Abstract
The vacuum expectation values of conserved currents play an essential role in the generalized hydrodynamics of integrable quantum field theories. We use analytic continuation to extend these results for the excited state expectation values in a finite volume. Our formulas are valid for diagonally scattering theories and incorporate all finite size corrections.
Highlights
There have been interesting developments in calculating expectation values in integrable finite temperature/volume systems
The vacuum expectation values of conserved currents play an essential role in the generalized hydrodynamics of integrable quantum field theories
In statistical physics the recent developments of the generalized hydrodynamics require the knowledge of the finite temperature expectation values of conserved charges and currents as they are the key inputs in formulating the Euler type hydrodynamic evolution [1, 6, 7]
Summary
There have been interesting developments in calculating expectation values in integrable finite temperature/volume systems. In statistical physics the recent developments of the generalized hydrodynamics require the knowledge of the finite temperature expectation values of conserved charges and currents as they are the key inputs in formulating the Euler type hydrodynamic evolution [1, 6, 7]. There were interesting direct calculations [8, 9], which expressed the current expectation values in spin chain Bethe states in terms of the charge eigenvalues and the inverse of the Gaudin matrix. These remarkable compact and simple expressions are valid in quantum field theories for finite volume expectation values in multiparticle states once the exponentially small vacuum polarization effects are neglected. We perform various tests of our results and conclude
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