Nonrelativistic Wave Equations with Gauge Fields

International Journal of Theoretical Physics

Volumn 42, Issue 4, 2003, Pages 649-671

  De Montigny, M ^a   Khanna, F C ^a,b   Santana, A E ^a,c  

^a UNIVERSITY OF ALBERTA   (Canada)

^b TRIUMF   (Canada)

^c FEDERAL UNIVERSITY OF BAHIA   (Brazil)

Author keywords

Galilean invariance; Gauge theory; Riemannian geometry; Wave equations

Indexed keywords

EID: 0038347665     PISSN: 00207748     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1024485810807     Document Type: Article

References (43)

1. Bacry, H. and Lévy-Leblond, J. M. (1968). Possible kinematics. Journal of Mathematical Physics, 9, 1605-1614.
2. Bargmann, V. (1947). Irreducible unitary representations of the Lorentz group. Annals of Mathematics, 48, 568-640.
3. Bazeia, D. and Jackiw, R. (1998). Nonlinear realization of a dynamical Poincaré symmetry by a field-dependent diffeomorphism. Annals of Physics (NY), 270, 246-259.
4. Bordemann, M. and Hoppe, J. (1993). The dynamics of relativistic membranes. Reduction to 2-dimensional fluid dynamics, Physics Letters B, 317, 315-320.
5. Cartan, É. (1923). Sur les variétés à connexion affine et la théorie de la relativité généralisée. Ann. Sci. École Norm. Sup. 40, 325-412.
6. Cartan, É. (1924). Sur les variétés à connexion affine et la théorie de la relativité généralisée (lère partie, chapitre 5). Ann. Sci. École Norm. Sup. 41, 1-25.
7. de Montigny, M., Khanna, F. C., and Santana, A. E. (2001a). Galilean covariance and applications in physics. In Recent Research Developments in Physics, Vol. 1 Transworld Research Network Trivandrum, India, 1, 45-92.
8. de Montigny, M., Khanna, F. C., Santana, A. E., and Santos, E. S. (2001b). Galilean covariance and the non-relativistic Bhabha equations. Journal of Physics A: Mathematical and General 34, 8901-8917.
9. de Montigny, M., Khanna, F. C., Santana, A. E., Santos, E. S., and Vianna, J. D. M. (2000). Galilean covariance and the Duffin-Kemmer-Petiau equation Journal of Physics A: Mathematical and General 33, L273-L278.
10. Duval, C. (1987). The Dirac and Lévy-Leblond equations and geometric quantization. In Lecture Notes in Mathematics, Vol. 1251, Springer, New York.
11. Duval, C., Burdet, G., Künzle, H. P., and Perrin, M. (1985). Bargmann structures and Newton-Cartan theory Physical Review D 31, 1841-1853.
12. Fuschich, W. I. and Nikitin, A. G. (1994). Symmetries of Equations in Quantum Mechanics, Allerton Press, New York.
13. Gelfand, I. M., Minlos, R. A., and Shapiro, Z. Ya. (1963). Representations of the Rotation and Lorentz Groups and their Applications, Pergamon Press, New York.
14. Goldstein, H. (1980). Classical Mechanics, Addison-Wesley, Reading, MA.
15. Havas, P. (1964). Four-dimensional formulations of Newtonian mechanics and their relation to the special and the general theory of relativity. Reviews of Modern Physics 36, 938-965.
16. Hassaïne, M. and Horváthy, P. A. (2000). Field-dependent symmetries of a non-relativistic fluid model. Annals of Physics (NY) 282, 218-246.
17. Hassaïne, M. and Horváthy, P. A. (2001). Relativistic Chaplygin gas with field-dependent Poincaré symmetry. Letters in Mathematical Physics 57, 33-40.
18. Horzela, A. and Kapuścik, E. (2002). Galilean covariant Dirac equation (Preprint).
19. Inönü, E., and Wigner, E. P. (1952). Representations of the Galilei group. Nuovo Cimento 9, 705-718.
