Stability and related properties of vacua and ground states

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...

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Published in:Annals of physics 2008-02, Vol.323 (2), p.251-266
Main Authors: Wreszinski, Walter F., Jäkel, Christian D.
Format: Article
Language:English
Subjects:
BOSONS
BOUND STATE
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
CONSTRUCTIVE FIELD THEORY
GROUND STATES
INSTABILITY
INTERACTIONS
MATTER
Non-relativistic limit
POTENTIALS
SCATTERING AMPLITUDES
Stability of matter
ULTRAVIOLET RADIATION
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container_title Annals of physics
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Jäkel, Christian D.
description 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 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→∞ 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.
doi_str_mv 10.1016/j.aop.2007.02.002
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subjects BOSONS
BOUND STATE
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
CONSTRUCTIVE FIELD THEORY
GROUND STATES
INSTABILITY
INTERACTIONS
MATTER
Non-relativistic limit
POTENTIALS
SCATTERING AMPLITUDES
Stability of matter
ULTRAVIOLET RADIATION
title Stability and related properties of vacua and ground states
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