{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:10:24Z","timestamp":1760137824945,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,3,1]],"date-time":"2022-03-01T00:00:00Z","timestamp":1646092800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"US - Italy Fulbright Commission","award":["."],"award-info":[{"award-number":["."]}]},{"name":"Whole Genome Science Foundation","award":["."],"award-info":[{"award-number":["."]}]},{"name":"Guy Foundation","award":["."],"award-info":[{"award-number":["."]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Free electron systems are ubiquitous in nature and have demonstrated intriguing effects in their collective interactions with weak electric and magnetic fields, especially in aqueous environments. Starting from the Dirac Hamiltonian, a fully relativistic expression is derived for the electron energy shift in the presence of a spatiotemporally constant, weak electromagnetic field. The expectation value of this energy shift is then computed explicitly using the Fourier transforms of the fermionic fields. To first order in the electromagnetic fields, the average relativistic energy shift is found to be completely independent of the electron spin-polarization coefficients. This effect is also considerably larger than that predicted in quantum mechanics by the analogous Zeeman shift. Finally, in the non-relativistic limit, it is shown how to discriminate between achiral and completely polarized states, which leads to a concluding discussion of possible mesoscopic and macroscopic manifestations of electron spin states across many orders of magnitude in the physical world, with stark implications for biological and other complex systems.<\/jats:p>","DOI":"10.3390\/e24030358","type":"journal-article","created":{"date-parts":[[2022,3,1]],"date-time":"2022-03-01T08:17:03Z","timestamp":1646122623000},"page":"358","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["From Micro to Macro: A Relativistic Treatment of the Chiral Energy Shifts Caused by Static Electromagnetic Effects on Free Electrons"],"prefix":"10.3390","volume":"24","author":[{"given":"Philip","family":"Kurian","sequence":"first","affiliation":[{"name":"Quantum Biology Laboratory, Howard University, Washington, DC 20060, USA"},{"name":"Department of Physics and Astronomy, University of Iowa, Iowa City, IA 52242, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,1]]},"reference":[{"key":"ref_1","first-page":"031061","article-title":"Out-of-Equilibrium Collective Oscillation as Phonon Condensation in a Model Protein","volume":"8","author":"Nardecchia","year":"2018","journal-title":"Phys. Rev. X"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"158101","DOI":"10.1103\/PhysRevLett.122.158101","article-title":"Quantum Fluctuations in the Fr\u00f6hlich Condensate of Molecular Vibrations Driven far from Equilibrium","volume":"122","author":"Zhang","year":"2019","journal-title":"Phys. Rev. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Azizi, K., Gori, M., Morzan, U., Heyden, M., Hassanali, A., and Kurian, P. (2022). Examining the Origins of Observed Terahertz Modes from an Optically Pumped Atomistic Model Protein in Aqueous Solution, in submission.","DOI":"10.1093\/pnasnexus\/pgad257"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"190404","DOI":"10.1103\/PhysRevLett.99.190404","article-title":"Semiclassical dynamics of electron wave packet states with phase vortices","volume":"99","author":"Bliokh","year":"2007","journal-title":"Phys. Rev. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"174802","DOI":"10.1103\/PhysRevLett.107.174802","article-title":"Relativistic electron vortex beams: Angular momentum and spin\u2013orbit interaction","volume":"107","author":"Bliokh","year":"2011","journal-title":"Phys. Rev. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"033824","DOI":"10.1103\/PhysRevA.86.033824","article-title":"Spatiotemporal vortex beams and angular momentum","volume":"86","author":"Bliokh","year":"2012","journal-title":"Phys. Rev. A"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1016\/j.physleta.2015.11.002","article-title":"Quantum field theory treatment of magnetic effects on the spin and orbital angular momentum of a free electron","volume":"380","author":"Kurian","year":"2016","journal-title":"Phys. Lett. A"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"482","DOI":"10.1016\/j.jmmm.2017.10.059","article-title":"Quantum field theory treatment of magnetic effects on a system of free electrons","volume":"449","author":"Verzegnassi","year":"2018","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"111002","DOI":"10.1088\/2399-6528\/aae876","article-title":"Chirality-energy conversion induced by static magnetic effects on free electrons in quantum field theory","volume":"2","author":"Kurian","year":"2018","journal-title":"J. Phys. Commun."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"610","DOI":"10.1098\/rspa.1928.0023","article-title":"The quantum theory of the electron","volume":"117","author":"Dirac","year":"1928","journal-title":"Proc. R. Soc. Lond. Ser. A"},{"key":"ref_11","unstructured":"Peskin, M.E., and Schroeder, D.V. (1995). An Introduction to Quantum Field Theory, Perseus."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1103\/PhysRev.115.485","article-title":"Significance of electromagnetic potentials in the quantum theory","volume":"115","author":"Aharonov","year":"1959","journal-title":"Phys. Rev."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2474","DOI":"10.1073\/pnas.1611467114","article-title":"Chirality-induced spin polarization places symmetry constraints on biomolecular interactions","volume":"114","author":"Kumar","year":"2017","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"092302","DOI":"10.1063\/1.4966237","article-title":"Structure dependent spin selectivity in electron transport through oligopeptides","volume":"146","author":"Kiran","year":"2017","journal-title":"J. Chem. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"20456","DOI":"10.1021\/jacs.0c10105","article-title":"Long-range charge reorganization as an allosteric control signal in proteins","volume":"142","author":"Ghosh","year":"2020","journal-title":"J. Am. Chem. Soc."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"975","DOI":"10.1126\/science.250.4983.975","article-title":"Chiral symmetry breaking in sodium chlorate crystallization","volume":"250","author":"Kondepudi","year":"1990","journal-title":"Science"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"094112","DOI":"10.1103\/PhysRevB.91.094112","article-title":"Using electron vortex beams to determine chirality of crystals in transmission electron microscopy","volume":"91","author":"Juchtmans","year":"2015","journal-title":"Phys. Rev. B"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"044006","DOI":"10.1063\/1.4974260","article-title":"Photoinduced molecular chirality probed by ultrafast resonant X-ray spectroscopy","volume":"4","author":"Rouxel","year":"2017","journal-title":"Struct. Dyn."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1357","DOI":"10.1073\/pnas.1120531109","article-title":"Are biochemical reactions affected by weak magnetic fields?","volume":"109","author":"Hore","year":"2012","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"38543","DOI":"10.1038\/srep38543","article-title":"The quantum biology of reactive oxygen species partitioning impacts cellular bioenergetics","volume":"6","author":"Usselman","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1016\/j.jtbi.2015.11.018","article-title":"How quantum entanglement in DNA synchronizes double-strand breakage by type II restriction endonucleases","volume":"391","author":"Kurian","year":"2016","journal-title":"J. Theor. Biol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"708","DOI":"10.1021\/acscentsci.7b00100","article-title":"DNA\u2019s chiral spine of hydration","volume":"3","author":"McDermott","year":"2017","journal-title":"ACS Cent. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1028","DOI":"10.1016\/j.molliq.2017.10.140","article-title":"DNA and the chiral water superstructure","volume":"248","author":"Elia","year":"2017","journal-title":"J. Molec. Liquids"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.physleta.2017.10.038","article-title":"Water-mediated correlations in DNA-enzyme interactions","volume":"382","author":"Kurian","year":"2018","journal-title":"Phys. Lett. A"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/3\/358\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:30:19Z","timestamp":1760135419000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/3\/358"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,1]]},"references-count":24,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,3]]}},"alternative-id":["e24030358"],"URL":"https:\/\/doi.org\/10.3390\/e24030358","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2022,3,1]]}}}