Wreszinski, Walter F. and Jakel, Christian Dieter 2008. Stability and related properties of vacua and ground states. Annals of Physics 323 (2) , pp. 251-266. 10.1016/j.aop.2007.02.002 |
Abstract
We consider the formal non-relativistic limit (nrl) of the :ϕ4: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 ; (ii) keeping the renormalized mass fixed and different from the bare mass . In the (infinite-volume) two-particle sector the scattering amplitude tends to zero as κ → ∞ 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
Item Type: | Article |
---|---|
Date Type: | Publication |
Status: | Published |
Schools: | Mathematics |
Subjects: | Q Science > QA Mathematics |
Publisher: | Elsevier |
ISSN: | 0003-4916 |
Last Modified: | 19 Mar 2016 22:22 |
URI: | https://orca.cardiff.ac.uk/id/eprint/13892 |
Citation Data
Cited 3 times in Scopus. View in Scopus. Powered By Scopus® Data
Actions (repository staff only)
![]() |
Edit Item |