Constructs a manifestly diagonal-BRST-invariant Schwinger-Keldysh path integral for open non-Abelian gauge theories with arbitrary physical initial states, yielding Ward-Takahashi-Slavnov-Taylor identities and a Keldysh BRST symmetry for the Open EFT.
Subsystem Trace Distance in Quantum Field Theory
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abstract
We develop a systematic method to calculate the trace distance between two reduced density matrices in 1+1 dimensional quantum field theories. The approach exploits the path integral representation of the reduced density matrices and an ad hoc replica trick. We then extensively apply this method to the calculation of the distance between reduced density matrices of one interval of length $\ell$ in eigenstates of conformal field theories. When the interval is short, using the operator product expansion of twist operators, we obtain a universal form for the leading order in $\ell$ of the trace distance. We compute the trace distances among the reduced density matrices of several low lying states in two-dimensional free massless boson and fermion theories. We compare our analytic conformal results with numerical calculations in XX and Ising spin chains finding perfect agreement.
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Schwinger-Keldysh Path Integral for Gauge theories
Constructs a manifestly diagonal-BRST-invariant Schwinger-Keldysh path integral for open non-Abelian gauge theories with arbitrary physical initial states, yielding Ward-Takahashi-Slavnov-Taylor identities and a Keldysh BRST symmetry for the Open EFT.