### Abstract

A new method is presented to determine the irreducible representations of the space group of a crystal contained in the representation whose basis functions are the components of a tensor field defined on the atoms of a crystal. This reducible representation is the direct product of a tensor representation, dependent only on the tensor, and a permutation representation dependent only on how the atoms permute under elements of the space group. The permutation representation is first separately reduced prior to the reduction of the direct product. The permutation representation is shown to be an induced representation and its reduction is facilitated using the theory of induced representations. Examples and tables of results of applying this method are given in the case of a polar vector tensor field, applicable to lattice vibrational problems, and crystals, as the diamond structure, of space group symmetry O_{h}^{7}.

Original language | English (US) |
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Pages (from-to) | 337-344 |

Number of pages | 8 |

Journal | Journal of Mathematical Physics |

Volume | 23 |

Issue number | 2 |

State | Published - Dec 1 1981 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

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*Journal of Mathematical Physics*, vol. 23, no. 2, pp. 337-344.

**Tensor fields on crystals.** / Litvin, Daniel Bernard.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Tensor fields on crystals

AU - Litvin, Daniel Bernard

PY - 1981/12/1

Y1 - 1981/12/1

N2 - A new method is presented to determine the irreducible representations of the space group of a crystal contained in the representation whose basis functions are the components of a tensor field defined on the atoms of a crystal. This reducible representation is the direct product of a tensor representation, dependent only on the tensor, and a permutation representation dependent only on how the atoms permute under elements of the space group. The permutation representation is first separately reduced prior to the reduction of the direct product. The permutation representation is shown to be an induced representation and its reduction is facilitated using the theory of induced representations. Examples and tables of results of applying this method are given in the case of a polar vector tensor field, applicable to lattice vibrational problems, and crystals, as the diamond structure, of space group symmetry Oh7.

AB - A new method is presented to determine the irreducible representations of the space group of a crystal contained in the representation whose basis functions are the components of a tensor field defined on the atoms of a crystal. This reducible representation is the direct product of a tensor representation, dependent only on the tensor, and a permutation representation dependent only on how the atoms permute under elements of the space group. The permutation representation is first separately reduced prior to the reduction of the direct product. The permutation representation is shown to be an induced representation and its reduction is facilitated using the theory of induced representations. Examples and tables of results of applying this method are given in the case of a polar vector tensor field, applicable to lattice vibrational problems, and crystals, as the diamond structure, of space group symmetry Oh7.

UR - http://www.scopus.com/inward/record.url?scp=36749104729&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36749104729&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:36749104729

VL - 23

SP - 337

EP - 344

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 2

ER -