Stability and related properties of vacua and ground states
- Departamento de Fisica Matematica, Universidade de Sao Paulo (Brazil), E-mail: wreszins@fma.if.usp.br
- Instituto de Matematica y Fisica, Universidad de Talca (Chile), E-mail: christian.jaekel@mac.com
We consider the formal non-relativistic limit (nrl) of the :{phi}{sup 4}:{sub 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.), Beg Memorial Volume, World Scientific, Singapore, 1991], we show that, for s = 2 and a given value of the ultraviolet cutoff {kappa}, there are two ways to perform the nrl: (i) fixing the renormalized mass m{sup 2} equal to the bare mass m{sub 0}{sup 2}; (ii) keeping the renormalized mass fixed and different from the bare mass m{sub 0}{sup 2}. In the (infinite-volume) two-particle sector the scattering amplitude tends to zero as {kappa} {yields} {infinity} 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.
- OSTI ID:
- 21077679
- Journal Information:
- Annals of Physics (New York), Vol. 323, Issue 2; Other Information: DOI: 10.1016/j.aop.2007.02.002; PII: S0003-4916(07)00028-0; Copyright (c) 2007 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
- Country of Publication:
- United States
- Language:
- English
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