Ralf Meelker · 2026

Precausal Substrate Theory

References

Appendix E of the book, all 187 sources in printed order.

Every reference in Precausal Substrate Theory, numbered as it is in the book. Each entry ends with a short link (meelker.nl/pst/ref<n>) that resolves to its source. The 28 entries marked mirrored are hosted here because they are public domain or openly licensed — those, gathered on their own with licence and provenance, are on the Library page. The rest link to their published homes.

[1]
A. Einstein, “Die Feldgleichungen der Gravitation,” Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften (Berlin), 844 (1915).
[2]
R. Penrose, “Gravitational collapse and space-time singularities,” Phys. Rev. Lett. 14, 57 (1965).
[3]
S. W. Hawking and R. Penrose, “The singularities of gravitational collapse and cosmology,” Proc. R. Soc. Lond. A 314, 529 (1970).
[4]
L. Bombelli, J. Lee, D. Meyer, R. D. Sorkin, “Space-time as a causal set,” Phys. Rev. Lett. 59, 521 (1987).
[5]
R. D. Sorkin, “Forks in the road, on the way to quantum gravity,” Int. J. Theor. Phys. 36, 2759 (1997).
[6]
C. Rovelli and L. Smolin, “Loop space representation of quantum general relativity,” Nucl. Phys. B 331, 80 (1990).
[7]
A. Ashtekar, “New variables for classical and quantum gravity,” Phys. Rev. Lett. 57, 2244 (1986).
[8]
V. L. Ginzburg and L. D. Landau, “On the theory of superconductivity,” Zh. Eksp. Teor. Fiz. 20, 1064 (1950). Reprinted in L. D. Landau, Collected Papers, Pergamon Press (1965).
[9]
S. Mac Lane, Categories for the Working Mathematician, Springer, New York (1971).
[10]
C. W. Misner, K. S. Thorne, J. A. Wheeler, Gravitation, W. H. Freeman, San Francisco (1973).
[11]
H. B. G. Casimir, “On the attraction between two perfectly conducting plates,” Proc. Kon. Ned. Akad. Wetensch. 51, 793 (1948).
[12]
S. K. Lamoreaux, “Demonstration of the Casimir force in the 0.6 to 6 range,” Phys. Rev. Lett. 78, 5 (1997).
[13]
G. Bressi, G. Carugno, R. Onofrio, G. Ruoso, “Measurement of the Casimir force between parallel metallic surfaces,” Phys. Rev. Lett. 88, 041804 (2002).
[14]
R. S. Decca, D. López, E. Fischbach, D. E. Krause, “Measurement of the Casimir force between dissimilar metals,” Phys. Rev. Lett. 91, 050402 (2003).
[15]
M. Bordag, U. Mohideen, V. M. Mostepanenko, “New developments in the Casimir effect,” Phys. Rept. 353, 1 (2001).
[16]
N. Arkani-Hamed, S. Dimopoulos, G. Dvali, “The hierarchy problem and new dimensions at a millimeter,” Phys. Lett. B 429, 263–272 (1998).
[17]
E. M. Lifshitz, “The theory of molecular attractive forces between solids,” Sov. Phys. JETP 2, 73 (1956).
[18]
E. P. Verlinde, “On the origin of gravity and the laws of Newton,” JHEP 04 (2011) 029.
[19]
T. Jacobson, “Thermodynamics of spacetime: The Einstein equation of state,” Phys. Rev. Lett. 75, 1260 (1995).
[20]
A. Einstein, “Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie,” Sitzungsber. Preuss. Akad. Wiss. 142 (1917).
[21]
E. Noether, “Invariante Variationsprobleme,” Nachr. D. König. Gesellsch. D. Wiss. Zu Göttingen, Math-phys. Klasse, 235 (1918). English translation: M. A. Tavel, Transp. Theory Stat. Phys. 1, 186 (1971).
[22]
D. Lovelock, “The Einstein tensor and its generalizations,” J. Math. Phys. 12, 498–501 (1971).
[23]
P. A. M. Dirac, The Principles of Quantum Mechanics, Clarendon Press, Oxford (1930); 4th ed. (1958).
[24]
J. von Neumann, Mathematische Grundlagen der Quantenmechanik, Springer, Berlin (1932). English translation: Mathematical Foundations of Quantum Mechanics, Princeton University Press (1955; reprint 2018).
[25]
R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill, New York (1965). Dover emended edition (2010).
