Foundations of Physics

, Volume 27, Issue 5, pp 625–729

Relativistic hadronic mechanics: Nonunitary, axiom-preserving completion of relativistic quantum mechanics

  • Ruggero Maria Santilli


The most majestic scientific achievement, of this century in mathematical beauty, axiomatic consistency, and experimental verifications has been special relativity with its unitary structure at the operator level, and canonical structure at the classical levels, which has turned out to be exactly valid for point particles moving in the homogenenous and isotropic vacuum (exterior dynamical problems). In recent decades a number of authors have studied nonunitary and noncanonical theories, here generally calleddeformations for the representation of broader conditions, such as extended and deformable particles moving within inhomogeneous and anisotrophic physical media (interior dynamical problems). In this paper we show that nonunitary deformations, including, q-, k-, quatum-, Lie-isotopic, Lie-admissible, and other deformations, even thoughmathematically correct, have a number of problematic aspects ofphysical character when formulated on conventional spaces over conditional fields, such as lack of invariance of the basic space-time units, ambiguous applicability to measurements, loss of Hermiticity-observability in time, lack of invariant numerical predictions, loss of the axions of special relativity, and others. We then show that the classical noncanonical counterparts of the above nonunitary deformations are equally afflicted by corresponding problems of physical consistency. We also show that the contemporary formulation of gravity is afflicted by similar problematic aspects because Riemannian spaces are noncanonical deformations of Minkowskian spaces, thus having noninvariant space-time units. We then point out that new mathematical methods, calledisotopies, genotopies, hyperstructures and their isoduals, offer the possibilities of constructing a nonunitary theory, known asrelativistic hadronic mechanics which: (1) is as axiomatically consistent as relativistic quantum mechanics, (2) preserves the abstract axioms of special relativity, and (3) results in a completion of the conventional mechanics much along the celebrated Einstein-Podolski-Rosen argument. A number of novel applications are indicated, such as a geometric unification of the special and general relativity via the isominkowskian geometry in which the two relativities are differentiated via the invariant basic unit, while preserving conventional Riemannian metrics, Einstein's field equations, and related experimental verifications; a novel operator form of gravity verifying the axioms of relativistic quantum mechanics under the universal isopoincaré symmetry; a new structure model of hadrons with conventional massive particles as physical constituents which is compatile with composite quarks and with established unitary classifications; and other novels applications in nuclear physics, astrophysics, theoretical biology, and other fields. The paper ends with the proposal of a number of new experiments, some of which may imply new practical applications, such as conceivable new forms of recycling nuclear waste. The achievement of axiomatic consistency in the study of the above physical problems has been possible for the first time in this paper thanks to mathematical advances that recently appeared in a special issue of theRendiconti Circolo Matematico Palermo, and in other journals identified in the Acknowledgements.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. A. Albert,Trans. Am. Math. Soc. 64, 552 (1948).CrossRefMathSciNetGoogle Scholar
  2. 2.
    R. M. Santilli,Nuovo Cimento 51, 570 (1967); [2a];Meccanica 1, 3 (1969) [2b];Suppl. Nuovo Cimento 6, 1225 (1968) [2c].MathSciNetGoogle Scholar
  3. 3.
    R. M. Santilli,Hadronic J. 1, 224 and 1267 (1978) [3a];Hadronic J. 1, 574 [3b];Phys. Rev. D. 20, 555 (1979) [3c];Foundations of Theoretical Mechanics, Vols. I (1978) and II (1983) (Springer, New York) [3d];Lie-Admissible Approach to the Hadronic Structure, Vol. I (1978), II (1982) (Hadronic Press, Palm Harbor, Florida) [3e];Ann. Phys. 103, 354 and 409,1105, 227 (1977) [3f]; “Invariant Lie-admissible formulation of Biedenharn's 1989 paper onq-deformations,” inBiedenharn's Memorial Volume, L. van der Merwe,et al., s., (Plenum, 1997), in press [3g]; M. Battler, M. McBee, and S. Smith, Web Site[3h].Google Scholar
  4. 4.
