Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1856293 | Annals of Physics | 2008 | 16 Pages |
Abstract
We consider the formal non-relativistic limit (nrl) of the :Ï4:s+1 relativistic quantum field theory (rqft), where s is the space dimension. Following the work of R. Jackiw [R. Jackiw, in: A. Ali, P. Hoodbhoy (Eds.), Bég Memorial Volume, World Scientific, Singapore, 1991], we show that, for s = 2 and a given value of the ultraviolet cutoff κ, there are two ways to perform the nrl: (i) fixing the renormalized mass m2 equal to the bare mass m02; (ii) keeping the renormalized mass fixed and different from the bare mass m02. In the (infinite-volume) two-particle sector the scattering amplitude tends to zero as κ â â in case (i) and, in case (ii), there is a bound state, indicating that the interaction potential is attractive. As a consequence, stability of matter fails for our boson system. We discuss why both alternatives do not reproduce the low-energy behaviour of the full rqft. The singular nature of the nrl is also nicely illustrated for s = 1 by a rigorous stability/instability result of a different nature.
Keywords
Related Topics
Physical Sciences and Engineering
Physics and Astronomy
Physics and Astronomy (General)
Authors
Walter F. Wreszinski, Christian D. Jäkel,