Tensor fields on crystals

Research output: Contribution to journalArticle

12 Citations (Scopus)

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 Oh7.

Original languageEnglish (US)
Pages (from-to)337-344
Number of pages8
JournalJournal of Mathematical Physics
Volume23
Issue number2
StatePublished - Dec 1 1981

Fingerprint

Permutation Representation
Crystal
Tensor
tensors
Induced Representations
Direct Product
crystals
permutations
Dependent
Symmetry Group
Strombus or kite or diamond
Irreducible Representation
Tables
Basis Functions
products
atoms
diamonds
symmetry

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

@article{ee1104d761114f6ebe02776a1b9e8575,
title = "Tensor fields on crystals",
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 Oh7.",
author = "Litvin, {Daniel Bernard}",
year = "1981",
month = "12",
day = "1",
language = "English (US)",
volume = "23",
pages = "337--344",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "American Institute of Physics Publising LLC",
number = "2",

}

Tensor fields on crystals. / Litvin, Daniel Bernard.

In: Journal of Mathematical Physics, Vol. 23, No. 2, 01.12.1981, p. 337-344.

Research output: Contribution to journalArticle

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 -