[26]
M. B. Green, J. H. Schwarz, E. Witten, Superstring Theory (2 vols.), Cambridge University Press (1987).
[27]
E. Witten, “String theory dynamics in various dimensions,” Nuclear Physics B 443 (1995) 85–126.
[28]
T. Kaluza, “Zum Unitätsproblem der Physik,” Sitzungsber. Preuss. Akad. Wiss. Berlin (1921) 966–972.
[29]
O. Klein, “Quantentheorie und fünfdimensionale Relativitätstheorie,” Zeitschrift für Physik 37 (1926) 895–906.
[30]
L. Randall, R. Sundrum, “A large mass hierarchy from a small extra dimension,” Physical Review Letters 83 (1999) 3370–3373.
[31]
J. Ambjrn, J. Jurkiewicz, R. Loll, “Reconstructing the universe,” Physical Review D 72 (2005) 064014.
[32]
G. 't Hooft, “Dimensional reduction in quantum gravity,” arXiv:gr-qc/9310026 (1993).
[33]
J. Maldacena, “The large N limit of superconformal field theories and supergravity,” International Journal of Theoretical Physics 38 (1999) 1113–1133.
[34]
I. Kant, Kritik der reinen Vernunft. Hartknoch, Riga, 1781. English translation: Critique of Pure Reason, trans. N. Kemp Smith, Macmillan, London, 1929.
[35]
J. Henson, “The causal set approach to quantum gravity,” in D. Oriti (ed.), Approaches to Quantum Gravity, Cambridge University Press, Cambridge, 2009, pp. 393–413.
[36]
J. B. Hartle and S. W. Hawking, “Wave function of the universe,” Physical Review D 28 (1983) 2960–2975.
[37]
R. Geroch, “Domain of dependence,” Journal of Mathematical Physics 11 (1970) 437–449.
[38]
R. M. Wald, General Relativity. University of Chicago Press, Chicago, 1984.
[39]
G. Ryle, The Concept of Mind. Hutchinson, London, 1949.
[40]
H. Putnam, Reason, Truth and History. Cambridge University Press, Cambridge, 1981.
[41]
G. W. Leibniz, “La Monadologie,” 1714. English translation: The Monadology, in Philosophical Papers and Letters, 2nd ed., trans. L. E. Loemker, Reidel, Dordrecht, 1969.
[42]
A. Vilenkin, “Creation of universes from nothing,” Physics Letters B 117 (1982) 25–28.
[43]
J. Goldstone, “Field Theories with Superconductor Solutions,” Il Nuovo Cimento 19 (1961) 154–164.
[44]
P. A. M. Dirac, “The cosmological constants,” Nature 139 (1937) 323.
[45]
B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), “Observation of gravitational waves from a binary black hole merger,” Physical Review Letters 116 (2016) 061102.
[46]
J. D. Bekenstein, “Black holes and entropy,” Physical Review D 7 (1973) 2333–2346.
[47]
S. W. Hawking, “Particle creation by black holes,” Communications in Mathematical Physics 43 (1975) 199–220.
[48]
A. Connes, Noncommutative Geometry. Academic Press, San Diego, 1994.
[49]
A. H. Chamseddine and A. Connes, “The spectral action principle,” Commun. Math. Phys. 186 (1997) 731–750, arXiv:hep-th/9606001.
[50]
A. H. Chamseddine, A. Connes, and M. Marcolli, “Gravity and the standard model with neutrino mixing,” Adv. Theor. Math. Phys. 11 (2007) 991–1089, arXiv:hep-th/0610241.
[51]
D. Buttazzo, G. Degrassi, P. P. Giardino, G. F. Giudice, F. Sala, A. Salvio, and A. Strumia, “Investigating the near-criticality of the Higgs boson,” JHEP 12 (2013) 089, arXiv:1307.3536.
[52]
A. H. Guth, “Inflationary universe: A possible solution to the horizon and flatness problems,” Physical Review D 23 (1981) 347–356.
