Understand
We find the density matrix corresponding to the vacuum state of a massless Dirac field in two dimensions reduced to a region of the space formed by several disjoint intervals.
- We calculate explicitly its spectral decomposition.
- The imaginary powers of the density matrix is a unitary operator implementing an internal time flow (the modular flow).
- We show that in the case of more than one interval this evolution is non-local, producing both, advance in the causal structure and "teleportation" between the disjoint intervals.
Built on
N. I. Muskhelishvili, Singular Integral Equations
1953
Earlier work this paper cites.
H. Araki, Publ. Res. Inst. Math. Sci. Kyoto 6
1971
Earlier work this paper cites.
W. G. Unruh, Phys. Rev. D 14
1976
Earlier work this paper cites.
J. J. Bisognano and E. H. Wichmann, J. Math. Phys. 17
1976
Earlier work this paper cites.
P. D. Hislop and R. Longo, Commun. Math. Phys. 84
1982
Earlier work this paper cites.
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