Thursday, 29 March 2018

quantum field theory - Bound State of Only Massless Particles? Follows a Time-Like Trajectory?


Is there any way in which a bound state could consist only of massless particles? If yes, would this "atom" of massless particles travel on a light-like trajectory, or would the interaction energy cause it to travel on a time-like trajectory?




Answer



John Rennie has answered the first part of the question. The second part was this:



If yes, would this "atom" of massless particles travel on a light-like trajectory, or would the interaction energy cause it to travel on a time-like trajectory?



The answer is that it would have a timelike world-line, and this is independent of any (probably uncertain) details of the system's dynamics or binding energy.


Mass is not additive. Mass is defined (in units with $c=1$) by $m^2=E^2-p^2$, where $E$ is the mass-energy and $p$ is the momentum. $(E,p)$ is the momentum four-vector, and the squared mass is its squared norm. For a massless particle, the momentum four-vector is lightlike. If four-vectors $p$ and $p'$ are both lightlike and future-directed, but not parallel, then $p+p'$ is timelike. Therefore a system of interacting, massless particles is guaranteed to have a nonzero mass.


No comments:

Post a Comment

Understanding Stagnation point in pitot fluid

What is stagnation point in fluid mechanics. At the open end of the pitot tube the velocity of the fluid becomes zero.But that should result...