Non-Abelian fluid dynamics in Lagrangian formulation

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 67, Issue 2, 2003, Pages

  Pi, S Y ^c   Nair, V P ^b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b CITY COLLEGE OF NEW YORK   (United States)

^c Boston University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CALCULATION; DYNAMICS; FLOW RATE; FORCE; KINETICS; MAGNETISM; MATHEMATICAL ANALYSIS; PLASMA; SPACE; TIME; VELOCITY;

EID: 0037438126     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.67.025013     Document Type: Article

References (17)

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8. Lagrangians for nonrelativistic and relativistic Abelian Eulerian fluids exist in the literature;see, for example, R. Jackiw, Lectures on Fluid Dynamics (Springer, New York, 2002) whose development and conventions are followed in this paper.
9. A. Clebsch, J. Reine Angew. Math. 56, 1 (1859);H. Lamb, Hydrodynamics (Cambridge University Press, Cambridge, UK, 1932), p. 248;C.C. Lin, in International School of Physics Enrino Fermi (XXI), edited by G. Careri (Academic, New York, 1963).
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12. When comparison is made with the usual expression for the energy-momentum tensor of a relativistic fluid, we see that (Formula presented) is the pressure and (Formula presented) is the pressure summed with the energy density, i.e., (Formula presented) is the energy density; see Ref. 3.
13. S.K. Wong, Nuovo Cimento A 65, 689 (1970).
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15. The canonical analysis presented in our paper (Appendix B) follows the method of D. Bak, R. Jackiw, and S.-Y. Pi, Phys. Rev. D 49, 6778 (1994) (Appendix).
16. In a previous paper, we presented a similar candidate Lagrangian for non-Abelian fluids, except that the (Formula presented) comprised all generators for a subgroup H of the group G to which g belongs, with the additional requirement that (Formula presented) be a symmetric space. This construction is based on a non-Abelian version of the Clebsch parametrization. But the equations that follow do not have a clear physical interpretation, so we have not pursued this approach.
17. R. Jackiw, V.P. Nair, and S.-Y. Pi, Phys. Rev. D 62, 085018 (2000).