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On a Unified Theory of Generalized Branes Coupled to Gauge Fields, Including the Gravitational and Kalb–Ramond Fields

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We investigate a theory in which fundamental objects are branes described in terms of higher grade coordinates \(X^{\mu{_1}\ldots \mu{_n}}\) encoding both the motion of a brane as a whole, and its volume evolution. We thus formulate a dynamics which generalizes the dynamics of the usual branes. Geometrically, coordinates \(X^{\mu{_1} \ldots \mu{_n}}\) and associated coordinate frame fields {\({\gamma_{\mu{_1}\ldots\mu{_n}}}\)} extend the notion of geometry from spacetime to that of an enlarged space, called Clifford space or C-space. If we start from four-dimensional spacetime, then the dimension of C-space is 16. The fact that C-space has more than four dimensions suggests that it could serve as a realization of Kaluza-Klein idea. The “extra dimensions” are not just the ordinary extra dimensions, they are related to the volume degrees of freedom, therefore they are physical, and need not be compactified. Gauge fields are due to the metric of Clifford space. It turns out that amongst the latter gauge fields there also exist higher grade, antisymmetric fields of the Kalb–Ramond type, and their non-Abelian generalization. All those fields are naturally coupled to the generalized branes, whose dynamics is given by a generalized Howe–Tucker action in curved C-space.

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References

  • See e.g., M. B. Green, J. H. Schwarz, and E. Witten, Superstring Theory (Cambridge University Press, Cambridge, 1987); M. Kaku, Introduction to Superstrings (Springer-Verlag, New York, 1988); U. Danielsson, Rep. Progr. Phys. 64, 51 (2001).

  • J. Polchinski, “Lectures on D-branes,” [arXiv:hep-th/9611050]; W. I. Taylor, “Lectures on D-branes, gauge theory and M(atrices),” arXiv:hep-th/9801182. H. Nicolai and R. Helling, “Supermembranes and M(atrix) theory,” arXiv:hep-th/9809103; J.H. Schwarz, Phys. Rep. 315, 107 (1999).

    Google Scholar 

  • L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999) [arXiv:hep-th/9906064]. M. J. Duff, “Benchmarks on the brane,” arXiv:hep-th/0407175.

  • M. J. Duff, R. R. Khuri, and J. X. Lu, Phys. Rept. 259, 213 (1995) [arXiv:hep-th/9412184]. M. J. Duff and J. X. Lu, Class. Quant. Grav. 9, 1 (1992). M. J. Duff and J. X. Lu, Phys. Rev. Lett. 66, 1402 (1991).

  • Schild A. (1977). Phys. Rev. D 16: 1722

    Article  ADS  Google Scholar 

  • Eguchi T. (1980). Phys. Rev. Lett. 44: 126

    Article  ADS  Google Scholar 

  • A. Aurilia, A. Smailagic, and E. Spallucci, Phys. Rev. D 47, 2536 (1993) [arXiv:hep-th/9301019]; A. Aurilia and E. Spallucci, Class. Quant. Grav. 10, 1217 (1993) [arXiv:hep-th/9305020]; S. Ansoldi, A. Aurilia, and E. Spallucci, Phys. Rev. D 53, 870 (1996) [arXiv:hep-th/9510133].

  • D. Hestenes, Space-Time Algebra (Gordon and Breach, New York, 1966); D. Hestenes and G. Sobcyk, Clifford Algebra to Geometric Calculus (D. Reidel, Dordrecht, 1984).