    R. M. Santilli,Nuovo Cimento Lett. 37, 545 (1983) [4a];Hadronic J. 8, 25 and 36 (1985) [4b];JINR Rapid Commun. 6, 24 (1993) [4c];J. Moscow Phys. Soc. 3, 255 (1993) [4d];Chin. J. Syst. Eng. Electr. 6, 177 (1996) [4e];Lett. Nuovo Cimento 3, 509, (1983) [4f].ADSMathSciNetGoogle Scholar
  5. 5.
    A. K. Aringazin, A. Jannussis, D. F. Lopez, M. Nishioka, and B. Veljanosky,Sanitlli's Lie-Isotopic Generalization of Galilei's and Einstein's Relativities (Kostarakis Publisher, Athens, Greece, 1990) [5a]. J. V. Kadeisvili,Santilli's Isotopies of contemporary Algebras, Geometries and Relativities (Hadronic Press, Florida, 1991, 2nd edn., Ukraine Academy of Sciences, Kiev, in press) [5b]. D. S. Sourlas and G. T. Tsagas,Mathematical Foundations of the Lie-Santilli Theory (Ukraine Academy of Science, Kiev, 1993) [5c]. Palm Harbor, Florida, 1994) [5d]. J. V. Kadeisvili,An introduction to the Lie-Santilli isotheory with Application to Quantum Gravity (Ukraine Academy of Science, Kiev in press) [5e]; J. V. Kadeisvili, inSymmetry Methods in Physics (Ya. S. Smorodinsky Memorial Volume, A. N. Sissakian, G. S. Pogosyan, and S. I. Vinitsky, eds, J.I.N.R., Dubna, Russia, 1994) [5f]. J. V. Kadeisvili,Math. Meth. Appl. Sci. 19, 362 (1996) [5g].Google Scholar
  6. 6.
    S. L. Adler,Phys. Rev. 17, 3212 (1978) [6a]. S. Okubo,Hadronic J. 5, 1667 (1982) [6b]. R. Mignani,Hadronic J. 5, 1120 (1982) [6c];Nuovo Cimento Lett. 39, 413 (1984) [6d]. A. Jannussis, R. Mignani, and D. SkaltsasPhysica A 187, 575 (1992) [6e]. A. O. E. Animalu,Hadronic J. 17, 349 (1995) [6f]. C. N. Ktorides, H. C. Myung, and R. M. Santilli,Phys. Rev. D. 22, 892 [6g]; T. Gill, J. Lindesay, and W. W. Zachary,Hadronic J. 17, 449 (1994) [6h]. E. B. Lin,Hadronic J. 11, 81 (1988) [6i]. A. J. Kalnay,Hadronic J.,6, 1 (1983) [6j]; A. Kalnay and R. M. Santilli,Hadronic J. 6, 1798 (1983) [6k]; J. Fronteay, A. Tellez Arenas, and R. M. Santilli,Hadronic J. 3 (1979) [6l]; R. Mignani, H. C. Myung, and R. M. Santilli,Hadronic J. 6, 1878 (1983) [6m]. A. O. E. Animalu,Hadronic J. 17, 349 (1994) [6n]. A. O. E. Animalu and R. M. Santilli, inHadronic Mechanics and Nonpotential Interactions (Nova Science, New York, 1990) [6o]. R. Mignani,Nuovo Cimento 43, 355 (1985) [6p]. M. Gasperinmi,Hadronic J. 7, 971 (1984) [6q]. A Jannussis, M. Mijatovic, and B. Veljanowski,Phys. Essays 4, 202 (1991) [6r]. D. Rapoport-Campodonico,Algebras, Groups and Geometries 8, 1 (1991) [6s]. M. Nishioka,Nuovo Cimento A 82, 351 (1984) [6t]. A. Jannussis, D. Brodimas, and R. Mignani,J. Phys. A. 24, L775 (1991) [6u]. G. Eder,Hadronic J. 4, 634 (1981) and5, 750 (1982) [6v]. R. M. Santilli,Revi. Tec. 18, 271 (1995) and19, 3 (1996) [6w]. R. M. Santilli,Lett. Nuovo Cimento 37, 337 (1983) [6x].CrossRefADSMathSciNetGoogle Scholar
  7. 7.
    D. M. Norris et al.,Tomber's Bibliography and Index in Nonassociative Algebras (Hadronic Press, Palm Harbor, Florida, 1984).Google Scholar
  8. 8.
