{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:05:11Z","timestamp":1760238311991,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2020,7,28]],"date-time":"2020-07-28T00:00:00Z","timestamp":1595894400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The anomalous nanoscale electromagnetic field arising from light\u2013matter interactions in a nanometric space is called a dressed photon. While the generic technology realized by utilizing dressed photons has demolished the conventional wisdom of optics, for example, the unexpectedly high-power light emission from indirect-transition type semiconductors, dressed photons are still considered to be too elusive to justify because conventional optical theory has never explained the mechanism causing them. The situation seems to be quite similar to that of the dark energy\/matter issue in cosmology. Regarding these riddles in different disciplines, we find a common important clue for their resolution in the form of the relevance of space-like momentum support, without which quantum fields cannot interact with each other according to a mathematical result of axiomatic quantum field theory. Here, we show that a dressed photon, as well as dark energy, can be explained in terms of newly identified space-like momenta of the electromagnetic field and dark matter can be explained as the off-shell energy of the Weyl tensor field.<\/jats:p>","DOI":"10.3390\/sym12081244","type":"journal-article","created":{"date-parts":[[2020,7,30]],"date-time":"2020-07-30T12:15:38Z","timestamp":1596111338000},"page":"1244","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Off-Shell Quantum Fields to Connect Dressed Photons with Cosmology"],"prefix":"10.3390","volume":"12","author":[{"given":"Hirofumi","family":"Sakuma","sequence":"first","affiliation":[{"name":"Research Origin for Dressed Photon, Yokohama-shi, Kanagawa 221-0022, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Izumi","family":"Ojima","sequence":"additional","affiliation":[{"name":"Research Origin for Dressed Photon, Yokohama-shi, Kanagawa 221-0022, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Motoichi","family":"Ohtsu","sequence":"additional","affiliation":[{"name":"Research Origin for Dressed Photon, Yokohama-shi, Kanagawa 221-0022, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hiroyuki","family":"Ochiai","sequence":"additional","affiliation":[{"name":"Institute of Mathematics for Industry, Kyushu University, Fukuoka-shi, Fukuoka 819-0395, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ohtsu, M., and Kobayashi, K. (2004). Optical Near Fields, Springer.","DOI":"10.1007\/978-3-662-09104-3"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Ohtsu, M. (2014). Dressed Photons, Springer.","DOI":"10.1007\/978-3-642-39569-7"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1007\/s00340-011-4375-9","article-title":"Two-dimensional array of room-temperature nano-photonic logic gates using InAs quantum dots in mesa structures","volume":"103","author":"Kawazoe","year":"2011","journal-title":"Appl. Phys. B"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"860","DOI":"10.5185\/amlett.2019.2264","article-title":"Principles and practices of Si light emitting diodes using dressed photons","volume":"10","author":"Ohtsu","year":"2019","journal-title":"Adv. Mater. Lett."},{"key":"ref_5","unstructured":"Visser, T. (2019). Progress in Optics, Elsevier. Chapter 1."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Ohtsu, M. (2016). Silicon Light-Emitting Diodes and Lasers, Springer. Chapter 8.","DOI":"10.1007\/978-3-319-42014-1"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"024715","DOI":"10.1063\/1.1828034","article-title":"Nonadiabatic photodissociation process using an optical near field","volume":"122","author":"Kawazoe","year":"2005","journal-title":"J. Chem. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1117\/12.533245","article-title":"Adiabatic and nonadiabatic nanofabrication by localized optical near fields","volume":"5339","author":"Kawazoe","year":"2004","journal-title":"Proc. SPIE"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1007\/s00340-006-2224-z","article-title":"Near-field optical chemical vapor deposition using Zn(acac)2 with a non-adiabatic photochemical process","volume":"84","author":"Kawazoe","year":"2006","journal-title":"Appl. Phys. B"},{"key":"ref_10","unstructured":"Ohtsu, M., and Kawazoe, T. (2018, February 16). Experimental Estimation of the Maximum Size of a Dressed Photon. Available online: http:\/\/offshell.rodrep.org\/?p=98."},{"key":"ref_11","first-page":"279","article-title":"Optical near fields as photon-matter interacting systems","volume":"202","author":"Sangu","year":"2001","journal-title":"J. Microsc."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/s00340-008-3142-z","article-title":"Realization of an ultra-flat silica surface with angstrom-scale average roughness using nonadiabatic optical near-field etching","volume":"93","author":"Yatsui","year":"2008","journal-title":"Appl. Phys. B"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"79210M","DOI":"10.1117\/12.875808","article-title":"Realization of high-performance optical element by optical near-field etching","volume":"7921","author":"Hirata","year":"2011","journal-title":"Proc. SPIE"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Teki, R., Kadaksham, A.J., Goodwin, F., Yatsui, T., and Ohtsu, M. (2013, January 24\u201328). Dressed-photon nanopolishing for EUV mask substrate defect mitigation. Proceedings of the Society of Photo-Optocal Instrumentation Engineers (SPIE) Advanced Lithography, San Jose, CA, USA. Paper 8679-14.","DOI":"10.1117\/12.2011260"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"701802","DOI":"10.1155\/2015\/701802","article-title":"Realization of ultraflat plastic film using Dressed-Photon-Phonon-Assisted selective etching of nanoscale structures","volume":"2015","author":"Yatsui","year":"2015","journal-title":"Adv. Opt. