LEADER 03277nam 22006495 450 001 9911015871503321 005 20250703130239.0 010 $a9789819637454$b(electronic bk.) 010 $z9789819637447 024 7 $a10.1007/978-981-96-3745-4 035 $a(MiAaPQ)EBC32196055 035 $a(Au-PeEL)EBL32196055 035 $a(CKB)39578196400041 035 $a(DE-He213)978-981-96-3745-4 035 $a(OCoLC)1527722185 035 $a(EXLCZ)9939578196400041 100 $a20250703d2025 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Dark Energy Paradigm $eThe Mysterious Universe /$fby B.G. Sidharth 205 $a1st ed. 2025. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2025. 215 $a1 online resource (241 pages) 311 08$aPrint version: Sidharth, B. G. The Dark Energy Paradigm Singapore : Springer,c2025 9789819637447 327 $aDark Energy Universe -- Violation of Lorentz Symmetry -- The Enigmatic Neutrino -- The Bizarre Spactime -- Mystery of the Missing Dark Matter -- Low-Dimensional Structures -- A Fifth Force in Nature -- An Explorer?s Miscellany. 330 $aThis book offers a compelling and philosophical exploration of the physical origins of inflation in the universe, grounded in the dimensional analysis of quantum mechanics and general relativity models. It posits that vacuum fluctuations drive inflation, presenting original ideas built upon the author?s previous work. In the late 1990s, the author introduced the concept of dark energy and an accelerating universe, which was promptly confirmed by the observations of Perlmutter, Kirschner, and Riess. The discovery of dark energy has led to several new paradigms, including the intriguing notion that spacetime is discrete, resembling a Cantor set. Additionally, the book provides the important insight that special relativity is founded on quantum mechanical amplitudes, rather than classical mechanics. Furthermore, the book delves into the noncommutative nature of spacetime. It investigates the potential existence of a fifth force, a new force, over and above the four well-known forces, supported by the experimental evidence that is analyzed and discussed. 606 $aQuantum theory 606 $aSpecial relativity (Physics) 606 $aElectrodynamics 606 $aStatistical mechanics 606 $aGravitation 606 $aQuantum Physics 606 $aSpecial Relativity 606 $aClassical Electrodynamics 606 $aStatistical Mechanics 606 $aGravitational Physics 615 0$aQuantum theory. 615 0$aSpecial relativity (Physics) 615 0$aElectrodynamics. 615 0$aStatistical mechanics. 615 0$aGravitation. 615 14$aQuantum Physics. 615 24$aSpecial Relativity. 615 24$aClassical Electrodynamics. 615 24$aStatistical Mechanics. 615 24$aGravitational Physics. 676 $a530.12 700 $aSidharth$b B. G$01833486 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9911015871503321 996 $aThe Dark Energy Paradigm$94408378 997 $aUNINA LEADER 05230nam 22007575 450 001 9910731456903321 005 20251113212104.0 010 $a3-031-28020-2 024 7 $a10.1007/978-3-031-28020-7 035 $a(MiAaPQ)EBC30592746 035 $a(Au-PeEL)EBL30592746 035 $a(DE-He213)978-3-031-28020-7 035 $a(CKB)26938277700041 035 $a(EXLCZ)9926938277700041 100 $a20230612d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aField Arithmetic /$fby Michael D. Fried, Moshe Jarden 205 $a4th ed. 2023. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2023. 215 $a1 online resource (839 pages) 225 1 $aErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,$x2197-5655 ;$v11 311 08$aPrint version: Fried, Michael D. Field Arithmetic Cham : Springer,c2023 9783031280191 327 $a1 Infinite Galois Theory and Profinite Groups -- 2 Valuations -- 3 Linear Disjointness -- 4 Algebraic Function Fields of One Variable -- 5 The Riemann Hypothesis for Function Fields -- 6 Plane Curves -- 7 The Chebotarev Density Theorem -- 8 Ultraproducts -- 9 Decision Procedures -- 10 Algebraically Closed Fields -- 11 Elements of Algebraic Geometry -- 12 Pseudo Algebraically Closed Fields -- 13 Hilbertian Fields -- 14 The Classical Hilbertian Fields -- 15 The Diamond Theorem -- 16 Nonstandard Structures -- 17 The Nonstandard Approach to Hilbert?s Irreducibility Theorem -- 18 Galois Groups over Hilbertian Fields -- 19 Small Profinite Groups -- 20 Free Profinite Groups -- 21 The Haar Measure -- 22 Effective Field Theory and Algebraic Geometry -- 23 The Elementary Theory of ????-Free PAC Fields -- 24 Problems of Arithmetical Geometry -- 25 Projective Groups and Frattini Covers -- 26 PAC Fields and Projective Absolute Galois Groups -- 27 Frobenius Fields -- 28 Free Profinite Groups of Infinite Rank -- 29 Random Elements in Profinite Groups -- 30 Omega-free PAC Fields -- 31 Hilbertian Subfields of Galois Extensions -- 32 Undecidability -- 33 Algebraically Closed Fields with Distinguished Automorphisms -- 34 Galois Stratification -- 35 Galois Stratification over Finite Fields -- 36 Problems of Field Arithmetic. 330 $aThis book uses algebraic tools to study the elementary properties of classes of fields and related algorithmic problems. The first part covers foundational material on infinite Galois theory, profinite groups, algebraic function fields in one variable and plane curves. It provides complete and elementary proofs of the Chebotarev density theorem and the Riemann hypothesis for function fields, together with material on ultraproducts, decision procedures, the elementary theory of algebraically closed fields, undecidability and nonstandard model theory, including a nonstandard proof of Hilbert's irreducibility theorem. The focus then turns to the study of pseudo algebraically closed (PAC) fields, related structures and associated decidability and undecidability results. PAC fields (fields K with the property that every absolutely irreducible variety over K has a rational point) first arose in the elementary theory of finite fields and have deep connections with number theory. Thisfourth edition substantially extends, updates and clarifies the previous editions of this celebrated book, and includes a new chapter on Hilbertian subfields of Galois extensions. Almost every chapter concludes with a set of exercises and bibliographical notes. An appendix presents a selection of open research problems. Drawing from a wide literature at the interface of logic and arithmetic, this detailed and self-contained text can serve both as a textbook for graduate courses and as an invaluable reference for seasoned researchers. 410 0$aErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,$x2197-5655 ;$v11 606 $aAlgebra 606 $aMathematics 606 $aGeometry, Algebraic 606 $aAlgebraic fields 606 $aPolynomials 606 $aGeometry 606 $aLogic, Symbolic and mathematical 606 $aAlgebra 606 $aMathematics 606 $aAlgebraic Geometry 606 $aField Theory and Polynomials 606 $aGeometry 606 $aMathematical Logic and Foundations 615 0$aAlgebra. 615 0$aMathematics. 615 0$aGeometry, Algebraic. 615 0$aAlgebraic fields. 615 0$aPolynomials. 615 0$aGeometry. 615 0$aLogic, Symbolic and mathematical. 615 14$aAlgebra. 615 24$aMathematics. 615 24$aAlgebraic Geometry. 615 24$aField Theory and Polynomials. 615 24$aGeometry. 615 24$aMathematical Logic and Foundations. 676 $a658.40301 676 $a512.3 700 $aFried$b Michael D$055735 701 $aJarden$b Moshe$055736 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910731456903321 996 $aField arithmetic$9717341 997 $aUNINA