    L. C. Biernharn,J. Phys. A. 22, L873 (1989) [8a]. A. J. Macfarlane,J. Phys. A 22, L4581 (1989) [8b].CrossRefADSGoogle Scholar
  9. 9.
    V. Dobrev., inProceedings of the Second Wigner Symposium (World Scientific, Singapore, 1991). J. Lukierski, A. Novicki, H. Ruegg, and V. Tolstoy,Phys. Lett. B 264, 331 (1991). O. Ogivetski, W. B. Schmidke, J. Wess, and B. Zumino,Commun. Math. Phys. 50, 495 (1992). S. Giller, J. Kunz, P. Kosinky, M. Majewski, and P. Maslanka,Phys. Lett. B. 286, 57 (1992).Google Scholar
  10. 10.
    J. Lukierski, A. Nowiski, and H. Ruegg,Phys. Lett. B 293, 344 (1992). J. Lukierski, H. Ruegg and W. Rühl,Phys. Lett. B 313, 357 (1993). J. Lukierski and H. Ruegg,Phys. Lett. B 329, 189 (1994). S. Majid and H. Ruegg,Phys. Lett. B 334, 348 (1994).CrossRefADSMathSciNetGoogle Scholar
  11. 11.
    T. L. Curtis, B. Fairlie, and Z. K. Zachos, eds.,Quantum Groups (World, Scientific, Singapore, 1991). Mo-Lin Ge and Bao Heng Zhao, eds.Introduction to Quantum Groups and Integrable Massive Models of Quantum Field Theory (World Scientific, Singapore 1991). Yu. F. Smirnov and R. M. Asherova, eds.,Proceedings of the Fifth Workshop Symmetry Methods in Physics (JINR, Dubna, Russia, 1992).Google Scholar
  12. 12.
    D. F. Lopez, inSymmetry Methods in Physics (Memorial Volume dedicated to Ya. S. Smorodinsky, A. N. Sissakian, G. S. Pogosyan, and S. I. Vinitsky, eds., J.I.N.R., Dubna. Russia, 1994); andHadronic J. 16, 429 (1993).Google Scholar
  13. 13.
    Ellis, N. E., Mavromatos, and D. V. Nanopoulos inProceedings of the Erice Summer School, 31st Course: From Superstrings to the Origin of Space-Time (World Scientific, Singapore, 1996).Google Scholar
  14. 14.
    A. Jannussis and D. Skaltzas,Ann. Fond. L. de Broglie 18, 1137 (1993).Google Scholar
  15. 15.
    M. Razavy,Z. Phys. B 26, 201 (1977). H.-D. Doebner and G. A. Goldin,Phys. Lett. A 162, 397 (1992). H.-J. Wagner,Z. Phys. B 95, 261 (1994).CrossRefMathSciNetGoogle Scholar
  16. 16.
    D. Schuch,Phys. Rev. A 55, 935 [16a]; and inNew Frontiers of Hadronic Mechanics, T. L. Gill, Editor (Hadronic Press, Palm Harbor, Florida, 1996) [16b].Google Scholar
  17. 17.
    S. Weinberg,Ann. Phys. 194, 336 (1989) [17a]. T. F. Jordan,Ann. Phys. 225, 83 (1993) [17b].CrossRefADSMathSciNetGoogle Scholar
  18. 18.
    A. Jannussis, R. Mignani, and R. M. Santilli,Ann. Fond L. de Broglie 18, 371 (1993).Google Scholar
  19. 19.
    A. Jannussis et al.,Nuovo Cimento B 103, 17 and 537 (1989).104, 33 and 53 (1989),108, 57 (1993);Phys. Lett. A 132, 324 (1988). S. Sebawe Abdallahet al., Physica A. 163, 822 (1990).202, 301 (1994);Phys. Rev. A 48, 1526 and 3174 (1993),J. Mod. Opt. 39, 771 and 1067 (1992);40, 441, 1351, and 1369 (1993);Phys. Lett. A 181, 341 (1993). R. J. McDermott and A. I. Solomon, “Double squeezing in generalq-coherent states,”J. Phys. A, in press.ADSMathSciNetGoogle Scholar
  20. 20.