[53]
A. D. Linde, “Chaotic inflation,” Physics Letters B 129 (1983) 177–181.
[54]
A. M. Gleason, “Measures on the closed subspaces of a Hilbert space,” J. Math. Mech. 6 (1957) 885–893.
[55]
B. Efron and C. Stein, “The jackknife estimate of variance,” Ann. Statist. 9 (1981) 586–596.
[56]
R. O'Donnell, Analysis of Boolean Functions, Cambridge University Press (2014). ISBN 978-1107038325.
[57]
B. S. DeWitt, Dynamical Theory of Groups and Fields, Gordon and Breach, New York (1965).
[58]
P. B. Gilkey, “The spectral geometry of a Riemannian manifold,” J. Differential Geometry 10 (1975) 601–618.
[59]
D. V. Vassilevich, “Heat kernel expansion: User's manual,” Phys. Rept. 388 (2003) 279–360.
[60]
B. S. DeWitt, “Quantum Theory of Gravity. I. The Canonical Theory,” Physical Review 160 (1967) 1113–1148.
[61]
G. Spencer-Brown, Laws of Form. Allen & Unwin, London, 1969.
[62]
J. A. Wheeler, “Information, Physics, Quantum: The Search for Links,” in W. H. Zurek (ed.), Complexity, Entropy and the Physics of Information, Addison-Wesley, Redwood City, CA, 1990 [reprinted in Feynman and Computation, CRC Press].
[63]
M. Tegmark, “The Mathematical Universe,” Foundations of Physics 38 (2008) 101–150.
[64]
J. Ladyman, “What is Structural Realism?” Studies in History and Philosophy of Science 29 (1998) 409–424.
[65]
S. French, The Structure of the World: Metaphysics and Representation. Oxford University Press, Oxford, 2014. ISBN 978-0-19-968484-7.
[66]
D. Bohm, Wholeness and the Implicate Order. Routledge & Kegan Paul, London, 1980.
[67]
G. W. F. Hegel, Science of Logic, trans. A. V. Miller. Allen & Unwin, London, 1969 (original: Wissenschaft der Logik, Cotta, Nuremberg, 1812–1816).
[68]
A. Friedmann, “Über die Krümmung des Raumes,” Zeitschrift für Physik 10 (1922) 377–386.
[69]
A. G. Riess et al. (High-z Supernova Search Team), “Observational evidence from supernovae for an accelerating universe and a cosmological constant,” The Astronomical Journal 116 (1998) 1009–1038.
[70]
S. Perlmutter et al. (Supernova Cosmology Project), “Measurements of Ømega and Łambda from 42 high-redshift supernovae,” The Astrophysical Journal 517 (1999) 565–586.
[71]
N. Aghanim et al. (Planck Collaboration), “Planck 2018 results. VI. Cosmological parameters,” Astronomy & Astrophysics 641 (2020) A7.
[72]
H. Bondi and T. Gold, “The steady-state theory of the expanding universe,” Monthly Notices of the Royal Astronomical Society 108 (1948) 252–270.
[73]
F. Hoyle, “A new model for the expanding universe,” Monthly Notices of the Royal Astronomical Society 108 (1948) 372–382.
[74]
A. A. Penzias and R. W. Wilson, “A measurement of excess antenna temperature at 4080 Mc/s,” The Astrophysical Journal 142 (1965) 419–421.
[75]
P. W. Higgs, “Broken symmetries and the masses of gauge bosons,” Phys. Rev. Lett. 13 (1964) 508–509.
[76]
F. Englert and R. Brout, “Broken symmetry and the mass of gauge vector mesons,” Phys. Rev. Lett. 13 (1964) 321–323.
[77]
S. Weinberg, “A model of leptons,” Phys. Rev. Lett. 19 (1967) 1264–1266.
[78]
A. Salam, “Weak and electromagnetic interactions,” in Proceedings of the 8th Nobel Symposium, ed. N. Svartholm, Almqvist & Wiksell, Stockholm (1968), pp. 367–377 [reprinted in Selected Papers of Abdus Salam, World Scientific Series in 20th Century Physics (1994)].
[79]
S. L. Glashow, “Partial symmetries of weak interactions,” Nucl. Phys. 22 (1961) 579–588.
[80]
H. Fritzsch, M. Gell-Mann, and H. Leutwyler, “Advantages of the color octet gluon picture,” Phys. Lett. B 47 (1973) 365–368.
[81]
D. J. Gross and F. Wilczek, “Ultraviolet behavior of non-Abelian gauge theories,” Phys. Rev. Lett. 30 (1973) 1343–1346.
[82]
H. D. Politzer, “Reliable perturbative results for strong interactions?” Phys. Rev. Lett. 30 (1973) 1346–1349.
[83]
T. D. Lee and C. N. Yang, “Question of parity conservation in weak interactions,” Phys. Rev. 104 (1956) 254–258.
[84]
C. S. Wu, E. Ambler, R. W. Hayward, D. D. Hoppes, and R. P. Hudson, “Experimental test of parity conservation in beta decay,” Phys. Rev. 105 (1957) 1413–1415.
