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A relativistic toy model for back-reaction

Plunien, Günter
Schützhold, Ralf
Published in Classical and Quantum Gravity. 2007, vol. 24, p. 4361-4376
Abstract We consider a quantized massless and minimally coupled scalar field on a circular closed string with a time-dependent radius $R(t)$, whose undisturbed dynamics is governed by the Nambu-Goto action. Within the semi-classical treatment, the back-reaction of the quantum field onto the string dynamics is taken into account in terms of the renormalized expectation value of the energy-momentum tensor including the trace anomaly. The results indicate that the back-reaction could prevent the collapse of the circle $Rdownarrow0$ -- however, the semi-classical picture fails to describe the string dynamics at the turning point (i.e., possible bounce) at finite values of $R$ and $dot R$. The fate of the closed string after that point (e.g., oscillation or eternal acceleration) cannot be determined within the semi-classical picture and thus probably requires the full quantum treatment. PACS: 04.62.+v, 03.70.+k, 11.15.Kc, 04.60.-m.
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Deposited on : 2011-01-04

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