String Worldsheet Area

Classical Mechanics Level pending

Consider a relativistic string lying on the y-axis at time \(\tau = 0\), stretching from \(y=0\) to \(y=1\). The string is parameterized so that one endpoint is at \(\sigma=0\) and the other is at \(\sigma=1\), and so that \(\tau = t\). Now allow the string to propagate from time \(\tau = 0\) to time \(\tau = 1\), leaving the string fixed on the y-axis. Find the area of the resulting string worldsheet.

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