[85]
S. L. Adler, “Axial-vector vertex in spinor electrodynamics,” Phys. Rev. 177 (1969) 2426–2438.
[86]
J. S. Bell and R. Jackiw, “A PCAC puzzle: ^0 in the -model,” Nuovo Cim. A 60 (1969) 47–61.
[87]
G. Aad et al. (ATLAS Collaboration), “Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC,” Phys. Lett. B 716 (2012) 1–29.
[88]
S. Chatrchyan et al. (CMS Collaboration), “Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC,” Phys. Lett. B 716 (2012) 30–61.
[89]
S. Weinberg, “Implications of dynamical symmetry breaking,” Phys. Rev. D 13 (1976) 974–996; addendum 19 (1979) 1277–1280.
[90]
L. Susskind, “Dynamics of spontaneous symmetry breaking in the Weinberg-Salam theory,” Phys. Rev. D 20 (1979) 2619–2625.
[91]
S. Coleman and E. Weinberg, “Radiative corrections as the origin of spontaneous symmetry breaking,” Phys. Rev. D 7 (1973) 1888–1910.
[92]
N. Arkani-Hamed, A. G. Cohen and H. Georgi, “Electroweak symmetry breaking from dimensional deconstruction,” Phys. Lett. B 513 (2001) 232–240.
[93]
R. L. Workman et al. (Particle Data Group), “Review of particle physics,” Prog. Theor. Exp. Phys. 2022 (2022) 083C01.
[94]
M. J. G. Veltman, “The Infrared–Ultraviolet Connection,” Acta Phys. Polon. B 12 (1981) 437–457.
[95]
G. 't Hooft, “Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking,” in Recent Developments in Gauge Theories, NATO ASI Series B59, eds. G. 't Hooft et al., Plenum Press, New York (1980), pp. 135–157.
[96]
J. Polchinski, “Renormalization and effective lagrangians,” Nucl. Phys. B 231 (1984) 269–295.
[97]
R. Rajaraman, Solitons and Instantons: An Introduction to Solitons and Instantons in Quantum Field Theory, North-Holland, Amsterdam (1982). ISBN 978-0-444-86229-7.
[98]
U. Mosco, “Composite media and asymptotic Dirichlet forms,” J. Funct. Anal. 123 (1994) 368–421.
[99]
M. E. Taylor, Partial Differential Equations I: Basic Theory, Springer, New York (1996); 2nd ed. (2011).
[100]
C. McDiarmid, “On the method of bounded differences,” in Surveys in Combinatorics 1989, London Math. Soc. Lecture Note Ser. 141, Cambridge Univ. Press (1989), pp. 148–188.
[101]
W. Feller, An Introduction to Probability Theory and Its Applications, Vol. II, 2nd ed., Wiley, New York (1971).
[102]
S. C. Brenner and L. R. Scott, The Mathematical Theory of Finite Element Methods, 3rd ed., Springer, New York (2008).
[103]
C.-G. Esseen, “A moment inequality with an application to the central limit theorem,” Skandinavisk Aktuarietidskrift 39 (1956) 160–170.
[104]
I. G. Shevtsova, “An improvement of convergence rate estimates in the Lyapunov theorem,” Doklady Mathematics 82 (2010) 862–864, arXiv:1111.6554.
[105]
P. Jordan and E. Wigner, “Über das Paulische Äquivalenzverbot,” Zeitschrift für Physik 47 (1928) 631–651.
[106]
W. H. Zurek, “Decoherence, einselection, and the quantum origins of the classical,” Rev. Mod. Phys. 75 (2003) 715–775, arXiv:quant-ph/0105127.
[107]
A. Kitaev and J. Preskill, “Topological entanglement entropy,” Phys. Rev. Lett. 96 (2006) 110404, arXiv:hep-th/0510092.
[108]
R. F. Streater and A. S. Wightman, PCT, Spin and Statistics, and All That, Benjamin, New York (1964).
[109]
R. Haag, Local Quantum Physics: Fields, Particles, Algebras, 2nd ed., Springer, Berlin (1996).
[110]
J. Hadamard, Lectures on Cauchy's Problem in Linear Partial Differential Equations, Yale University Press, New Haven (1923; Dover reprint 1952).
