Short-range Interaction and Nonrelativistic Phi**4 Theory in Various Dimensions

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dc.creatorJia, Yu
dc.date2004-01-23
dc.date.accessioned2026-07-07T04:16:32Z
dc.date.available2026-07-07T04:16:32Z
dc.descriptionWe employ the effective field theory method to systematically study the short-range interaction in two-body sector in 2, 3 and 4 spacetime dimensions, respectively. The phi**4 theory is taken as a specific example and matched onto the nonrelativistic effective theory to one loop level. An exact, Lorentz-invariant expression for the S-wave amplitude is presented, from which the nonperturbative information can be easily extracted. We pay particular attention to the renormalization group analysis in the 3 dimensions, and show that relativistic effects qualitatively change the renormalization group flow of higher-dimensional operators. There is one ancient claim that triviality of the 4-dimensional phi**4 theory can be substantiated in the nonrelativistic limit. We illustrate that this assertion arises from treating the interaction between two nonrelativistic particles as literally zero-range, which is incompatible with the Uncertainty Principle. The S-wave effective range in this theory is identified to be approximately 16/3pi times the Compton wavelength.
dc.description36 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/hep-th/0401171
dc.identifierhttp://arxiv.org/abs/hep-th/0401171
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/52391
dc.subjectHigh Energy Physics - Theory
dc.subjectHigh Energy Physics - Phenomenology
dc.subjectNuclear Theory
dc.titleShort-range Interaction and Nonrelativistic Phi**4 Theory in Various Dimensions
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