Recent content by DrInfinity

yes but mostly useful for Hadrons ;-)

Yes Vanhees71 and yourself have both put me on the right path so thank you both. I will derive equation (3) and post the derivation here for everyone. However, please note that the (2T+1) iso-spin factor you have both mentioned has nothing to do with vacuum energy which arises from elementary...

Thank you, I will check the reference your provided.

ok thank for this reply but I am unsure how this is related to my original question? I was looking for a derivation of equation (3) in the mentioned paper.

Yes I agree. However, in equation (3), ##j## is in fact the spin or momentum-spin basis and not the total angular momentum. I understand that some authors use ##s## for momentum-spin basis but in the paper we are discussing, the author uses ##j## instead.

Thank you very much for your prompt reply. So I think we both agree that the equation (3) is correct, however one has to be careful in applying it blindly, and this is the reason I initially questioned this equation, I explain: As I stated before in an earlier reply, for the EM field (i.e. the...

Thank you for your reply. Your final expression given above is indeed close to equation (3). How does one obtain it, is there a reference that gives more details on this? For example, when you apply the Hamiltonian above on ##\Omega## to obtain the vacuum energy how does one end up with the...

Thank you for you reply. So is iso-spin t=0 in the case of the vacuum energy contribution of a specific field? And that is why we get only the (2j+1) term? Also, can you kindly refer me to a reference that has more info on your statement: "the factor (2j+1)(2t+1) arises from the summation over...

Thank you for your answer but my question is not related to the CC problem (I have read Weinberg's article), nor is it about the claimed divergence of the vacuum energy or other aspects of the original paper I referred too. I am only interested in the derivation of equation (3) in the paper I...

Thank you, I own a copy of this very good book but it does not discuss the spin effect on vacuum energy. At least, I could not see it. If you know where it is in the book, please let me know.

Thank you for your reply. Indeed, the integral in equation (3) is derived using a quantum harmonic oscillator to model vacuum energy. My interest is to understand what effect spin has on the harmonic oscillator, if any, and hence what is the effect on vacuum energy. Also please note that each...

In equation (3) of this article https://arxiv.org/pdf/astro-ph/0605418.pdf , on page 3, you can see an expression for the vacuum energy density of a field as a function of its particle spin, particle mass and the wave number k. It is fairly straight forward to derive the integral portion of...