Spatio-temporal symmetry-Point groups with time translations

Haricharan Padmanabhan, Maggie L. Kingsland, Jason M. Munro, Daniel B. Litvin, Venkatraman Gopalan

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Spatial symmetries occur in combination with temporal symmetries in a wide range of physical systems in nature, including time-periodic quantum systems typically described by the Floquet formalism. In this context, groups formed by three-dimensional point group symmetry operations in combination with time translation operations are discussed in this work. The derivation of these 'spatio-temporal' groups from conventional point groups and their irreducible representations is outlined, followed by a complete listing. The groups are presented in a template similar to space group operations, and are visualized using a modified version of conventional stereographic projections. Simple examples of physical processes that simultaneously exhibit symmetry in space and time are identified and used to illustrate the application of spatio-temporal groups.

Original languageEnglish (US)
Article number187
Issue number9
StatePublished - Sep 1 2017

All Science Journal Classification (ASJC) codes

  • Computer Science (miscellaneous)
  • Chemistry (miscellaneous)
  • General Mathematics
  • Physics and Astronomy (miscellaneous)


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