On The Problem of Particle Production in c=1 Matrix Model

Details On The Problem of Particle Production in c=1 Matrix Model On The Problem of Particle Production in c=1 Matrix Model

2004-06-02

arxiv.org/abs/hep-th/0406029v2

JHEP 0408 (2004) 032

Physics

High Energy Physics

High Energy Physics - Theory

37 pages, 5 figures. Section 6 is modified to clarify main accomplishments of the paper including a discussion comparing stres

Scientific paper

10.1088/1126-6708/2004/08/032

We reconsider and analyze in detail the problem of particle production in the time dependent background of $c=1$ matrix model where the Fermi sea drains away at late time. In addition to the moving mirror method, which has already been discussed in hep-th/0403169 and hep-th/0403275, we describe yet another method of computing the Bogolubov coefficients which gives the same result. We emphasize that these Bogolubov coefficients are approximately correct for small value of the deformation parameter. We also study the time evolution of the collective field theory stress-tensor with a special point-splitting regularization. Our computations go beyond the approximation of the previous treatments and are valid at large coordinate distances from the boundary at a finite time and up-to a finite coordinate distance from the boundary at late time. In this region of validity our regularization produces a certain singular term that is precisely canceled by the collective field theory counter term in the present background. The energy and momentum densities fall off exponentially at large distance from the boundary to the values corresponding to the static background. This clearly shows that the radiated energy reaches the asymptotic region signaling the space-time decay.

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