[111]
R. Courant and D. Hilbert, Methods of Mathematical Physics, Volume II: Partial Differential Equations, Interscience Publishers, New York (1962).
[112]
S. W. Hawking, “The occurrence of singularities in cosmology. III. Causality and singularities,” Proc. Roy. Soc. A 300 (1967) 187–201.
[113]
T. Friedrich, “Der erste Eigenwert des Dirac-Operators einer kompakten, Riemannschen Mannigfaltigkeit nichtnegativer Skalarkrümmung,” Math. Nachr. 97 (1980) 117–146.
[114]
C. Bär, “The Dirac operator on space forms of positive curvature,” J. Math. Soc. Japan 48 (1996) 69–83.
[115]
M. A. Rieffel, “Matrix algebras converge to the sphere for quantum Gromov–Hausdorff distance,” Mem. Amer. Math. Soc. 168 (2004) 67–91.
[116]
M. A. Rieffel, “Gromov–Hausdorff distance for quantum metric spaces,” Mem. Amer. Math. Soc. 168 (2004) 1–65.. The bridge construction (Definition 5.1) and the metric-via-bridge theorem (Theorem 5.2) used to lift the section round-trip lemma to quantum Gromov–Hausdorff convergence.
[117]
F. Latrémolière, “The dual-modular Gromov–Hausdorff propinquity and completeness,” J. Noncommut. Geom. (2022).
[118]
F. Latrémolière, “The Gromov–Hausdorff propinquity for metric spectral triples,” Adv. Math. 404 (2022) 108393.
[119]
T. Bhattacharyya and S. Singla, “Sequences of operator algebras converging to odd spheres in the quantum Gromov–Hausdorff distance,” preprint (2022).
[120]
P. Diaconis and M. Shahshahani, “Time to reach stationarity in the Bernoulli–Laplace diffusion model,” SIAM J. Math. Anal. 18 (1987) 208–218.
[121]
C. Furey, “Generations: three prints, in colour,” J. High Energy Phys. 10 (2014) 046.
[122]
C. Furey, “Three generations, two unbroken gauge symmetries, and one eight-dimensional algebra,” Phys. Lett. B 785 (2018) 84–89. %, References cited only in Appendix D (substrate-theory comparison) —.
[123]
S. Wolfram, “A Class of Models with the Potential to Represent Fundamental Physics,” Complex Systems 29 (2020) 107–536.
[124]
G. 't Hooft, The Cellular Automaton Interpretation of Quantum Mechanics, Fundamental Theories of Physics, vol. 185, Springer, Cham (2016).
[125]
D. Oriti, “Group field theory as the second quantization of loop quantum gravity,” Class. Quantum Grav. 33 (2016) 085005.
[126]
R. Penrose, “Twistor algebra,” J. Math. Phys. 8 (1967) 345–366.
[127]
M. Cortês and L. Smolin, “Quantum energetic causal sets,” Phys. Rev. D 90 (2014) 044035, arXiv:1308.2206.
[128]
L. Hardy, “Probability theories with dynamic causal structure: A new framework for quantum gravity,” arXiv:gr-qc/0509120 (2005).
[129]
F. Finster and J. Kleiner, “Causal Fermion Systems as a Candidate for a Unified Physical Theory,” J. Phys. Conf. Ser. 626 (2015) 012020.
[130]
T. Banks, W. Fischler, S. H. Shenker and L. Susskind, “M theory as a matrix model: A conjecture,” Phys. Rev. D 55 (1997) 5112–5128.
[131]
A. D. Sakharov, “Vacuum quantum fluctuations in curved space and the theory of gravitation,” Sov. Phys. Dokl. 12 (1968) 1040–1041 [reprinted Gen. Rel. Grav. 32 (2000) 365–367].
[132]
T. Padmanabhan, “Thermodynamical aspects of gravity: New insights,” Rep. Prog. Phys. 73 (2010) 046901.
[133]
E. P. Verlinde, “Emergent gravity and the dark universe,” SciPost Phys. 2 (2017) 016.
[134]
J. Maldacena and L. Susskind, “Cool horizons for entangled black holes,” Fortschr. Phys. 61 (2013) 781–811.
[135]
M. Van Raamsdonk, “Building up spacetime with quantum entanglement,” Gen. Rel. Grav. 42 (2010) 2323–2329.
[136]
B. Swingle, “Entanglement renormalization and holography,” Phys. Rev. D 86 (2012) 065007.
[137]
G. Vidal, “Entanglement renormalization,” Phys. Rev. Lett. 99 (2007) 220405.
[138]
G. M. Dixon, Division Algebras: Octonions, Quaternions, Complex Numbers and the Algebraic Design of Physics, Kluwer Academic Publishers, Dordrecht (1994).