    Cl. George, F. Henin, F. Mayné, and I. Prigogine,Hadronic J. 1, 520 (1978).MathSciNetGoogle Scholar
  21. 21.
    M. J. G. Veltman, inMethods in Field Theory (R. Ballan and J. Zinn-Justin, eds., North-Holland, Amsterdam, 1976) [21a]. C. J. Isham, R. Penrose, and D. W. Sciama, eds.,Quantum Gravity 2 (Oxford University Press, Oxford, 1981) [21b]. M. Keiser and R. Jantzen, eds.,Proceedings of the VII M. Grossmann Meeting, on General Relativity (World Scientific, Singapore, 1996) [21a].Google Scholar
  22. 22.
    R. M. Santilli,Elements of Hadronic Mechanics, Vol. 1:Mathematical Foundations [22a], II:Theoretical Foundations [22b] (2nd edn., Ukraine Academy of Sciences Kiev, 1995).Google Scholar
  23. 23.
    P. Vetro, ed.,Rend. Circ. Mat. Palermo. Suppl. 42 (1996) [23a]. R. M. Santilli,Rend. Circ. Mat Palermo, Suppl. 42, 7 (1996) [23b]. J. V. Kadeisvili,Rend. Circ. Mat. Palermo, Suppl. 42, 83 (1996) [23c].Google Scholar
  24. 24.
    H. C. Myung and R. M. Santilli,Hadronic J. 5, 1277 (1982).MathSciNetGoogle Scholar
  25. 25.
    R. Mignani,Hadronic J. 5, 1120 (1982).MathSciNetGoogle Scholar
  26. 26.
    R. M. Santilli,Algebras, Groups and Geometries 10, 273 (1993).MathSciNetGoogle Scholar
  27. 27.
    D. Bohm,Quantum Theory (Dover, New York, 1979) [27a]. R. M. Santili,Commun. Theor. Phys. 3, 47 (1994) [27b].Google Scholar
  28. 28.
    A. Einstein, B. Podolsky, and N. Rosen,Phys. Rev. 47, 777 (1935).CrossRefADSGoogle Scholar
  29. 29.
    J. Von Neumann,The Mathermatical Foundations of Quantum Mechanics (Princeton University Press, Princeton, N. J., 1955).Google Scholar
  30. 30.
    J. S. Bell,Physics 1, 195 (1965).Google Scholar
  31. 31.
    P. Caldirola,Nuovo Cimento 3, 297 (1956);Lett. Nuovo Cimento 16, 151 (1976). A. Jannussiset al. Lett. Nuovo Cimento 29 427 (1980). D. Lee,Phys. Rev. Lett. 122b, 217 (1983). D. Finkelstein,Int. J. Theor. Phys. 27, 473 (1985). C. Wolf,Ann. Fond. L. de Broglie 21, 1 (1996).MathSciNetGoogle Scholar
  32. 32.
    J. V. Kadeisvili,Algebras, Groups and Geometries 9, 283, and 319 (1992) [32a]. G. T. Tsagas and D. S. Sourlas,Algebras, Groups and Geometries 12, 1 (1995) [32b].MathSciNetGoogle Scholar
  33. 33.
    A. K. Aringazin,Hadronic J. 12, 71 (1989); A. K. Aringazin and K. M. Aringazin, inFrontiers of Fundamental Physics, M. Barone and F. Selleri, eds., (Plenum, New York, 1994).Google Scholar
  34. 34.
    R. M. Santilli, inProceedings of the VII M. Grossmann Meeting on General Relativity (M. Keiser and R. Jantzen, eds., World Scientific, Singapore, 1996) [34a]; inGravity Particles and Space-Time (P. Pronin and G. Sardanashvily, eds., World Scientific, Singapore, 1995) [34b];Commun. Theor. Phys. 4, 1 (1995) [34c]; “Isominkowskian geometry and its isodual,” submitted for publication [34d].Google Scholar
  35. 35.
    C. Illert and R. M. Santilli,Foundations of Theoretical Conchology (Hadronic Press, Palm Harbor, Florida, 1995) [35a]. R. M. Santilli,Isotopic, Genotopic and Hyperstructural Methods in Theoretical Biology (Ukraine Academy of Science, Kiev, 1996) [35b].MATHGoogle Scholar
  36. 36.