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1007\/BF02826501","article-title":"Zur Formulierung quantisierter Feldtheorien","volume":"1","author":"Lehmann","year":"1955","journal-title":"Nuovo Cim."},{"key":"ref_17","unstructured":"Jost, R. (1963). The General Theory of Quantized Fields, American Mathematical Society."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"759","DOI":"10.1063\/1.1724219","article-title":"Support of a field in p space","volume":"2","year":"1961","journal-title":"J. Math. Phys."},{"key":"ref_19","unstructured":"Kuper, C.G., and Peres, A. (1971). The impossibility of free tachyons. Relativity and Gravitation, Gordon and Breach Science Publishers."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.pquantelec.2017.07.006","article-title":"Dressed photons in a new paradigm of off-shell quantum fields","volume":"55","author":"Sakuma","year":"2017","journal-title":"Progr. Quantum Electron."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"750","DOI":"10.1007\/s00339-017-1364-9","article-title":"Gauge symmetry breaking and emergence of Clebsch-dual electromagnetic field as a model of dressed photons","volume":"123","author":"Sakuma","year":"2017","journal-title":"Appl. Phys. A"},{"key":"ref_22","first-page":"53","article-title":"Virtual Photon Model by Spatio-Temporal Vortex Dynamics","volume":"Volume 5","author":"Yatsui","year":"2018","journal-title":"Progress in Nanophotonics"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1023\/A:1025175907589","article-title":"A unified scheme for generalized sectors based on selection criteria\u2014order parameters of symmetries and of thermal situations and physical meanings of classifying categorical adjunctions","volume":"10","author":"Ojima","year":"2003","journal-title":"Open Syst. Inf. Dyn."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Ojima, I. (2004, January 1\u20135). Micro-macro duality in quantum physics. Proceedings of the International Conference on Stochastic Analysis: Classical and Quantum, Meijo University, Nagoya, Japan.","DOI":"10.1142\/9789812701541_0012"},{"key":"ref_25","first-page":"217","article-title":"Micro-Macro duality and emergence of macroscopic levels","volume":"21","author":"Ojima","year":"2008","journal-title":"Quantum Probab. White Noise Anal."},{"key":"ref_26","first-page":"29","article-title":"Nakanishi-Lautrup B-Field, Crossed Product & Duality","volume":"1524","author":"Ojima","year":"2006","journal-title":"RIMS Kokyuroku"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Nakanishi, N., and Ojima, I. (1990). Covariant Operator Formalism of Gauge Theories and Quantum Gravity, World Scientific.","DOI":"10.1142\/0362"},{"key":"ref_28","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_29","doi-asserted-by":"crossref","unstructured":"Bratteli, O., and Robinson, D. (1987). Operator Algebra and Statistical Mechanics, Springer. [2nd ed.].","DOI":"10.1007\/978-3-662-02520-8"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1103\/PhysRev.71.38","article-title":"Quantized space-time","volume":"71","author":"Snyder","year":"1947","journal-title":"Phys. Rev."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1400","DOI":"10.1103\/PhysRev.182.1400","article-title":"Superluminal behavior, causality, and instability","volume":"182","author":"Aharonov","year":"1969","journal-title":"Phys. Rev."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01645267","article-title":"Fields, observables and gauge transformations I & II","volume":"13","author":"Doplicher","year":"1969","journal-title":"Comm. Math. Phys."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1089","DOI":"10.1103\/PhysRev.159.1089","article-title":"Possibility of Faster-Than-Light Particles","volume":"159","author":"Feinberg","year":"1967","journal-title":"Phys. Rev."},{"key":"ref_34","unstructured":"Liu, H. (2020, April 15). Available online: https:\/\/www.quora.com\/What-is-the-best-estimate-of-the-cosmological-constant."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/BF00627375","article-title":"Twin Universes Cosmology","volume":"226","author":"Petit","year":"1995","journal-title":"Astrophys. Space Sci."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Jezierski, J., and Lukasik, M. (2005). Conformal Yano-Killing tensor for the Kerr metric and conserved quantities. arXiv.","DOI":"10.1088\/0264-9381\/23\/9\/008"},{"key":"ref_37","unstructured":"Sakuma, H., and Ochiai, H. (2020, April 15). Note on the Physical Meaning of the Cosmological Term. Available online: http:\/\/offshell.rodrep.org\/?p=249."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"231","DOI":"10.4310\/ATMP.1998.v2.n2.a1","article-title":"The large N limit of superconformal field theories and supergravity","volume":"2","author":"Maldacena","year":"1998","journal-title":"Adv. Theor. Math. Phys."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"3727","DOI":"10.1103\/PhysRevA.41.3727","article-title":"Longitudinal field components for laser beams in vacuum","volume":"41","author":"Cicchitelli","year":"1990","journal-title":"Phys. Rev. A"},{"key":"ref_40","unstructured":"Landau, L.D., and Lifshitz, E.M. (1987). Fluid Mechanics. Course of Theoretical Physics, Elsevier. [2nd ed.]."},{"key":"ref_41","unstructured":"Lamb, S.H. (1930). Hydrodynamics, Cambridge University Press. [6th ed.]."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1038\/s41586-018-0274-0","article-title":"Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid","volume":"559","author":"Kasahara","year":"2018","journal-title":"Nature"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/8\/1244\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:52:17Z","timestamp":1760176337000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/8\/1244"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,28]]},"references-count":42,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2020,8]]}},"alternative-id":["sym12081244"],"URL":"https:\/\/doi.org\/10.3390\/sym12081244","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2020,7,28]]}}}