We show that the mixed quantum-classical Liouville equation is equivalent to linearizing the forward-backward action in the influence functional. Derivations are provided in terms of either the diabatic or adiabatic basis sets. An application of the mixed quantum-classical Liouville equation for calculating the memory kernel of the generalized quantum master equation is also presented. The accu...

Two-dimensional supergravity theory is quantized as an anomalous gauge theory. In the Batalin-Fradkin (BF) formalism, the anomaly-canceling super-Liouville fields are introduced to identify the original second-class constrained system with a gauge-fixed version of a first-class system. The BFV-BRST quantization applies to formulate the theory in the most general class of gauges. A local effecti...

We construct Euclidean Liouville conformal field theories in odd number of dimensions. The are nonlocal and non-unitary with a log-correlated field, ${\cal Q}$-curvature background, an exponential Liouville-type potential. study the classical quantum properties these including finite entanglement entropy part sphere partition function $F$, boundary anomaly vertex operators' correlation function...

In this paper we prove a Liouville type theorem for the stationary magnetohydrodynamics (MHD) system in R 3 . Let ( v , B p ) be smooth solution to MHD equations We show that if there exist matrix valued potential functions Φ Ψ such ∇ ⋅ = and whose L 6 mean oscillations have certain growth condition near infinity, namely ⨍ r | − d x + ≤ C ∀ 1 < ∞ then 0 =constant. With additional assumption of ...

The Lax pair of the Ruijsenaars-Schneider model with interaction potential of trigonometric type based on Dn Lie algebra is presented. We give a general form for the Lax pair and prove partial results for small n. Liouville integrability of the corresponding system follows a series of involutive Hamiltonians generated by the characteristic polynomial of the Lax matrix. The rational case appears...

We present a new necessary condition for similarity of indefinite Sturm-Liouville operators to self-adjoint operators. This condition is formulated in terms of Weyl-Titchmarsh m-functions. Also we obtain necessary conditions for regularity of the critical points 0 and∞ of J-nonnegative Sturm-Liouville operators. Using this result, we construct several examples of operators with the singular cri...

We investigate N -point string scattering amplitudes in AdS3 space. Based on recent observations on the solutions of KZ and BPZ-type differential equations, we discuss how to describe the string theory in AdS3 as a marginal deformation of a (flat) linear dilaton background. This representation resembles the called “discrete light-cone Liouville” realization as well as the FZZ dual description i...

‎This paper deals with the singular Sturm-Liouville expressions‎ ‎$ ‎ell y =‎ -‎y''+q(x)y=lambda y‎ ‎$‎ ‎on a finite interval‎, ‎where the potential function $q$ is real and‎ ‎has a singularity inside the interval‎. ‎Using the asymptotic estimates of a‎ ‎spectral fundamental system of solutions of Sturm-Liouville‎ ‎equation‎, ‎the asymptotic form of the solution of the‎ ‎equation (0.1) and the ...

Abstract We study a Sturm–Liouville-type operator with operator-valued coefficients and its iso-spectral deformations, related to new two-component Camassa–Holm-type completely integrable dynamical systems. Based on specially devised gradient-holonomic scheme, generalizing the one before developed for studying spectral problem spatially multidimensional Hilbert–Schmidt Hilbert space, we constru...