- #1

jcap

- 170

- 12

According to [Dark Energy and the Accelerating Universe](https://ned.ipac.caltech.edu/level5/March08/Frieman/Frieman5.html) quantum field theory says that the energy density of the vacuum, ##\rho_{vac}##, should be given by

$$\rho_{vac}=\frac{1}{2}\sum_{\rm fields}g_i\int_0^{\infty}\sqrt{k^2+m^2}\frac{d^3k}{(2\pi)^3}\approx\sum_{\rm fields}\frac{g_i k^4_{max}}{16\pi^2}$$

where ##g_i## is positive/negative for bosons/fermions and ##k_{max}## is some momentum cutoff.

My question is why do we only take the positive square root terms?

According to the Feynman-Stueckelberg interpretation a positive energy antiparticle going forward in time is equivalent to a negative energy particle going backwards in time. Maybe we cannot rule out negative energy virtual particles moving backwards in time?

Therefore, in order to include anti-particles in the above sum, maybe we should include the negative square root terms? If we do then we find that the energy density ##\rho_{vac}=0##.

$$\rho_{vac}=\frac{1}{2}\sum_{\rm fields}g_i\int_0^{\infty}\sqrt{k^2+m^2}\frac{d^3k}{(2\pi)^3}\approx\sum_{\rm fields}\frac{g_i k^4_{max}}{16\pi^2}$$

where ##g_i## is positive/negative for bosons/fermions and ##k_{max}## is some momentum cutoff.

My question is why do we only take the positive square root terms?

According to the Feynman-Stueckelberg interpretation a positive energy antiparticle going forward in time is equivalent to a negative energy particle going backwards in time. Maybe we cannot rule out negative energy virtual particles moving backwards in time?

Therefore, in order to include anti-particles in the above sum, maybe we should include the negative square root terms? If we do then we find that the energy density ##\rho_{vac}=0##.

Last edited: