Galilean covariant Lagrangian models

Journal of Physics A: Mathematical and General

Volumn 37, Issue 41, 2004, Pages 9771-9789

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

^a UNIVERSITY OF ALBERTA   (Canada)

^b SÃO PAULO STATE UNIVERSITY UNESP   (Brazil)

^c TRIUMF   (Canada)

^d UNIVERSITY OF BRASILIA   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 7544229741     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/37/41/011     Document Type: Article

References (41)

1. Inönü E and Wigner E P 1952 Representations of the Galilei group Nuovo Cimenta 9 705-18 Bargmann V 1954 On unitary ray representations of continuous groups Ann. Math. 59 1-46 Lévy-Leblond J M 1963 Galilei group and nonrelativistic quantum mechanics J. Math. Phys. 4 776-88 Lévy-Leblond J M 1971 Galilei group and galilean invariance Group Theory and Applications ed E M Loebl vol 2 (New York: Academic) pp 221-99 Brennich R H 1970 The irreducible ray representations of the full inhomogeneous Galilei group Ann. Inst. H Poincaré 13 137-61
2. Inönü E and Wigner E P 1952 Representations of the Galilei group Nuovo Cimenta 9 705-18 Bargmann V 1954 On unitary ray representations of continuous groups Ann. Math. 59 1-46 Lévy-Leblond J M 1963 Galilei group and nonrelativistic quantum mechanics J. Math. Phys. 4 776-88 Lévy-Leblond J M 1971 Galilei group and galilean invariance Group Theory and Applications ed E M Loebl vol 2 (New York: Academic) pp 221-99 Brennich R H 1970 The irreducible ray representations of the full inhomogeneous Galilei group Ann. Inst. H Poincaré 13 137-61
3. Inönü E and Wigner E P 1952 Representations of the Galilei group Nuovo Cimenta 9 705-18 Bargmann V 1954 On unitary ray representations of continuous groups Ann. Math. 59 1-46 Lévy-Leblond J M 1963 Galilei group and nonrelativistic quantum mechanics J. Math. Phys. 4 776-88 Lévy-Leblond J M 1971 Galilei group and galilean invariance Group Theory and Applications ed E M Loebl vol 2 (New York: Academic) pp 221-99 Brennich R H 1970 The irreducible ray representations of the full inhomogeneous Galilei group Ann. Inst. H Poincaré 13 137-61
4. Inönü E and Wigner E P 1952 Representations of the Galilei group Nuovo Cimenta 9 705-18 Bargmann V 1954 On unitary ray representations of continuous groups Ann. Math. 59 1-46 Lévy-Leblond J M 1963 Galilei group and nonrelativistic quantum mechanics J. Math. Phys. 4 776-88 Lévy-Leblond J M 1971 Galilei group and galilean invariance Group Theory and Applications ed E M Loebl vol 2 (New York: Academic) pp 221-99 Brennich R H 1970 The irreducible ray representations of the full inhomogeneous Galilei group Ann. Inst. H Poincaré 13 137-61
5. Inönü E and Wigner E P 1952 Representations of the Galilei group Nuovo Cimenta 9 705-18 Bargmann V 1954 On unitary ray representations of continuous groups Ann. Math. 59 1-46 Lévy-Leblond J M 1963 Galilei group and nonrelativistic quantum mechanics J. Math. Phys. 4 776-88 Lévy-Leblond J M 1971 Galilei group and galilean invariance Group Theory and Applications ed E M Loebl vol 2 (New York: Academic) pp 221-99 Brennich R H 1970 The irreducible ray representations of the full inhomogeneous Galilei group Ann. Inst. H Poincaré 13 137-61
6. Le Bellac M and Lévy-Leblond J M 1973 Galilean electromagnetism Nuovo Cimenta B 14 217-33
7. Hagen C R 1972 Scale and conformai transformations in Galilean-covariant field theory Phys. Rev. D 5 377-88 Hagen C R and Hurley W J 1970 Magnetic moment of a particle with arbitrary spin Phys. Rev. lett. 26 1381-4 Carinena J F and Santander M 1982 Galilean relativistic wave equations J. Phys. A: Math. Gen. 15 343-53 Fushchich W I and Nikitin A G 1976 On the Galilei-invariant equations for particles with arbitrary spin Lett. Nuovo Cimenta 16 81-5 Fushchich W I and Nikitin A G 1984 On one- and two-particle Galilei-invariant wave equations for any spin Nuovo Cimenta A 81 664-80 Kraus K 1980 Galilei covariance does not imply minimal electromagnetic coupling Ann. Phys. 37 82-101 Krause J 1988 Galilean quantum kinematics J. Phys. A: Math. Gen. 29 393-7 Lévy-Leblond J M 1967 Galilean quantum field theories and a ghostless Lee model Commun. Math. Phys. 4 157-76
