How does temperature affect the mass of the axion particle?

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Axion mass is said to depend on temperature. I don't understand this. Can somebody explain how the mass of an elementary particle depend on temperature at all? Temperature is the average kinetic energy of particles. So what does it have anything to do with the mass of an elementary particle?
 
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I think that there is considerable confusion over "mass". As far as I understand it, mass only refers to the rest mass of something usually. Trying to add in different types of mass such as relativistic mass is confusing and does nothing to help anything. As far as I am concerned the temp of an object has nothing to do with the mass. (However I am not sure on this, as I said there is much confusion and misunderstanding.)
 
Temperature is an average of quantum states. A laser pointer beam has a temperature of over 1000K for a tiny fraction of a second. Energy and mass are the same so higher temperature means higher energy and higher mass equivalence.
 
memento, The axion is a Nambu-Goldstone boson whose mass is dynamically determined, and evolves during the inflationary period of the universe. For a good recent review, see

http://arxiv.org/abs/0910.1066
 
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I'm following this paper by Kitaev on SL(2,R) representations and I'm having a problem in the normalization of the continuous eigenfunctions (eqs. (67)-(70)), which satisfy \langle f_s | f_{s'} \rangle = \int_{0}^{1} \frac{2}{(1-u)^2} f_s(u)^* f_{s'}(u) \, du. \tag{67} The singular contribution of the integral arises at the endpoint u=1 of the integral, and in the limit u \to 1, the function f_s(u) takes on the form f_s(u) \approx a_s (1-u)^{1/2 + i s} + a_s^* (1-u)^{1/2 - i s}. \tag{70}...
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