A comment on finite temperature correlations in integrable QFT

I discuss and extend the recent proposal of Leclair and Mussardo for finite temperature correlation functions in integrable QFTs. I give further justification for its validity in the case of one point functions of conserved quantities. I also argue that the proposal is not correct for two (and higher) point functions, and give some counterexamples to justify that claim.Comment: 11 page

Riemann Hypothesis and Random Walks: the Zeta case

In previous work it was shown that if certain series based on sums over primes of non-principal Dirichlet characters have a conjectured random walk behavior, then the Euler product formula for its $L$-function is valid to the right of the critical line $\Re (s) > \tfrac{1}{2}$, and the Riemann Hypothesis for this class of $L$-functions follows. Building on this work, here we propose how to extend this line of reasoning to the Riemann zeta function and other principal Dirichlet $L$-functions. We apply these results to the study of the argument of the zeta function. In another application, we define and study a 1-point correlation function of the Riemann zeros, which leads to the construction of a probabilistic model for them. Based on these results we describe a new algorithm for computing very high Riemann zeros, and we calculate the googol-th zero, namely $10^{100}$-th zero to over 100 digits, far beyond what is currently known.Comment: version 2: A significantly better estimate of the error incurred in computing zeros from the primes has been include. version 3: Re-written in a more informal style; change of notation to avoid confusion with S(t

Errata for: Differential Equations for Sine-Gordon Correlation Functions at the Free Fermion Point

We present some important corrections to our work which appeared in Nucl. Phys. B426 (1994) 534 (hep-th/9402144). Our previous results for the correlation functions $\langle e^{i\alpha \Phi(x)} e^{i\alpha' \Phi (0) } \rangle$ were only valid for $\alpha = \alpha'$, due to the fact that we didn't find the most general solution to the differential equations we derived. Here we present the solution corresponding to $\alpha \neq \alpha'$.Comment: 4 page