{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T04:38:53Z","timestamp":1775104733071,"version":"3.50.1"},"reference-count":20,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2017,9,8]],"date-time":"2017-09-08T00:00:00Z","timestamp":1504828800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMR 1210588"],"award-info":[{"award-number":["DMR 1210588"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Science Fundation","award":["DMR 1420620"],"award-info":[{"award-number":["DMR 1420620"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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 \u2019spatio-temporal\u2019 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.<\/jats:p>","DOI":"10.3390\/sym9090187","type":"journal-article","created":{"date-parts":[[2017,9,11]],"date-time":"2017-09-11T02:01:30Z","timestamp":1505095290000},"page":"187","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Spatio-Temporal Symmetry\u2014Point Groups with Time Translations"],"prefix":"10.3390","volume":"9","author":[{"given":"Haricharan","family":"Padmanabhan","sequence":"first","affiliation":[{"name":"Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16801, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maggie","family":"Kingsland","sequence":"additional","affiliation":[{"name":"Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16801, USA"},{"name":"Department of Physics, University of South Florida, Tampa, FL 33620, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jason","family":"Munro","sequence":"additional","affiliation":[{"name":"Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16801, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel","family":"Litvin","sequence":"additional","affiliation":[{"name":"Department of Physics, The Eberly College of Science, The Pennsylvania State University, Penn State Berks, P.O. Box 7009, Reading, PA 19610, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Venkatraman","family":"Gopalan","sequence":"additional","affiliation":[{"name":"Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16801, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,9,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Aroyo, M.I. (2016). International Tables for Crystallography, Volume A, International Union of Crystallography.","DOI":"10.1107\/97809553602060000114"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1103\/PhysRevLett.78.2100","article-title":"High Harmonic Generation Spectra of Neutral Helium by the Complex-Scaled (t, t0) Method: Role of Dynamical Electron Correlation","volume":"78","author":"Moiseyev","year":"1997","journal-title":"Phys. Rev. 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