8. Hagen C R 1972 Scale and conformai transformations in Galilean-covariant field theory Phys. Rev. D 5 377-88 Hagen C R and Hurley W J 1970 Magnetic moment of a particle with arbitrary spin Phys. Rev. lett. 26 1381-4 Carinena J F and Santander M 1982 Galilean relativistic wave equations J. Phys. A: Math. Gen. 15 343-53 Fushchich W I and Nikitin A G 1976 On the Galilei-invariant equations for particles with arbitrary spin Lett. Nuovo Cimenta 16 81-5 Fushchich W I and Nikitin A G 1984 On one- and two-particle Galilei-invariant wave equations for any spin Nuovo Cimenta A 81 664-80 Kraus K 1980 Galilei covariance does not imply minimal electromagnetic coupling Ann. Phys. 37 82-101 Krause J 1988 Galilean quantum kinematics J. Phys. A: Math. Gen. 29 393-7 Lévy-Leblond J M 1967 Galilean quantum field theories and a ghostless Lee model Commun. Math. Phys. 4 157-76
9. Hagen C R 1972 Scale and conformai transformations in Galilean-covariant field theory Phys. Rev. D 5 377-88 Hagen C R and Hurley W J 1970 Magnetic moment of a particle with arbitrary spin Phys. Rev. lett. 26 1381-4 Carinena J F and Santander M 1982 Galilean relativistic wave equations J. Phys. A: Math. Gen. 15 343-53 Fushchich W I and Nikitin A G 1976 On the Galilei-invariant equations for particles with arbitrary spin Lett. Nuovo Cimenta 16 81-5 Fushchich W I and Nikitin A G 1984 On one- and two-particle Galilei-invariant wave equations for any spin Nuovo Cimenta A 81 664-80 Kraus K 1980 Galilei covariance does not imply minimal electromagnetic coupling Ann. Phys. 37 82-101 Krause J 1988 Galilean quantum kinematics J. Phys. A: Math. Gen. 29 393-7 Lévy-Leblond J M 1967 Galilean quantum field theories and a ghostless Lee model Commun. Math. Phys. 4 157-76
10. Hagen C R 1972 Scale and conformai transformations in Galilean-covariant field theory Phys. Rev. D 5 377-88 Hagen C R and Hurley W J 1970 Magnetic moment of a particle with arbitrary spin Phys. Rev. lett. 26 1381-4 Carinena J F and Santander M 1982 Galilean relativistic wave equations J. Phys. A: Math. Gen. 15 343-53 Fushchich W I and Nikitin A G 1976 On the Galilei-invariant equations for particles with arbitrary spin Lett. Nuovo Cimenta 16 81-5 Fushchich W I and Nikitin A G 1984 On one- and two-particle Galilei-invariant wave equations for any spin Nuovo Cimenta A 81 664-80 Kraus K 1980 Galilei covariance does not imply minimal electromagnetic coupling Ann. Phys. 37 82-101 Krause J 1988 Galilean quantum kinematics J. Phys. A: Math. Gen. 29 393-7 Lévy-Leblond J M 1967 Galilean quantum field theories and a ghostless Lee model Commun. Math. Phys. 4 157-76
11. Hagen C R 1972 Scale and conformai transformations in Galilean-covariant field theory Phys. Rev. D 5 377-88 Hagen C R and Hurley W J 1970 Magnetic moment of a particle with arbitrary spin Phys. Rev. lett. 26 1381-4 Carinena J F and Santander M 1982 Galilean relativistic wave equations J. Phys. A: Math. Gen. 15 343-53 Fushchich W I and Nikitin A G 1976 On the Galilei-invariant equations for particles with arbitrary spin Lett. Nuovo Cimenta 16 81-5 Fushchich W I and Nikitin A G 1984 On one- and two-particle Galilei-invariant wave equations for any spin Nuovo Cimenta A 81 664-80 Kraus K 1980 Galilei covariance does not imply minimal electromagnetic coupling Ann. Phys. 37 82-101 Krause J 1988 Galilean quantum kinematics J. Phys. A: Math. Gen. 29 393-7 Lévy-Leblond J M 1967 Galilean quantum field theories and a ghostless Lee model Commun. Math. Phys. 4 157-76