  • P. Lounesto, Clifford Algebras and Spinors (Cambridge University Press, Cambridge, 2001); B. Jancewicz, Multivectors and Clifford Algebra in Electrodynamics (World Scientific, Singapore, 1988); R. Porteous, Clifford Algebras and the Classical Groups (Cambridge University Press, 1995); W. Baylis, Electrodynamics, A Modern Geometric Approach (Boston, Birkhauser, 1999); A. Lasenby and C. Doran, Geometric Algebra for Physicists (Cambridge University Press, Cambridge, 2002); Clifford Algebras and their applications in Mathematical Physics, Vol 1: Algebras and Physics, eds. R. Ablamowicz and B. Fauser; Vol 2: Clifford analysis. eds. J. Ryan and W. Sprosig (Birkhauser, Boston, 2000); A. M. Moya, V. V Fernandez, and W. A. Rodrigues, Int. J. Theor. Phys. 40, 2347 (2001) [arXiv: math-ph/0302007]; “Multivector functions of a multivector variable” [arXiv: math.GM/0212223]; Multivector functionals [arXiv: math.GM/0212224]; W. A. Rodrigues, Jr., J. Vaz, Jr., Adv. Appl. Clifford Algebras 7, 457 (1997); E. C de Oliveira and W. A. Rodrigues, Jr., Ann. der Physik 7, 654 (1998). Phys. Lett A 291, 367 (2001). W. A. Rodrigues, Jr., J. Y. Lu, Found. Phys. 27, 435 (1997); S. Vacaru, P. Stavrinos, E. Gaburov, and D. Gonta, “Clifford and Riemann-Finsler structures in geometric mechanics and gravity,” [arXiv:gr-qc/0508023].

  • M. Pavšič, Found. Phys. 33, 1277 (2003) [arXiv:gr-qc/0211085].

    Google Scholar 

  • M. Pavšič, The Landscape of Theoretical Physics: A Global View; From Point Particle to the Brane World and Beyond, in Search of Unifying Principle (Kluwer Academic, Dordrecht, 2001).

  • S. Ansoldi, A. Aurilia, C. Castro, and E. Spallucci, Phys. Rev. D 64, 026003 (2001) [arXiv:hep-th/0105027].

    Google Scholar 

  • A. Aurilia, S. Ansoldi, and E. Spallucci, Class. Quant. Grav. 19, 3207 (2002) [arXiv:hep-th/0205028].

  • C. Castro and M. Pavšič, Progr. Phys. 1, 31 (2005).

  • M. Pavšič, Found. Phys. 35, 1617 (2005) [arXiv:hep-th/0501222].

    Google Scholar 

  • E. C. G. Stueckelberg, Helv. Phys. Acta 14, 322 (1941); 14, 588 (1941); 15, 23 (1942).

  • Feynman R.P. (1951). Phys. Rev. 84: 108

    Article  MATH  ADS  Google Scholar 

  • Schwinger J. (1951). Phys. Rev. 82: 664

    Article  MATH  ADS  Google Scholar 

  • W. C. Davidon, Phys. Rev. 97, 1131 (1955); 97, 1139 (1955).

  • L. P. Horwitz and C. Piron, Helv. Phys. Acta 46, 316 (1973); L. P. Horwitz and F. Rohrlich, Phys. Rev. D 24, 1528 (1981); 26, 3452 (1982); L. P. Horwitz, R. I. Arshansky, and A. C. Elitzur Found. Phys 18, 1159 (1988); R. Arshansky, L. P. Horwitz, and Y. Lavie, Found. Phys. 13, 1167 (1983); L. P. Horwitz, in Old and New Questions in Physics, Cosmology, Philosophy and Theoretical Biology, A. van der Merwe, ed. (Plenum, New York, 1983); L. P. Horwitz and Y. Lavie, Phys. Rev. D 26, 819 (1982); L. Burakovsky, L. P. Horwitz, and W. C. Schieve, Phys. Rev. D 54, 4029 (1996); L. P. Horwitz and W. C. Schieve, Ann. Phys. 137, 306 (1981).

  • J. R. Fanchi, Phys. Rev. D 20, 3108 (1979); see also the review J. R. Fanchi, Found. Phys. 23, 287 (1993), and many references therein; J. R. Fanchi Parametrized Relativistic Quantum Theory (Kluwer, Dordrecht, 1993).

    Google Scholar 

  • H. Enatsu, Progr. Theor. Phys. 30, 236 (1963); Nuovo Cimento A 95, 269 (1986); F. Reuse, Found. Phys. 9, 865 (1979); A. Kyprianidis Phys. Rep. 155, 1 (1987); R. Kubo, Nuovo Cim. A, 293 (1985); M. B. Mensky and H. von Borzeszkowski, Phys. Lett. A 208, 269 (1995); J. P. Aparicio, F. H. Gaioli, and E. T. Garcia-Alvarez, Phys. Rev. A 51, 96 (1995); Phys. Lett. A 200, 233 (1995); L. Hannibal, Int. J. Theoret. Phys. 30, 1445 (1991); F. H. Gaioli and E. T. Garcia-Alvarez, Gen. Relat. Grav. 26, 1267 (1994).

