(adsbygoogle = window.adsbygoogle || []).push({}); An expression for the "mass"?..

Let,s suppose we have a NOn-renormalizable theory, and that we wish to calculate the mass of a particle for that theory with lagrangian L, the "mass" will have an expression in terms of an infinite series:

[tex] m \sim a(0)+ga(1)+g^{2}a(2)+g^{3}a(3)+......... [/tex]

where every a(n) diverges in the form [tex] a(n)=\Lambda ^{n+1} [/tex] [tex] \Lambda \rightarrow \infty [/tex] (regulator)

then my question is let,s suppose we truncate the series for a number N :

[tex] m \sim a(0)+ga(1)+g^{2}a(2)+g^{3}a(3)+......g^{N}a(N) [/tex]

where g is a finite constant and N say N=139 (for example), of course in that case we have 139 types of divergences, but let,s suppose we could express every divergence recursively in the form:

.a(n)= c(n)+a(n-1)+a(n-2)+.............+a(0) where c(n) are finite constants and a(0) is the value of the regulator, being this formula valid for every n=1,2,3,4,..........139 so we could calculate our value for the mass in the form:

[tex] m \sim C(0)a(0)+gc(1)b(1)+g^{2}b(2)c(2)+g^{3}b(3)c(3)+......... [/tex]

so we have only the divergence a(0) left, then we apply the renormalization process to 2absorb2 this a(0)-->k (finite value) so our finite value for the mass would be:

[tex] m \sim C(0)k+gc(1)b(1)+g^{2}b(2)c(2)+g^{3}b(3)c(3)+.........g^{N}c(N)b(N) [/tex] finite due to the fact that c(n),b(n) and k are finite constants.

The question is if we could express always the ultraviolet divergences by a recursion formula...could we calculate any physical parameter truncating the series..even for Non-renormalizable theories?..thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# An expression for the mass ?

**Physics Forums | Science Articles, Homework Help, Discussion**