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- W4387364946 abstract "We continue the study of the Tomita-Takesaki modular conjugation for a massless Dirac field in a generic multicomponent region in $1+1$ spacetime dimensions. In this paper we focus on the computations for a thermal state on a circle, namely on the euclidean torus. By analytic continuation from the modular flow we arrive at an explicit expression for the modular conjugation in this scenario and derive its relevant limits. In contrast to the case of the vacuum on the line, this new result has a nonlocal behavior even for connected regions. It also presents a novel contribution coming from the purification one has to introduce in order to deal with a mixed state; a term that maps the algebra of operators of the region to a copy of the global one, the so-called ``second world'' algebra." @default.
- W4387364946 created "2023-10-06" @default.
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- W4387364946 date "2023-10-05" @default.
- W4387364946 modified "2023-10-06" @default.
- W4387364946 title "Modular conjugation for the chiral fermion in multicomponent regions on the torus" @default.
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- W4387364946 doi "https://doi.org/10.1103/physrevd.108.085003" @default.
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