p=0 and therefore you have only energy. This is not different than the classical energy.

   Respect to the vacuum it is necessary also to explain a littel bit what vacuum are you speaking on. In quantum mechanics the energy is given by oscillators whose minimum energy is non zero, in fact it is 1/2 h angular frequency. Thus in principle the vacuum of quantum mechanics is with infinite energy if you add all these oscillators, but obviously this is a physical non-sense if is not considered as a density of energy that can be measured by the Casimir effect for the energy zero field (electromagnetic if these fields are the sources of the photons which are the oscillators considered).

All of above comments & specifics with relativistic versus quantum metrics bring out key understanding of energy quantum relativity, probably conference material!!!!!Thank you.