Rotating Relativistic Systems

Rotating Relativistic Systems NASA/JPL-Caltech NASA/Tod Strohmayer binary star merger neutron star black hole noncentral heavy-ion collision Angular momentum of heavy-ions Vorticity (or Rotation) First evidence: global Λ-polarization (2017) 21 & 10 <latexit sha1_base64="ndyehz3ksfd0fgvno0gcvbpxlhk=">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</latexit> Hz ' 10 2 m Necessary to know Rotational eﬀect on QFT

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sha1_base64="ktljh817btd/u4avd8zw4y6wq3u=">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</latexit> angular momentum conservation 10 22 Hz ' 10 MeV STAR (2017) Ampere's law eb 10 18 G ' m 2 Skokov, Illarionov, Toneev (2009) How are the magnetic properties modified by rotation? e.g. anomalous transport and chiral symmetry breaking

v edge = R apple 1 R apple 1/ < 1 R Ω v edge = R Ω x µ lab x µ rot

Ω eb Ω eb

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T = 0 q " = p 2? + p2 z p? = l,4 /R p? = l,3 /R p? = l,2 /R p? = l,1 /R l,1 /R p z

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T = 0 apple 1/R " l,1 /R > (l +1/2) l T = 0 p z j 5 = T 2 12

1/ p eb R eb R p? = p 2neB l 1/ p eb 1/ p eb. R l p? ' p 2neB eb l

eb [i µ (@ µ + iea µ ) m] =0 R p l l = ebr 2 /2 p l [R 1 ] p 0 [R 1 ] p 0 = 0,1 /R ' 2.4/R l<0 eb l 0 p 0 =0

eb p 0 [R 1 ] R = ebr 2 /2 l,1 /R p z p z

eb p 0 [R 1 ] R = ebr 2 /2 (l +1/2) l,1 /R (l +1/2) p z p z

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sha1_base64="tqpv1s0jb2dqdqwugoxzno8idw8=">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</latexit> [i µ (@ µ + iea µ + µ )] =0 R Ω eb n(r) =h (x) (x)i = X h i f + (") f (") p z,p? 1 f ± (") = e (" j) +1 r-dependence n(r = 0)! p eb eb 4 2 S S µb = µg ij B i j g ij T ij =#eb i j

M T =0 R = 10 3 [ 1 ] eb M eb M

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T ij =#eb i j B