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Qmechanic ♦
Qmechanic ♦
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The Weyl invariance symmetry of the Polyakov action is said to be considered as the invariance of the theory under a local change of scale which preserves the angles between all lines.

However, why does the Weyl transformation $g_{\alpha \beta} (\sigma) \to \Lambda ^2 (\sigma) g_{\alpha \beta} (\sigma)$, where $\sigma$ is the worldsheet coordinate, preserve the angles  ? Could somebody prove it mathematically  ?

The Weyl invariance symmetry of the Polyakov action is said to be considered as the invariance of the theory under a local change of scale which preserves the angles between all lines.

However, why does the Weyl transformation $g_{\alpha \beta} (\sigma) \to \Lambda ^2 (\sigma) g_{\alpha \beta} (\sigma)$, where $\sigma$ is the worldsheet coordinate, preserve the angles  ? Could somebody prove it mathematically  ?

The Weyl invariance symmetry of the Polyakov action is said to be considered as the invariance of the theory under a local change of scale which preserves the angles between all lines.

However, why does the Weyl transformation $g_{\alpha \beta} (\sigma) \to \Lambda ^2 (\sigma) g_{\alpha \beta} (\sigma)$, where $\sigma$ is the worldsheet coordinate, preserve the angles? Could somebody prove it mathematically?

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Simon
Simon
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Why does the Weyl transformation preserve angles in string theory?

The Weyl invariance symmetry of the Polyakov action is said to be considered as the invariance of the theory under a local change of scale which preserves the angles between all lines.

However, why does the Weyl transformation $g_{\alpha \beta} (\sigma) \to \Lambda ^2 (\sigma) g_{\alpha \beta} (\sigma)$, where $\sigma$ is the worldsheet coordinate, preserve the angles ? Could somebody prove it mathematically ?