20. Jackiw, R. (2002). Lectures on Fluid Dynamics-A Particle Theorist's View of Supersymmetric, Non-Abelian, Noncommutative Fluid Mechanics and d-Branes, Springer, Berlin. [Preprint physics/0010042]
21. Jackiw, R. and Polychronakos, A. P. (1999). Fluid dynamical profiles and constants of motion from d-branes. Communications in Mathematical Physics 207, 107-129.
22. Julia, B. and Nicolai, H. (1995). Null-Killing vector dimensional reduction and Galilean geometrodynamics Nuclear Physics B 439, 291-326.
23. Kapuścik, E. (1980). On nonrelativistic gauge theories. Nuovo Cimento 58 A 113-124.
24. Kapuścik, E. (1981). The non-relativistic space-time manifolds. Acta Physica Polonika B 12, 81-86.
25. Kapuścik, E. (1985). On the relation between Galilean, Poincaré and Euclidean field equations. Acta Physica Polonika B 16, 937-945.
26. Kapuścik, E. (1986). On the physical meaning of the Galilean space-time coordinates Acta Physica Polonika B 17, 569-575.
27. Künzle, H. P. and Duval, C. (1994). Relativistic and nonrelativistic physical theories on five-dimensional space-time. In Semantical Aspects of Spacetime Theories, U. Majer and H. J. Schmidt, eds., BI-Wissenschaftsverlag, Mannheim, Germany, pp. 113-129 (and the references therein).
28. Le Bellac, M. and Lévy-Leblond. (1973). Galilean electromagnetism Nuovo Cimento 14B 217-233.
29. Lévy-Leblond, J. M. (1963). Galilei group and nonrelativistic quantum mechanics. Journal of Mathematical Physics 4, 776-788.
30. Lévy-Leblond, J. M. (1965). Une nouvelle limite non-relativiste du groupe de Poincaré. Annales de l'Institut Henri Poincaré, Section B 3, 1-12.
31. Lévy-Leblond, J. M. (1967). Nonrelativistic particles and wave equations. Communications in Mathematical Physics 6, 286-311.
32. Lévy-Leblond, J. M. (1971). Galilei group and galilean invariance. In Group Theory and Applications, Vol. II, E. M. Loebl, eds. Academic New York, pp. 221-299.
33. Nikitin, A. G. and Fuschich, W. I. (1980). Equations of motion for particles of arbitrary spin invariant under the Galilei group Theoretical and Mathematical Physics 44, 584-592.
34. Nurowski, P., Schlüling, E., and Trautmant, A. (1999). Relativistic gravitational fields with close Newtonian analogs. In On Einstein's Path: Essays in Honor of Engelbert Schuking, A. Harvey, ed. Springer, New York, Chap. 23.
35. Omote, M., Kamefuchi, S., Takahashi, Y., and Ohnuki, Y. (1989). Galilean covariance and the Schrödinger equation. Fortschritte der Physics 37, 933-950.
36. Pinski, G. (1968). Galilean tensor calculus Journal of Mathematical Physics 9, 1927-1930.
37. Santana, A. E., Khanna, F. C., and Takahashi, Y. (1998). Galilei covariance and (4,1)-de Sitter space. Progress in Theoretical Physics 99, 327-336.
38. Soper, D. E. (1976). Classical Field Theory, Wiley, New York, Sec. 7.3.
39. Susskind, L. (1968). Model of self-dual strong interactions. Physics Report 165, 1535-1546.
40. Takahashi, Y. (1987). An invitation to a Galilei invariant world. In Wandering in the Fields: Festschrift for Professor Kazahiko Nishijima on the Occasion of his Sixtieth Birthday, K. Kwarabayashi and A. Ukawa, eds., Singapore, World Scientific, pp. 117-127.
41. Takahashi, Y. (1988a). Towards the many-body theory with the Galilei invariance as a guide. I. Fortschritte der Physik 36, 63-81.
42. Takahashi, Y. (1988b). Towards the many-body theory with the Galilei invariance as a guide. II. Fortschritte der Physik 36, 83-96.
43. Wigner, E. P. (1939). On unitary representations of the inhomogeneous Lorentz group. Annals of Mathematics 40, 149-204.