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...

The two-dimensional (2d) manifestly locally supersymmetric actions describing the N=2 and N=4 extended super-Liouville theory coupled to the N=2 and N=4 conformal supergravity, respectively, are constructed in superspace. It is shown that the N=4 super-Liouville multiplet is described by the improved twisted-II scalar mul-tiplet TM-II, whose kinetic terms are given by the SU(2) ⊗ U(1) WZNW model.

An analogue to the theory of Riesz potentials and Liouville operators in R for arbitrary fractal d-sets is developed. Corresponding function spaces agree with traces of euclidean Besov spaces on fractals. By means of associated quadratic forms we construct strongly continuous semigroups with Liouville operators as infinitesimal generator. The case of Dirichlet forms is discussed separately. As ...

Application of our algebraic approach to Liouville integrable defects is proposed for the sine-Gordon model. Integrability of the model is ensured by the underlying classical r-matrix algebra. The first local integrals of motion are identified together with the corresponding Lax pairs. Continuity conditions imposed on the time components of the entailed Lax pairs give rise to the sewing conditi...

In this paper, we apply spectral method based on the Bernstein polynomials for solving a class of optimal control problems with Jumarie’s modified Riemann-Liouville fractional derivative. In the first step, we introduce the dual basis and operational matrix of product based on the Bernstein basis. Then, we get the Bernstein operational matrix for the Jumarie’s modified Riemann-Liouville fractio...

We prove some results on the behavior of infinite sums of the form ∑ f ◦ T(x) 1 n , where T : S → S is an irrational circle rotation and f is a mean-zero function on S. In particular, we show that for a certain class of functions f , there are Liouville α for which this sum diverges everywhere and Liouville α for which the sum converges everywhere.

We evaluate the three point function for arbitrary states in bosonic minimal models on the sphere coupled to quantum gravity in two dimensions. The validity of the formal continuation in the number of Liouville screening charge insertions is shown directly from the Liouville functional integral using semi-classical methods. ⋆ Work supported in part by the National Science Foundation grant PHY–8...

In this paper Quantum Mechanics with Fundamental Length is built as a deformation of Quantum Mechanics. To this aim an approach is used which does not take into account commutator deformation as usually it is done, but density matrix deformation. The corresponding deformed density matrix, which is called density pro-matrix is given explicitly. It properties have been investigated as well as som...

We present a non-perturbative solution of large N matrix models modified by terms of the form g(TrΦ4)2, which add microscopic wormholes to the random surface geometry. For g < gt the sum over surfaces is in the same universality class as the g = 0 theory, and the string susceptibility exponent is reproduced by the conventional Liouville interaction ∼ eα+φ. For g = gt we find a different univers...

In this paper Quantum Mechanics with Fundamental Length is built as a deformation of Quantum Mechanics. To this aim an approach is used which does not take into account commutator deformation as usually it is done, but density matrix deformation. The corresponding deformed density matrix, which is called density pro-matrix is given explicitly. It properties have been investigated as well as som...