[139]
T. Dray and C. A. Manogue, “Quaternionic spin,” in Clifford Algebras and their Applications in Mathematical Physics, R. Ablamowicz and B. Fauser (eds.), Birkhäuser, Boston (2000), pp. 21–37.
[140]
D. Deutsch and C. Marletto, “Constructor theory of information,” Proc. R. Soc. A 471 (2015) 20140540.
[141]
B. Kriger, “The Information Substrate Theory, Volume VII: Information as the Name of Differentiatedness, and the Known Measures as Projections of One Substrate,” IIIR Cosmology and Theoretical Physics (2026).
[142]
C. S. Montanari, “Foundations and Replication Dynamics (Paper I),” Fermilab Technical Note FERMILAB-TM-2923-PPD (2025).
[143]
J. Reed, The Substrate Theory of Everything: A Comprehensive Technical Thesis, independently published (2024); ISBN 9798198320833. See also The Substrate Theory of Everything: A Technical Paper, ISBN 9798198317031; The Substrate Theory of Everything: A Comprehensive Textbook, ISBN 9798198310933; and The Substrate: A New Theory of Everything, ISBN 9798198228726. Released for public review on 26 June 2026 with a proposed resolution of the cosmological-constant problem.
[144]
M. Englis, Toeplitz operators on Bergman-type spaces, Ph.D. thesis, Mathematical Institute, Czechoslovak Academy of Sciences, Prague (1991).
[145]
K. Zhu, Operator Theory in Function Spaces, 2nd ed., Mathematical Surveys and Monographs vol. 138, American Mathematical Society (2007).
[146]
G.M. Dixon, Division Algebras; Spinors; Idempotents; The Algebraic Structure of Reality, talk given at the 2nd Mile High Conference on Nonassociative Mathematics, Denver (2009); arXiv:1012.1304 [hep-th] (2010). See also G.M. Dixon, Division Algebras: Octonions, Quaternions, Complex Numbers and the Algebraic Design of Physics, Kluwer Academic Publishers (1994).
[147]
F. Hoyle, J.V. Narlikar, A new theory of gravitation, Proc. R. Soc. Lond. A 282, 191 (1964); see also Mach's principle and the creation of matter, Proc. R. Soc. Lond. A 273, 1 (1963), and J.V. Narlikar, Introduction to Cosmology, 3rd ed., CUP (2002).
[148]
R. Bott, “The stable homotopy of the classical groups,” Ann. of Math. (2) 70, 313 (1959).
[149]
M. F. Atiyah, K-Theory, Westview Press / Addison-Wesley Advanced Book Classics, Boulder, CO (1989). [Originally Benjamin, 1967.].
[150]
A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications, 2nd ed., Stochastic Modelling and Applied Probability 38, Springer, Berlin Heidelberg (2010).
[151]
P. R. Halmos and L. J. Savage, “Application of the Radon–Nikodym theorem to the theory of sufficient statistics,” Annals of Mathematical Statistics 20 (1949) 225–241.
[152]
A. Lichnerowicz, “Spineurs harmoniques,” C. R. Acad. Sci. Paris 257, 7 (1963).
[153]
H. B. Lawson and M.-L. Michelsohn, Spin Geometry, Princeton Mathematical Series 38, Princeton University Press (1989).
[154]
P. Lounesto, Clifford Algebras and Spinors, 2nd ed., London Mathematical Society Lecture Note Series 286, Cambridge University Press (2001).
[155]
C. N. Yang and R. L. Mills, “Conservation of isotopic spin and isotopic gauge invariance,” Phys. Rev. 96, 191 (1954).
[156]
R. Bott, “Nondegenerate critical manifolds,” Ann. of Math. (2) 60, 248 (1954).
[157]
D. Hilbert, “Die Grundlagen der Physik (Erste Mitteilung),” Nachr. Ges. Wiss. Göttingen, Math.-Phys. Kl. 395 (1915).
[158]
I. Schur, “Neue Begründung der Theorie der Gruppencharaktere,” Sitzungsber. Königl. Preuss. Akad. Wiss. Berlin 406 (1905).
