# nLab light-cone gauge quantization

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## Surveys, textbooks and lecture notes

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• Axiomatizations

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• Tools

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• Structural phenomena

• Types of quantum field thories

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• examples

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# Contents

## Idea

What is called light-cone gauge quantization is one approach to the quantization of sigma models whose target space has a lightlike Killing vector. The strategy of this approach is to gauge fix the metric and diffeomorphisms of the worldvolume such that also the worldvolume has a lightlike Killing vector field and such that this is mapped to the given one on target space.

This typically fixes most of the available gauge freedom, and the strategy is then to apply quantization to what remains. For more on this general idea see at quantization commutes with reduction.

Often this is considered for target space being Minkowski spacetime $\mathbb{R}^{d-1,1}$ and with $X^+ \coloneqq X^0 - X^1$ denoting one of its canonical lightlike coordinates. If $\tau$ denotes similarly a lightlike coordinate function on the worldvolume, then the condition of light-cone gauge reads

$X^+ = p^+ \tau$

for some proportionality constant $p^+$. This is how light cone gauge appears in much of the physics literature.

## Applications

### Quantization of Green-Schwarz super $p$-brane sigma models

Light cone gauge quantization is the only method by which Green-Schwarz super p-brane sigma models have been quantized, to date.

## References

All the standard introductory texts on string theory have sections devoted to light-cone quantization. For instance

Last revised on January 11, 2017 at 08:01:29. See the history of this page for a list of all contributions to it.