  • M. Pavšič, Found. Phys. 21, 1005 (1991); M. Pavšič, Nuovo Cim. A 104, 1337 (1991); Doga, Turkish J. Phys. 17, 768 (1993).

  • Pavšič M. (1996). Found. Phys. 26: 159 [arXiv:gr-qc/9506057].

    Article  Google Scholar 

  • M. Pavšič, Found. Phys. 31, 1185 (2001) [arXiv:hep-th/0011216].

    Google Scholar 

  • M. Riesz, “Sur certaines notions fondamentales en théorie quantiques relativiste’, in Dixième Congrès Math. des Pays Scandinaves, Copenhagen, 1946 (Jul. Gjellerups Forlag, Copenhagen, 1947), pp. 123–148; M. Riesz, Clifford Numbers and Spinors, E. Bolinder and P. Lounesto, eds. (Kluwer, 1993); S. Teitler, Supplemento al Nuovo Cimento III, 1 (1965) and references therein; Supplemento al Nuovo Cimento III, 15 (1965); J. Math. Phys. 7, 1730 (1966); 7, 1739 (1966); W. A. Rodrigues, Jr., J. Math. Phys. 45, 2908 (2004).

  • Pavšič M. (2005) . Phys. Lett. B 614: 85 [arXiv:hep-th/0412255].

    Article  ADS  Google Scholar 

  • M. Pavšič, “Spin gauge theory of gravity in Clifford space: A realization of Kaluza-Klein theory in 4-dimensional spacetime,” Int. J. Mod. Phys. A 21, 5905 (2006). arXiv:gr-qc/0507053.

  • L. P. Eisenhart, Riemannian Geometry (Princeton University Press, Princeton, 1926).

  • H. Rund, Invariant Theory of Variational Problems on Subspaces of a Riemannian Manifold (Van Den Hoeck & Rupert, Göottingen, 1971).

  • C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (W.H. Freeman and Company, San Francisco, 1973).

  • M. Pavšič, Class. Quant. Grav. 20, 2697 (2003) [arXiv:gr-qc/0111092].

  • P. S. Howe and R. W. Tucker, J. Phys. A: Math. Gen. 10, L155 (1977); A. Sugamoto, Nucl. Phys. B 215, 381 (1983); M. Pavšič, Class. Quant. Grav. 5, 247 (1988).

  • W. Pezzaglia, “Physical applications of a generalized geometric calculus,” in Dirac Operators in Analysis (Pitman Research Notes in Mathematics, Number 394), J. Ryan and D. Struppa, eds. (Longmann, 1997) pp. 191–202 [arXiv: gr-qc/9710027]; “Dimensionally democratic calculus and principles of polydimensional physics,” in Clifford Algebras and their Applications in Mathematical Physics, R. Ablamowicz and B. Fauser, eds. (Birkhauser, 2000), pp. 101–123,[arXiv: gr-qc/9912025]; “Classification of Multivector Theories and Modifications of the Postulates of Physics”, in Clifford Algebras and their Applications in Mathematical Physics, Brackx, Delanghe & Serras eds. (Kluwer, 1993) pp. 317–323, [arXiv: gr-qc/9306006].

  • C. Castro, Chaos, Solitons and Fractals 10, 295 (1999); 11, 1663 (2000); 12, 1585 (2001); “The search for the origins of M theory: loop quantum mechanics, loops/strings and bulk/boundary dualities,” arXiv: hep-th/9809102; C. Castro, Found. Phys. 30, 1301 (2000).

  • M. J. Duff, Nucl. Phys. B 335, 610 (1990). M. J. Duff and J. X. Lu, Nucl. Phys. B 347, 394 (1990).

  • C. Castro and M. Pavšič, Phys. Lett. B 539, 133 (2002) [arXiv:hep-th/0110079].

    Google Scholar 

  • M. Pavšič, “Clifford space as a generalization of spacetime: prospects for unification in physics,” arXiv:hep-th/0411053.

