Source: http://rgs.vniims.ru/abs/abs-17-252.html
Timestamp: 2019-04-19 00:42:41+00:00

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We consider a five-dimensional model in which fermions are confined in a hypersurface due to an interaction with a purely geometric field. Inspired by the Rubakov-Shaposhnikov field-theoretical model, in which massless fermions can be localized in a domain wall through the interaction of a scalar field, we show that particle confinement may also take place if we endow the five-dimensional bulk with a Weyl integrable geometric structure, or if we assume the existence of a torsion field acting in the bulk. In this picture, the kind of interaction considered in the Rubakov-Shaposhnikov model is replaced by an interaction of fermions with a geometric field, namely a Weyl scalar field or a torsion field. We show that in both cases the confinement is independent of the energy and mass of the fermionic particle. We generalize these results to the case in which the bulk is an arbitrary n-dimensional curved space.
C. H. Oh and K. Singh, Class. Quantum Grav. 6, 1053 (1989).
M. W. Kalinowski, Int. J. Theo. Phys. 20, 563 (1981).
Yong-Shi Wu and A. Zee, J. Math. Phys. 25, 2696 (1984).
K. C. Wali, J. Phys.: Conference Series, 259, 012030 (2010).
M. Yu. Konstantinov and V. N. Melnikov, Int. J. Mod. Phys. D 4, 339 (1995).
F. W. Hehl and B. K. Datta, J. Math. Phys. 12, 1334 (1971).
A. Zecca, Int. J. Theor. Phys. 41, 421 (2002).
M. Adak, T. Dereli, and L. H. Ryder, Int. J. Mod. Phys. 12, 145 (2003).
R. Portugal, J. Math. Phys. 36, 4296 (1995).
M. Novello, Nuovo Cim. 64, 954 (1969).
F. Gursey, Nuovo Cim. 5, 57 (1957).
R. Finkelstein, J. Math. Phys. 1, 440 (1960).
V. M. Villalba, J. Math. Phys. 36, 3332 (1995).
G. V. Shishkin and V. M. Villalba, J. Math. Phys. 34, 5037 (1993).
V. M. Villalba and E. I. Catala, J. Math. Phys. 43, 4909 (2002).
V. M. Villalba and U. Percoco, J. Math. Phys. 31, 715 (1990).
V. M. Villalba, J. Math. Phys. 31, 1483 (1990).
V. M. Villalba, J. Math. Phys. 31, 2702 (1990).
G. V. Shishkin and V. M. Villalba, J. Math. Phys. 33, 4037 (1992).
V. M. Villalba, Phys. Lett. A 136, 197 (1989).
A. O. Barut and I. H. Duru, Phys. Rev. D 36, 3705 (1987).
M. A. Castagnino, C. D. El Hasi, F.D. Mazzitelli, and J. P. Paz, Phys. Lett. A 128, 25 (1988).
S. K. Srivastava, J. Math. Phys. 30, 2838 (1989).
G. V. Shishkin and I. E. Andrushkevich, Phys. Lett. A 110, 84 (1985).
V. Bargmann, Sitzber. Akad. Wiss., Phys. Math. Kl., 346 (1932).
D. R. Brill and J. M. Cohen, J. Math. Phys. 7, 238 (1966).
V. A. Fock and D. Ivanenko, Z. Physik 57, 261 (1929).
E. Schrodinger, Sitzber. Akad. Wiss., Phys. Math. Kl., 105 (1932).
N. D. Birrel and P. C. W. Davies, Quantum Fields in Curved Space (Cambridge University Press, 1982).
S. A. Fulling, Aspects of Quantum Field Theory in Curved Space-Time (Cambridge University Press, 1989).
N. Poplawski, Mod. Phys. Lett. A 24, 431 (2009).
C. Kiefer, Quantum Gravity, 2nd edition (Oxford University Press, New York, 2007).
J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics (McGraw-Hill, 1964).
F. Hehl, P. von der Heyde, and G. Kerlick, Rev. Mod. Phys. 48, 393 (1976).
R. Hammond, Rep. Prog. Phys. 65, 599 (2002).
V. de Sabbata and M. Gasperini, Introduction to gravitation (World Scientific, 1985).
M. Blagojevic, Gravitation and Gauge Symmetries (IOP Publishing, 2002).