12. Hagen C R 1972 Scale and conformai transformations in Galilean-covariant field theory Phys. Rev. D 5 377-88 Hagen C R and Hurley W J 1970 Magnetic moment of a particle with arbitrary spin Phys. Rev. lett. 26 1381-4 Carinena J F and Santander M 1982 Galilean relativistic wave equations J. Phys. A: Math. Gen. 15 343-53 Fushchich W I and Nikitin A G 1976 On the Galilei-invariant equations for particles with arbitrary spin Lett. Nuovo Cimenta 16 81-5 Fushchich W I and Nikitin A G 1984 On one- and two-particle Galilei-invariant wave equations for any spin Nuovo Cimenta A 81 664-80 Kraus K 1980 Galilei covariance does not imply minimal electromagnetic coupling Ann. Phys. 37 82-101 Krause J 1988 Galilean quantum kinematics J. Phys. A: Math. Gen. 29 393-7 Lévy-Leblond J M 1967 Galilean quantum field theories and a ghostless Lee model Commun. Math. Phys. 4 157-76
13. Hagen C R 1972 Scale and conformai transformations in Galilean-covariant field theory Phys. Rev. D 5 377-88 Hagen C R and Hurley W J 1970 Magnetic moment of a particle with arbitrary spin Phys. Rev. lett. 26 1381-4 Carinena J F and Santander M 1982 Galilean relativistic wave equations J. Phys. A: Math. Gen. 15 343-53 Fushchich W I and Nikitin A G 1976 On the Galilei-invariant equations for particles with arbitrary spin Lett. Nuovo Cimenta 16 81-5 Fushchich W I and Nikitin A G 1984 On one- and two-particle Galilei-invariant wave equations for any spin Nuovo Cimenta A 81 664-80 Kraus K 1980 Galilei covariance does not imply minimal electromagnetic coupling Ann. Phys. 37 82-101 Krause J 1988 Galilean quantum kinematics J. Phys. A: Math. Gen. 29 393-7 Lévy-Leblond J M 1967 Galilean quantum field theories and a ghostless Lee model Commun. Math. Phys. 4 157-76
14. Hagen C R 1972 Scale and conformai transformations in Galilean-covariant field theory Phys. Rev. D 5 377-88 Hagen C R and Hurley W J 1970 Magnetic moment of a particle with arbitrary spin Phys. Rev. lett. 26 1381-4 Carinena J F and Santander M 1982 Galilean relativistic wave equations J. Phys. A: Math. Gen. 15 343-53 Fushchich W I and Nikitin A G 1976 On the Galilei-invariant equations for particles with arbitrary spin Lett. Nuovo Cimenta 16 81-5 Fushchich W I and Nikitin A G 1984 On one- and two-particle Galilei-invariant wave equations for any spin Nuovo Cimenta A 81 664-80 Kraus K 1980 Galilei covariance does not imply minimal electromagnetic coupling Ann. Phys. 37 82-101 Krause J 1988 Galilean quantum kinematics J. Phys. A: Math. Gen. 29 393-7 Lévy-Leblond J M 1967 Galilean quantum field theories and a ghostless Lee model Commun. Math. Phys. 4 157-76
15. Takahashi Y 1988 Towards the many-body theory with the Galilei invariance as a guide. I. Fortschr. Phys. 36 63-81
16. Takahashi Y 1988 Towards the many-body theory with the Galilei invariance as a guide. II. Fortschr. Phys. 36 83-96
17. Omote M, Kamefuchi S, Takahashi Y and Ohnuki Y 1989 Galilean covariance and the Schrödinger equation Fortschr. Phys. 37 933-50
18. Pinski G 1968 Galilean tensor Calculus J. Math. Phys. 9 1927-30 Soper D E 1976 Classical Field Theory (New York: Wiley) section 7.3
19. Pinski G 1968 Galilean tensor Calculus J. Math. Phys. 9 1927-30 Soper D E 1976 Classical Field Theory (New York: Wiley) section 7.3
20. Kapuścik E 1986 On the physical meaning of the Galilean spacetime coordinates Acta Phys. B 17 569-75
21. Duval C, Burdet G, Künzle H P and Perrin M 1985 Bargmann structures and Newton-Cartan theory Phys. Rev. D 31 1841-53
22. Künzle H P and Duval C 1994 Relativistic and nonrelativistic physical theories on five-dimensional spacetime Semantical Aspects of Spacetime Theories ed U Majer and H J Schmidt (Mannheim: BI-Wissenschaftsverlag) pp 113-29
23. Fushchich W I and Nikitin A G 1994 Symmetries of Equations in Quantum Mechanics (New York: Allerton) section 26 Fushchich W I and Nikitin A G 1980 Reduction of the representations of the generalized Poincaré algebra by the Galilei algebra J. Phys A: Math. Gen. 13 2319-30
24. Fushchich W I and Nikitin A G 1994 Symmetries of Equations in Quantum Mechanics (New York: Allerton) section 26 Fushchich W I and Nikitin A G 1980 Reduction of the representations of the generalized Poincaré algebra by the Galilei algebra J. Phys A: Math. Gen. 13 2319-30
