{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:34:16Z","timestamp":1760240056232,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,3,2]],"date-time":"2019-03-02T00:00:00Z","timestamp":1551484800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002261","name":"Russian Foundation for Basic Research","doi-asserted-by":"publisher","award":["19-02-00453 A"],"award-info":[{"award-number":["19-02-00453 A"]}],"id":[{"id":"10.13039\/501100002261","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The problem of an enormously large energy density of the quantum vacuum is discussed in connection with the concept of renormalization of physical parameters in quantum field theory. Using the method of dimensional regularization, it is recalled that the normal ordering procedure of creation and annihilation operators is equivalent to a renormalization of the cosmological constant leading to its zero and nonzero values in Minkowski space-time and in the standard cosmological model, respectively. It is argued that a frequently discussed gravitational effect, resulting from an enormously large energy density described by the nonrenormalized (bare) cosmological constant, might be nonobservable much like some other bare quantities introduced in the formalism of quantum field theory.<\/jats:p>","DOI":"10.3390\/sym11030314","type":"journal-article","created":{"date-parts":[[2019,3,4]],"date-time":"2019-03-04T05:45:36Z","timestamp":1551678336000},"page":"314","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Whether an Enormously Large Energy Density of the Quantum Vacuum Is Catastrophic"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8560-998X","authenticated-orcid":false,"given":"Vladimir M.","family":"Mostepanenko","sequence":"first","affiliation":[{"name":"Central Astronomical Observatory at Pulkovo of the Russian Academy of Sciences, Saint Petersburg 196140, Russia"},{"name":"Institute of Physics, Nanotechnology and Telecommunications, Peter the Great Saint Petersburg Polytechnic University, Saint Petersburg 195251, Russia"},{"name":"Kazan Federal University, Kazan 420008, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0495-5907","authenticated-orcid":false,"given":"Galina L.","family":"Klimchitskaya","sequence":"additional","affiliation":[{"name":"Central Astronomical Observatory at Pulkovo of the Russian Academy of Sciences, Saint Petersburg 196140, Russia"},{"name":"Institute of Physics, Nanotechnology and Telecommunications, Peter the Great Saint Petersburg Polytechnic University, Saint Petersburg 195251, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1103\/RevModPhys.61.1","article-title":"The cosmological constant problem","volume":"61","author":"Weinberg","year":"1989","journal-title":"Rev. Mod. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1146\/annurev.astro.46.060407.145243","article-title":"Dark Energy and the Accelerating Universe","volume":"46","author":"Frieman","year":"2008","journal-title":"Annu. Rev. Astron. Astrophys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1070\/PU1968v011n03ABEH003927","article-title":"The cosmological constant and the theory of elementary particles","volume":"11","year":"1968","journal-title":"Sov. Phys. Usp."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1119\/1.17850","article-title":"Vacuum catastrophe: An elementary exposition of the cosmological constant problem","volume":"63","author":"Adler","year":"1995","journal-title":"Am. J. Phys."},{"key":"ref_5","first-page":"12","article-title":"The 10 Biggest Unsolved Problems in Physics","volume":"1","author":"Hansson","year":"2015","journal-title":"Int. J. Mod. Phys. Appl."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Akhiezer, A.I., and Berestetskii, V.B. (1965). Quantum Electrodynamics, Interscience.","DOI":"10.1119\/1.1971111"},{"key":"ref_7","unstructured":"Bogoliubov, N., and Shirkov, D.V. (1980). Introduction to the Theory of Quantized Fields, John Wiley & Sons."},{"key":"ref_8","first-page":"793","article-title":"On the attraction between two perfectly conducting plates","volume":"51","author":"Casimir","year":"1948","journal-title":"Proc. K. Ned. Akad. Wet. B"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1827","DOI":"10.1103\/RevModPhys.81.1827","article-title":"The Casimir force between real materials: Experiment and theory","volume":"81","author":"Klimchitskaya","year":"2009","journal-title":"Rev. Mod. Phys."},{"key":"ref_10","unstructured":"Bordag, M., Klimchitskaya, G.L., Mohideen, U., and Mostepanenko, V.M. (2015). Advances in the Casimir Effect, Oxford University Press."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"085011","DOI":"10.1103\/PhysRevD.74.085011","article-title":"Energy-momentum tensor for a Casimir apparatus in a weak gravitational field","volume":"74","author":"Bimonte","year":"2006","journal-title":"Phys. Rev. D"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"025008","DOI":"10.1103\/PhysRevD.76.025008","article-title":"Relativistic mechanics of Casimir apparatuses in a weak gravitational field","volume":"76","author":"Bimonte","year":"2007","journal-title":"Phys. Rev. D"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"107701","DOI":"10.1103\/PhysRevD.78.107701","article-title":"Energy-momentum tensor for a scalar Casimir apparatus in a weak gravitational field: Neumann conditions","volume":"78","author":"Napolitano","year":"2006","journal-title":"Phys. Rev. D"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Elizalde, E. (2012). Ten Physical Applications of Spectral Zeta Function, Springer.","DOI":"10.1007\/978-3-642-29405-1"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3308","DOI":"10.1063\/1.530469","article-title":"The Vacuum Energy Density for Spherical and Cylindrical Universes","volume":"35","author":"Elizalde","year":"1994","journal-title":"J. Math. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"063515","DOI":"10.1103\/PhysRevD.67.063515","article-title":"Casimir effect in de Sitter and anti-de Sitter braneworlds","volume":"67","author":"Elizalde","year":"2003","journal-title":"Phys. Rev. D"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"021301","DOI":"10.1103\/PhysRevD.72.021301","article-title":"Casimir effect and the quantum vacuum","volume":"72","author":"Jaffe","year":"2005","journal-title":"Phys. Rev. D"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/0550-3213(72)90279-9","article-title":"Regularization and renormalization of gauge fields","volume":"44","author":"Veltmann","year":"1972","journal-title":"Nucl. Phys. B"},{"key":"ref_19","unstructured":"Gradshteyn, I.S., and Ryzhik, I.M. (2007). Table of Integrals, Series, and Products, Academic Press."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Birrell, N.D., and Davies, P.C.D. (1982). Quantum Fields in Curved Space, Cambridge University Press.","DOI":"10.1017\/CBO9780511622632"},{"key":"ref_21","unstructured":"Grib, A.A., Mamayev, S.G., and Mostepanenko, V.M. (1994). Vacuum Quantum Effects in Strong Fields, Friedmann Laboratory Publishing."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"366","DOI":"10.1007\/BF01017836","article-title":"Method of dimensional regularization for scalar and vector fields in homogeneous isotropic spaces","volume":"63","author":"Mamaev","year":"1985","journal-title":"Theor. Math. Phys."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/3\/314\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:35:46Z","timestamp":1760186146000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/3\/314"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,2]]},"references-count":22,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,3]]}},"alternative-id":["sym11030314"],"URL":"https:\/\/doi.org\/10.3390\/sym11030314","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2019,3,2]]}}}