[159]
S. L. Sobolev, “Sur un théorème d'analyse fonctionnelle,” Mat. Sbornik 4(46), 471 (1938).
[160]
H. Yukawa, “On the interaction of elementary particles. I,” Proc. Phys.-Math. Soc. Japan (3rd Ser.) 17, 48 (1935).
[161]
G. C. Wick, “Properties of Bethe-Salpeter wave functions,” Phys. Rev. 96, 1124 (1954).
[162]
H. Weyl, “Elektron und Gravitation. I,” Z. Phys. 56, 330 (1929).
[163]
E. C. G. Stueckelberg, “Die Wechselwirkungskräfte in der Elektrodynamik und in der Feldtheorie der Kernkräfte,” Helv. Phys. Acta 11, 225 (1938).
[164]
A. Hurwitz, “Über die Komposition der quadratischen Formen,” Math. Ann. 88, 1 (1923).
[165]
J. L. Walsh, “A closed set of normal orthogonal functions,” Amer. J. Math. 45, 5 (1923).
[166]
S.-T. Yau, “On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation. I,” Comm. Pure Appl. Math. 31, 339 (1978).
[167]
M. Gell-Mann, “Symmetries of baryons and mesons,” Phys. Rev. 125, 1067 (1962).
[168]
P. Billingsley, Probability and Measure, 3rd ed., Wiley, New York (1995).
[169]
I. Chavel, Eigenvalues in Riemannian Geometry, Pure and Applied Mathematics 115, Academic Press, Orlando (1984).
[170]
I. M. Gelfand and S. V. Fomin, Calculus of Variations, Prentice-Hall, Englewood Cliffs, NJ (1963).
[171]
H. Georgi, Lie Algebras in Particle Physics, 2nd ed., Frontiers in Physics 54, Westview Press, Boulder, CO (1999).
[172]
J. W. Milnor and J. D. Stasheff, Characteristic Classes, Annals of Mathematics Studies 76, Princeton University Press (1974).
[173]
M. Reed and B. Simon, Methods of Modern Mathematical Physics I: Functional Analysis, rev. ed., Academic Press, New York (1980).
[174]
I. Newton, Philosophi Naturalis Principia Mathematica, Royal Society, London (1687).
[175]
H. Minkowski, “Raum und Zeit,” Phys. Z. 10, 104 (1909).
[176]
V. A. Fock, “Konfigurationsraum und zweite Quantelung,” Z. Phys. 75, 622 (1932).
[177]
E. Majorana, “Teoria simmetrica dell'elettrone e del positrone,” Nuovo Cimento 14, 171 (1937).
[178]
M. F. Atiyah and I. M. Singer, “The index of elliptic operators on compact manifolds,” Bull. Amer. Math. Soc. 69, 422 (1963).
[179]
H. P. Robertson, “Kinematics and world-structure,” Astrophys. J. 82, 284 (1935).
[180]
A. G. Walker, “On Milne's theory of world-structure,” Proc. London Math. Soc. (2) 42, 90 (1937).
[181]
H. A. Lorentz, “Electromagnetic phenomena in a system moving with any velocity smaller than that of light,” Proc. Roy. Neth. Acad. Arts Sci. 6, 809 (1904).
[182]
B. Riemann, “Über die Hypothesen, welche der Geometrie zu Grunde liegen,” Abh. Königl. Ges. Wiss. Göttingen 13, 133 (1868).
[183]
L. Boltzmann, “Über die Beziehung zwischen dem zweiten Hauptsatze der mechanischen Wärmetheorie und der Wahrscheinlichkeitsrechnung,” Wiener Berichte 76, 373 (1877). English translation: K. Sharp and F. Matschinsky, Entropy 17, 1971 (2015).
[184]
C. Hermite, “Remarque sur un théorème de M. Cauchy,” C. R. Acad. Sci. Paris 41, 181 (1855).
[185]
Euclid, The Thirteen Books of Euclid's Elements, transl. T. L. Heath, 2nd ed., Cambridge University Press (1926).
[186]
B. Taylor, Methodus Incrementorum Directa et Inversa, Gulielmus Innys, London (1715).
[187]
G. W. Leibniz, “Nova methodus pro maximis et minimis,” Acta Eruditorum 467 (1684).
v31.2.23