Magnetofluid Unification in the Yang-Mills Lagrangian

Transcription

1 PAQFT Singapore, November 2008 p. 1 Magnetofluid Unification in the Yang-Mills Lagrangian L.T. Handoko in collaboration with A. Fajarudin, A. Sulaiman, T.P. Djun handoko@teori.fisika.lipi.go.id Group for Theoretical & Computational Physics Indonesian Institute of Sciences - LIPI

2 PAQFT Singapore, November 2008 p. 2 Background Experimental discoveries : deconfined quark gluon matter behaves more like a quark gluon plasma liquid. (STAR & RHIC, 2005)

3 PAQFT Singapore, November 2008 p. 2 Background Experimental discoveries : deconfined quark gluon matter behaves more like a quark gluon plasma liquid. (STAR & RHIC, 2005)

4 PAQFT Singapore, November 2008 p. 2 Background Experimental discoveries : deconfined quark gluon matter behaves more like a quark gluon plasma liquid. (STAR & RHIC, 2005)

5 PAQFT Singapore, November 2008 p. 3 Background (2) Motivates works in constructing non-abelian fluid models = magnetohydrodynamics (MHD). Unification of the electromagnetic and fluid fields.

6 PAQFT Singapore, November 2008 p. 3 Background (2) Motivates works in constructing non-abelian fluid models = magnetohydrodynamics (MHD). Unification of the electromagnetic and fluid fields. But, most works starts from the EOM of fluid-like system inspired by the classical fluid mechanics. Eg. The hybrid MHD : M µν F µν + m S q µν where S µν is the fluid strength tensor

7 PAQFT Singapore, November 2008 p. 4 Our proposal The relativistic plasma fluid is modelled as a fluid system of gluon cloud with matters (quarks and anti-quarks) inside.

8 PAQFT Singapore, November 2008 p. 4 Our proposal The relativistic plasma fluid is modelled as a fluid system of gluon cloud with matters (quarks and anti-quarks) inside. construct the model from first principle...

9 PAQFT Singapore, November 2008 p. 4 Our proposal The relativistic plasma fluid is modelled as a fluid system of gluon cloud with matters (quarks and anti-quarks) inside. construct the model from first principle... Introduce a lagrangian involves non-abelian fluid fields U µ interacting with another Abelian / non-abelian gauge fields A µ with some matters inside. Certain gauge symmetry G(n) F G(n) G (eg. MHD is U(1) F U(n) G ).

10 PAQFT Singapore, November 2008 p. 4 Our proposal The relativistic plasma fluid is modelled as a fluid system of gluon cloud with matters (quarks and anti-quarks) inside. construct the model from first principle... Introduce a lagrangian involves non-abelian fluid fields U µ interacting with another Abelian / non-abelian gauge fields A µ with some matters inside. Certain gauge symmetry G(n) F G(n) G (eg. MHD is U(1) F U(n) G ). Intended for physics at scale of order transport mean free paths : the transition region where neither hydrodynamics nor kinetic theory is really valid.

11 PAQFT Singapore, November 2008 p. 5 The Model : G(n) F G(n) G with, L = L matter + L gauge + L int. L matter L gauge L int. = iψ / Ψ m Ψ ΨΨ = 1 4 Sa µν Saµν 1 4 F a µν F aµν = g F J a Fµ Uaµ g G J a Gµ Aaµ while, S a µν µ U a ν ν U a µ + g F f abc U b µu c ν J a Xµ ΨT a X γ µψ

12 PAQFT Singapore, November 2008 p. 6 EOM for relativistic fluid The EOM in term of fluid field U µ is, Introduce : ν S µν = g F J F µ for Abelian D ν S a µν = g F J a Fµ for non Abelian U a µ = (U a 0,U a ) u a µφ and u µ γ a (1, v a ) A µ ǫ µ e ip x Constraint : U µ must be massive gauge bosons, so there are still 3 degree of freedoms to represent the spatial velocity v!

13 PAQFT Singapore, November 2008 p. 7 EOM for relativistic fluid (2) Summing up all components, 0 ( µ U a 0 0U a µ) i ( µ U a i i U a µ where, F a µ f abc F i +i [ ( 0 UµU b 0 c ( TFU d d0 + g G ) i ( U b µu c i )] ( T d FU di + g G g F T d GA di ) ( µ T d g GA d0 U a F ) ( ) = gf JFµ a + F µ a 0 0 U a µ + g F f abc F U b µu c 0 ) ( µ U a i i U a µ + g F f abc F U b µu c i F a µ : additional force from the fluid self-interaction ) )

14 PAQFT Singapore, November 2008 p. 8 EOM for relativistic fluid (3) t Ua U a 0 = g F dt (J a F + F a ) = g F dx (J a F0 + F a 0 ) which always satisfies ω a U a = 0 irrortational fluid. Finally, t (γa v a φ) + (γ a φ) = g F dx (J a F0 + F a 0 ) a general relativistic fluid equation?

15 PAQFT Singapore, November 2008 p. 9 EOM for relativistic fluid (4) Reason At non-relativistic limit, γ 1 + 1/2 v 2 up to O( v 2 ) accuracy and φ 1 : v a t va 2 = g F dx (JF0 a + F 0 a ) non rel. and v a t + (va )v a = g F dx (JF0 a + F 0 a ) non rel. just the classical irrotational fluid equation!

16 PAQFT Singapore, November 2008 p. 10 Modelling the QGP Let s consider SU(3) F U(1) G Describe macroscopically non-abelian fluid formed by dense gluon surrounding the (quarks and anti-quarks) matters in an electromagnetic field. L = iq / Q m Q QQ 1 4 Sa µνs aµν 1 4 F µνf µν +g F J a Fµ Uaµ + qj G µa µ and, its relativistic fluid dynamics obeys, t (γa v a φ) + (γ a φ) = g F dx (ρ a F + F a 0 )

17 PAQFT Singapore, November 2008 p. 11 Modelling the QGP (2) According to the experiments at RHIC : the hot QGP is dense and flows with tiny viscosity approximating to the ideal fluid. This draws : U a 0 affecting some terms in Fµ a. No turbulence, i.e. ω a 0, that is always satisfied. Also, since q/g F α/α s O(10 1 ) the EM force is negligible (no long range EM forces in non-abelian plasmas) the pure SU(3) F model : L = 1 4 Sa µνs aµν g F J a Fµ Uaµ

18 PAQFT Singapore, November 2008 p. 12 Consequences For instance, one can deduce the Hamiltonian density : H = g2 F 2 ( dx (ρ a F + F0 a ) +g F γ a φ (ρ a F + v a J a F) ) f abc U b U c 2 Another type of energy momentum tensor in general relativity etc. Perform numeric calculation using lattice gauge theory.

19 PAQFT Singapore, November 2008 p. 13 Summary The magnetofluid is described using gauge invariant lagrangian. It provides alternative insight into macroscopic dynamics of relativistic fluids relevent for plasma etc.

20 PAQFT Singapore, November 2008 p. 13 Summary The magnetofluid is described using gauge invariant lagrangian. It provides alternative insight into macroscopic dynamics of relativistic fluids relevent for plasma etc. THANK YOU!