How Does Quantum Field Theory Explain Vacuum Energy and Momentum?

[touqra]

I read that quantum field theory predicts that the vacuum should have some sort of energy and momentum.

I could this be when the concept of energy is not absolute? All we measure in the lab is the difference in energy.

In addition, I also read that the cosmological constant in Einstein equation can be interpreted as the energy density of the vacuum. What are the current research and theories on these?

 

[marlon]

I read that quantum field theory predicts that the vacuum should have some sort of energy and momentum.

Are you referring to the fact that in QM/QFT, the vacuum energy value is NON ZERO because of HUP ? If so, you are asking about vacuum fluctuations, right ?

such fluctuations are a manifestation of
1) HUP (vacuum energy value is non zero)
2) HUP (short timed violation of energy conservation)
3) the transistion from QM to QFT (virtual particles)
4) Appropriate conservation laws that are valid for the appropriate interaction (like charge conservation for EM-interaction)

Point 3 means that in quantummechanical perturbation theory the interaction goes from the initial state to the final state by passing over the "virtual transition states". These states have a short lifetime because of the HUP for time and energy.

Due to the fact that energy is uncertain, such states can (and will) violate total energy conservation. Beware that if you compare initial and final state, total energyconservation is ALWAYS respected. Momentum conservation is always respected in ALL states. In QFT, these transition states correspond to virtual particles (ie fluctuations of fields).

Virtual particles correspond to internal Feyman lines. They are always off mass shell (ie they don't respect the Einstein energy relationship). The bigger the difference between the particle's four momentum and it's mass (thus the bigger the violation of E=mc^2) the smaller the probability for such an interaction (mediated by the virtual particles) to occur. Hence, there is a price to pay for being virtual...isn't that nice ? :)


regards
marlon