    P. A. M. Dirac,The Principles of Quantum Mechanics (Clarendon Press, Oxford, 1958).MATHGoogle Scholar
  37. 37.
    R. M. Santilli,Commun. Theor. Phys. 3, 153 (1994) [37a],Hadronic J. 17, 257 (1994) [37b]; inNew Frontiers of Hadronic Mechanics, T. L. Gill, ed., (Hadronic Press, Palm Harbor, Florida, 1996) [37c];Hyperfine Interaction 20 (1997) in press. [37d];Ann. Phys. 83, 108 (1974) [37e]; M. Holzsheiteret al. Hyperfine Interactions 20, (1997), in press [37f].MathSciNetGoogle Scholar
  38. 38.
    R. M. Santilli,Found Phys. 111, 383 (1981).CrossRefMathSciNetGoogle Scholar
  39. 39.
    D. I. Bloch'intsev,Phys. Rev. Lett. 12, 272 (1964); [39a]. L. B. Redei,Phys. Rev. 145, 999 (1996) [39b]. D. Y. Kim,Hadronic J. 1, 343 (1978) [39c]. J. Elliset al. Nucl. Phys. B 176, 61 (1980) [39d]. A. Zee,Phys. Rev. D 25, 1864 (1982) [39e]. R. M. Santilli,Lett. Nuovo Cimento 33, 145 (1982) [39f]. V. de Sabbata and M. Gasperini,Lett. Nuovo Cimento 34, 337 (1982) [39g]. H. B. Nielsen and I. Picek,Nucl. Phys. B. 211, 269 (1983) [39g]. M. Gasperini,Phys. Lett. B 177, 51 (1986) [39i]. Yu. Aronson,Hadronic J. 19, 205 (1996) [39i].Google Scholar
  40. 40.
    B. H. Aronson et al.Phys. Rev. D 28, 476 and 495 (1983).CrossRefADSGoogle Scholar
  41. 41.
    N. Grossman et al.,Phys. Rev. Lett. 59, 18 (1987).CrossRefADSGoogle Scholar
  42. 42.
    B. Lörstad,Int. J. Mod. Phys. A 4, 2861 (1989).CrossRefADSGoogle Scholar
  43. 43.
    UA1 Collaboration,Phys. Lett. B 226, 410 (1989).CrossRefGoogle Scholar
  44. 44.
    R. Adler et al.Phys. Rev. C 63, 541 (1994).Google Scholar
  45. 45.
    F. Cardone, R. Mignani, and R. M. Santilli,J. Phys. G. 18, L61 [42a] and L141 [42b] (1992).CrossRefADSGoogle Scholar
  46. 46.
    R. M. Santilli,Hadronic J. 15 (1992).Google Scholar
  47. 47.
    F. Cardone and R. Mignani, Preprint University of Rome No. 894.Google Scholar
  48. 48.
    R. M. Santilli,Commun. Theor. Phys. 4, 123 (1995) [48a];Int. J. Phys. 1, 1 (1995) [48b].MathSciNetGoogle Scholar
  49. 49.
    A. O. Animalu and R. M. Santilli,Int. J. Quant. Chem. 29, 175 (1995).CrossRefGoogle Scholar
  50. 50.
    R. M. Santilli, inProceedings International Conference “Dubna Deuteron 1993,” V. K. Lukyanov, et al., eds., (J.I.N.R., Dubna, Russia, 1994) [50a]; “Exact representation of total nuclear magnetic moments via relativistic hadronic mechanics,” submitted for publication [50b].Google Scholar
  51. 51.
    R. M. Santilli,Hadronic J. Suppl. 4A, 267 (1988) [51a]. R. Mignani,Phys. Essay 5, 531 (1992) [51b]. R. M. Santilli, inFrontiers of Fundamental Physics, M. Barone and F. Selleri, eds., (Plenum, New York, 1994) [51c].MathSciNetGoogle Scholar
  52. 52.
    H. Rauch,Hadronic J. 4, 1280 (1984).Google Scholar
  53. 53.
    A. P. Mills, Jr.,Hadronic J. 19, 77 (1996).Google Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • Ruggero Maria Santilli
    • 1
  1. 1.Institute for Basic ResearchPalm Harbor

Personalised recommendations