advanced_notions:topological_defects
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advanced_notions:topological_defects [2017/12/20 11:09] jakobadmin [Layman] |
advanced_notions:topological_defects [2017/12/20 11:10] jakobadmin [Student] |
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| * A great introduction is http://www.dartmouth.edu/~dbr/topdefects.pdf and | * A great introduction is http://www.dartmouth.edu/~dbr/topdefects.pdf and | ||
| - | * see also http://www.lassp.cornell.edu/sethna/pubPDF/OrderParameters.pdf | + | * see also http://www.lassp.cornell.edu/sethna/pubPDF/OrderParameters.pdf and |
| + | * [[https://www.scribd.com/document/85012149/From-Monopoles-to-Textures-A-Survey-of-Topological-Defects-in-Cosmological-Quantum-Field-Theory|From Monopoles to Textures]] by Damian Sowinski | ||
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| * If the second homotopy class of $G/H$ is non-trivial, we get a **zero-dimensional** topological defect, a "a pointlike singularity" that is called a **[[advanced_notions:topological_defects:magnetic_monopoles|monopole]]**. An example is when a scalar potential with $SU(2)$ symmetry breaks to $U(1)$. The vacuum manifold is $SU(2)/U(1)\simeq S^2$. | * If the second homotopy class of $G/H$ is non-trivial, we get a **zero-dimensional** topological defect, a "a pointlike singularity" that is called a **[[advanced_notions:topological_defects:magnetic_monopoles|monopole]]**. An example is when a scalar potential with $SU(2)$ symmetry breaks to $U(1)$. The vacuum manifold is $SU(2)/U(1)\simeq S^2$. | ||
| * If the third homotopy class of $G/H$ is non-trivial, we get so called “**textures**”. In fact the notion "textures" is more popular among condensed matter physicists and particle physicists call this kind of topological defect **Skyrmions**. "If space is a three sphere, we can have a texture wrapped around the entire three sphere and this would give a static solution in the model." ([[https://arxiv.org/pdf/hep-ph/9710292.pdf|source]]). An example is when a scalar potential with $SU(2)$ symmetry breaks to the trivial subgroup $1$. The vacuum manifold is $SU(2)/1 =SU(2) \simeq S^3$. | * If the third homotopy class of $G/H$ is non-trivial, we get so called “**textures**”. In fact the notion "textures" is more popular among condensed matter physicists and particle physicists call this kind of topological defect **Skyrmions**. "If space is a three sphere, we can have a texture wrapped around the entire three sphere and this would give a static solution in the model." ([[https://arxiv.org/pdf/hep-ph/9710292.pdf|source]]). An example is when a scalar potential with $SU(2)$ symmetry breaks to the trivial subgroup $1$. The vacuum manifold is $SU(2)/1 =SU(2) \simeq S^3$. | ||
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| + | ---- | ||
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| + | **Recommended Resources:** | ||
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advanced_notions/topological_defects.txt · Last modified: 2017/12/20 11:11 by jakobadmin
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