Stability and related properties of vacua and ground states

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

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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

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