  • Castro C. (2005). Found. Phys. 35: 971

    Article  MATH  Google Scholar 

  • Luciani J.F (1978). Nucl. Phys. B 135: 111

    Article  ADS  Google Scholar 

  • Witten E. (1981). Nucl. Phys. B 186: 412

    Article  ADS  Google Scholar 

  • Kalb M., Ramond P. (1974). Phys. Rev. D 9: 2273

    Article  ADS  Google Scholar 

  • Castro C. (2004). Mod. Phys. Lett. A 19: 19

    Article  MATH  ADS  Google Scholar 

  • Aurilia A., Takahashi Y. (1981). Progr. Theor. Phys. 66: 693

    Article  ADS  Google Scholar 

  • P. A. M. Dirac, Proc. R. Soc.(London) A 268, 57 (1962).

    Google Scholar 

  • A. O. Barut and M. Pavšič, Mod. Phys. Lett. A 7, 1381 (1992).

    Google Scholar 

  • A. O. Barut and M. Pavšič, Phys. Lett. B 306, 49 (1993); Phys. Lett. B 331, 45 (1994).

  • G. Savidy “Non-Abelian tensor gauge fields: enhanced symmetries,” arXiv:hep-th/0604118.

  • Castro C. (1998). Int. J. Mod. Phys. A 13: 1263

    Article  MATH  ADS  Google Scholar 

  • C. Castro, Int. J. Mod. Phys. A 21, 2149 (2006). D. V. Alekseevsky, V. Cortes, C. Devchand, and A. Van Proeyen, Commun. Math. Phys. 253, 385 (2004) [arXiv:hep-th/0311107].

  • C. Castro, J. Math. Phys. 47, 112301 (2006); Z. Kuznetsova and F. Toppan, arXiv:hep-th/0610122.

  • C. Castro, Ann. Phys. 321, 813 (2006). C. Castro, Found. Phys. 34, 1091 (2004). M. Land, Found. Phys. 35, 1245 (2005) [arXiv:hep-th/0603169].

  • Castro C. (2006). J. Phys. A: Math. Gen. 39: 14205

    Article  MATH  ADS  Google Scholar 

  • Penrose R. (1999). Chaos, Solitons Fractals 10: 581

    Article  MATH  Google Scholar 

  • F. Smith, Intern. J. Theor. Phys. 24, 155 (1985); 25, 355 (1985); G. Trayling and W. E. Baylis, Int. J. Mod. Phys. A 16, Suppl. 1C (2001) 900; J. Phys. A: Math. Gen. 34, 3309 (2001); G. Roepstorff, “A class of anomaly-free gauge theories,” arXiv:hep-th/0005079; “Towards a unified theory of gauge and Yukawa interactions,” arXiv:hep-ph/0006065; “Extra dimensions: will their spinors play a role in the standard model?,” arXiv:hep-th/0310092; F. D. Smith, “From sets to quarks: deriving the standard model plus gravitation from simple operations on finite sets,” arXiv:hep-ph/9708379. J. S. R. Chisholm and R. S. Farwell, J. Phys. A: Math. Gen. 20, 6561 (1987); 33, 2805 (1999); 22, 1059 (1989); J. S. R. Chisholm, J. Phys. A: Math. Gen. 35, 7359 (2002); Nuov. Cim. A 82, 145 (1984); 185; 210; “Properties of Clifford algebras for fundamental particles”, in Clifford (Geometric) Algebras, W. Baylis, ed. (Birkhauser, 1996), Chapter 27, pp. 365–388. J. P. Crawford, J. Math. Phys. 35, 2701 (1994); in Clifford (Geometric) Algebras, W. Baylis, ed. (Birkhauser, 1996), Chapters 21–26, pp. 297–364; Class. Quant. Grav. 20, 2945 (2003); A. Garrett Lisi, arXiv:gr-qc/0511120.

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Pavšič, M. On a Unified Theory of Generalized Branes Coupled to Gauge Fields, Including the Gravitational and Kalb–Ramond Fields. Found Phys 37, 1197–1242 (2007). https://doi.org/10.1007/s10701-007-9147-3

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