25. de Montigny M, Khanna F C, Santana A E and Santos E S 2001 Galilean covariance and the non-relativistic Bhabha equations J. Phys. A: Math. Gen. 34 8901-17
26. de Montigny M, Khanna F C and Santana A E 2003 Nonrelativistic wave equations with gauge fields Int. J. Theor. Phys. 42 649-71
27. de Montigny M, Khanna F C and Santana A E 2003 Lorentz-like covariant equations of non-relativistic fluids J. Phys. A: Math. Gen. 36 2009-26
28. Abreu L, de Montigny M, Khanna F C and Santana A E 2003 Galilei-covariant path-integral quantization of non-relativistic complex scalar fields Ann. Phys. 308 244-62
29. Santos E S, de Montigny M, Khanna F C and Santana A E 'Canonical quantization of Galilean covariant field theories' (in preparation)
30. Schwinger J 1951 The theory of quantized fields, I Phys. Rep. 82 914-27 Roman P 1969 Introduction to Quantum Field Theory (New York: Wiley) Pauli W 1941 Relativistic field theories of elementary particles Rev. mod. Phys. 13 203-32
31. Schwinger J 1951 The theory of quantized fields, I Phys. Rep. 82 914-27 Roman P 1969 Introduction to Quantum Field Theory (New York: Wiley) Pauli W 1941 Relativistic field theories of elementary particles Rev. mod. Phys. 13 203-32
32. Schwinger J 1951 The theory of quantized fields, I Phys. Rep. 82 914-27 Roman P 1969 Introduction to Quantum Field Theory (New York: Wiley) Pauli W 1941 Relativistic field theories of elementary particles Rev. mod. Phys. 13 203-32
33. Jackiw J and Nair V P 2000 Anyon spin and the exotic central extension of the planar Galilei group Phys. Lett. B 480 237-8 Hagen C R 2002 Second central extension in Galilean covariant field theory Phys. Lett. B 539 168-71 Jackiw J and Nair V P 2003 Remarks on the exotic central extension of the planar Galilei group Phys. Lett. B 551 166-8
34. Jackiw J and Nair V P 2000 Anyon spin and the exotic central extension of the planar Galilei group Phys. Lett. B 480 237-8 Hagen C R 2002 Second central extension in Galilean covariant field theory Phys. Lett. B 539 168-71 Jackiw J and Nair V P 2003 Remarks on the exotic central extension of the planar Galilei group Phys. Lett. B 551 166-8
35. Jackiw J and Nair V P 2000 Anyon spin and the exotic central extension of the planar Galilei group Phys. Lett. B 480 237-8 Hagen C R 2002 Second central extension in Galilean covariant field theory Phys. Lett. B 539 168-71 Jackiw J and Nair V P 2003 Remarks on the exotic central extension of the planar Galilei group Phys. Lett. B 551 166-8
36. Crawford F S 1992 Magnetic monopoles, Galilean invariance, and Maxwell's equations Am. J. Phys. 60 109-14 Horzela A, Kapuscik E and Uzes C A 1993 Comment on 'Magnetic monopoles, Galilean invariance, and Maxwell's equations' Am. J. Phys. 61 471-2 Crawford F S 1993 A response to A. Horzela, E. Kapuscik and C.A. Uzes' Comment on 'Magnetic monopoles, Galilean invariance, and Maxwell's equations' Am. J. Phys. 61 472
37. Crawford F S 1992 Magnetic monopoles, Galilean invariance, and Maxwell's equations Am. J. Phys. 60 109-14 Horzela A, Kapuscik E and Uzes C A 1993 Comment on 'Magnetic monopoles, Galilean invariance, and Maxwell's equations' Am. J. Phys. 61 471-2 Crawford F S 1993 A response to A. Horzela, E. Kapuscik and C.A. Uzes' Comment on 'Magnetic monopoles, Galilean invariance, and Maxwell's equations' Am. J. Phys. 61 472
38. Crawford F S 1992 Magnetic monopoles, Galilean invariance, and Maxwell's equations Am. J. Phys. 60 109-14 Horzela A, Kapuscik E and Uzes C A 1993 Comment on 'Magnetic monopoles, Galilean invariance, and Maxwell's equations' Am. J. Phys. 61 471-2 Crawford F S 1993 A response to A. Horzela, E. Kapuscik and C.A. Uzes' Comment on 'Magnetic monopoles, Galilean invariance, and Maxwell's equations' Am. J. Phys. 61 472
39. Jackson J D 1975 Classical Electrodynamics (New York: Wiley)
40. Lévy-Leblond J M 1967 Nonrelativistic particles and wave equations Commun. Math. Phys. 6 286-311
41. Nikitin A G and Fuschich WI 1980 Equations of motion for particles of arbitrary spin invariant under the Galilei group Theor. Math. Phys. 44 584-92