M. P. do Carmo, Riemannian Geometry (Birkhauser, Boston, 1991).
J. Crawford, Class. Quantum Grav. 20, 2945 (2003).
Kun-Feng Shie, J. M. Nester, and Hwei-Jang Yo, Phys. Rev. D 78, 023522 (2008); arXiv: 0805.3834.
A. Trautman, Einstein-Cartan Theory, in: Encyclopedia of Mathematical Physics, vol. 2, pages 189-195, Ed. J. P. Francoise, G. L. Naber and Tsou S.T. (Oxford: Elsevier, 2006). See also R. Aldrovandi and J. G. Pereira, arXiv: 0801.4148.
R. Kerner, Ann. Inst. H. Poincare, 34, 473 (1981).
V. de Sabatta and C. Sivaram, Spin and Torsion in Gravitation (World Scientific, 1994).
M. Gasperini and V. De Sabatta, Introduction to Gravitation (World Scientific, 1986).
J. E. Madriz Aguilar and C. Romero, Found. Phys. 39, 1205 (2009).
E. Cartan, Comptes Rendus Acad. Sci (Paris) 174, 437 (1922).
F. W. Hehl, P. von der Heyde, G. D. Kerlick, and J. M. Nester, Rev. Mod. Phys. 48, 393 (1976).
F. Dahia, G. A. T. Gomez, and C. Romero, J. Math. Phys. 49, 102501 (2008).
O. Arias, R. Cardenas, and I. Quiros, Nucl. Phys. B643, 187 (2002).
J. Miritzis, J. Phys. Conf. Ser. 8, 131 (2005).
M. Israelit, Found. Phys. 35, 1725 (2005).
J. Miritzis, Class. Quantum Grav. 21, 3043 (2004).
H. P. de Oliveira, J. M. Salim, and S. L. Sautu, Class. Quantum Grav. 14, 2833 (1997).
V. Melnikov, Classical Solutions in Multidimensional Cosmology, in: Proc. VIII Brazilian School of Cosmology and Gravitation II (1995), ed. M. Novello (Editions Frontieres), pp. 542-560, ISBN 2-86332-192-7.
M. Novello, L. A. R. Oliveira, J. M. Salim, and E. Elbas, Int. J. Mod. Phys. D 1, 641-677 (1993).
J. M. Salim and S. L. Sautu, Class. Quantum Grav. 13, 353 (1996).
M. Novello and H. Heintzmann, Phys. Lett. A 98, 10 (1983).
K. A. Bronnikov, Yu. M. Konstantinov and V. N. Melnikov, Grav. Cosmol. 1, 60 (1995).
H. Weyl, Space, Time, Matter (Dover, New York, 1952).
A nice account of Weyl's ideas as well as the refutation of his gravitational theory may be found in W. Pauli, Theory of Relativity (Dover, New York, 1981). See also, L. O'Raiefeartaigh and N. Straumann, Rev. Mod. Phys. 72, 1 (2000).
C. Romero, J. B. Formiga, and L. F. P. da Silva, Int. J. Geom. Meth. Mod. Phys. 8, 1 (2011).
H. Weyl, Sitzungesber Deutsch. Akad. Wiss. Berlin, 465 (1918).
F. Dahia, G. A. T. Gomez, J. Math. Phys. 49, 102501 (2008).
V. A. Rubakov, Phys. lett. B 125, 136 (1983). See also M. Visser, Phys. Lett. B 159, 22 (1985).
F. Dahia and C. Romero, Phys. Lett. B 51, 232 (2007).
F. Dahia, C. Romero, and L. D. P. da Silva, Gen. Rel. Grav. 40 (2008).
F. Dahia, L. F. P. da Silva, C. Romero, and R. Tavakol, J. Math. Phys. 48, 72501 (2007).
J. M. Hoff da Silva and R. da Rocha, Class. Quantum Grav. 26, 055007 (2009).
S. S. Seahra, Phys. Rev. D 68, 104027 (2003).
I. J. Muzinich, J. Math. Phys. 26, 1942 (1985).
M. W. Kalinowski, Int. J. Theor. Phys. 20, 563 (1981).
G. German, A. Macias, and O. Obregon, Class. Quantum Grav. 10, 1045 (1993).
K. H. Shankar and K. C. Wali, Mod. Phys. Lett. A 25, 2121 (2010).
O. Arias, R. Cardenas, and I. Quiros, Nucl. Phys. B 643, 187 (2002).
N. Barbosa-Cendejas and A. Herrera-Aguilar, Phys. Rev. D 73, 084022 (2006).
R. Maartens, Brane-World Gravity, Living Rev. Relativity 7 (2004).

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V. 

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V. 
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