Two and three-point functions in Liouville theory

Based on our generalization of the Goulian-Li continuation in the power of the 2D cosmological term we construct the two and three-point correlation functions for Liouville exponentials with generic real coefficients. As a strong argument in favour of the procedure we prove the Liouville equation of motion on the level of three-point functions. The analytical structure of the correlation functions as well as some of its consequences for string theory are discussed. This includes a conjecture on the mass shell condition for excitations of noncritical strings. We also make a comment concerning the correlation functions of the Liouville field itself.Comment: 15 pages, Latex, Revised version: A sign error in formula (50) is correcte

Quantum Exchange Algebra and Exact Operator Solution of A2A_2-Toda Field Theory

Locality is analyzed for Toda field theories by noting novel chiral description in the conventional nonchiral formalism. It is shown that the canonicity of the interacting to free field mapping described by the classical solution is automatically guaranteed by the locality. Quantum Toda theories are investigated by applying the method of free field quantization. We give Toda exponential operators associated with fundamental weight vectors as bilinear forms of chiral fields satisfying characteristic quantum exchange algebra. It is shown that the locality leads to nontrivial relations among the ${\cal R}$-matrix and the expansion coefficients of the exponential operators. The Toda exponentials are obtained for $A_2$-system by extending the algebraic method developed for Liouville theory. The canonical commutation relations and the operatorial field equations are also examined.Comment: 38 pages, Late

Quantum Group Structure and Local Fields in the Algebraic Approach to 2D Gravity

This review contains a summary of work by J.-L. Gervais and the author on the operator approach to 2d gravity. Special emphasis is placed on the construction of local observables -the Liouville exponentials and the Liouville field itself - and the underlying algebra of chiral vertex operators. The double quantum group structure arising from the presence of two screening charges is discussed and the generalized algebra and field operators are derived. In the last part, we show that our construction gives rise to a natural definition of a quantum tau function, which is a noncommutative version of the classical group-theoretic representation of the Liouville fields by Leznov and Saveliev.Comment: 38 pages, LaTex file. Proceedings of the Vth International Conference on Mathematical Physics, Strings and Quantum gravity, Alushta, Ukraine 199

Defectors cannot be detected during"small talk" with strangers.

To account for the widespread human tendency to cooperate in one-shot social dilemmas, some theorists have proposed that cooperators can be reliably detected based on ethological displays that are difficult to fake. Experimental findings have supported the view that cooperators can be distinguished from defectors based on "thin slices" of behavior, but the relevant cues have remained elusive, and the role of the judge's perspective remains unclear. In this study, we followed triadic conversations among unacquainted same-sex college students with unannounced dyadic one-shot prisoner's dilemmas, and asked participants to guess the PD decisions made toward them and among the other two participants. Two other sets of participants guessed the PD decisions after viewing videotape of the conversations, either with foreknowledge (informed), or without foreknowledge (naïve), of the post-conversation PD. Only naïve video viewers approached better-than-chance prediction accuracy, and they were significantly accurate at predicting the PD decisions of only opposite-sexed conversation participants. Four ethological displays recently proposed to cue defection in one-shot social dilemmas (arms crossed, lean back, hand touch, and face touch) failed to predict either actual defection or guesses of defection by any category of observer. Our results cast doubt on the role of "greenbeard" signals in the evolution of human prosociality, although they suggest that eavesdropping may be more informative about others' cooperative propensities than direct interaction

Reparametrization Invariance of Path Integrals

We demonstrate the reparametrization invariance of perturbatively defined one-dimensional functional integrals up to the three-loop level for a path integral of a quantum-mechanical point particle in a box. We exhibit the origin of the failure of earlier authors to establish reparametrization invariance which led them to introduce, superfluously, a compensating potential depending on the connection of the coordinate system. We show that problems with invariance are absent by defining path integrals as the epsilon-> 0 -limit of 1+ epsilon -dimensional functional integrals.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper also at http://www.physik.fu-berlin.de/~kleinert/kleiner_re289/preprint.htm

Light-Cone Quantization of the Liouville Model

We present the quantization of the Liouville model defined in light-cone coordinates in (1,1) signature space. We take advantage of the representation of the Liouville field by the free field of the Backl\"{u}nd transformation and adapt the approch by Braaten, Curtright and Thorn. Quantum operators of the Liouville field $\partial_{+}\phi$, $\partial_{-}\phi$, $e^{g\phi}$, $e^{2g\phi}$ are constructed consistently in terms of the free field. The Liouville model field theory space is found to be restricted to the sector with field momentum $P_{+}=-P_{-}$, $P_{+}> 0$ , which is a closed subspace for the Liouville theory operator algebra.Comment: 16 p, EFI-92-6

Soliton quantization and internal symmetry

We apply the method of collective coordinate quantization to a model of solitons in two spacetime dimensions with a global $U(1)$ symmetry. In particular we consider the dynamics of the charged states associated with rotational excitations of the soliton in the internal space and their interactions with the quanta of the background field (mesons). By solving a system of coupled saddle-point equations we effectively sum all tree-graphs contributing to the one-point Green's function of the meson field in the background of a rotating soliton. We find that the resulting one-point function evaluated between soliton states of definite $U(1)$ charge exhibits a pole on the meson mass shell and we extract the corresponding S-matrix element for the decay of an excited state via the emission of a single meson using the standard LSZ reduction formula. This S-matrix element has a natural interpretation in terms of an effective Lagrangian for the charged soliton states with an explicit Yukawa coupling to the meson field. We calculate the leading-order semi-classical decay width of the excited soliton states discuss the consequences of these results for the hadronic decay of the $\Delta$ resonance in the Skyrme model.Comment: 23 pages, LA-UR-93-299

Schwinger-Dyson and Large NcN_{c} Loop Equation for Supersymmetric Yang-Mills Theory

We derive an infinite sequence of Schwinger-Dyson equations for $N=1$ supersymmetric Yang-Mills theory. The fundamental and the only variable employed is the Wilson-loop geometrically represented in $N=1$ superspace: it organizes an infinite number of supersymmetrizing insertions into the ordinary Wilson-loop as a single entity. In the large $N_{c}$ limit, our equation becomes a closed loop equation for the one-point function of the Wilson-loop average.Comment: 9 pages, Late

Spontaneous superconductivity and optical properties of high-Tc cuprates

We suggest that the high temperature superconductivity in cuprate compounds may emerge due to interaction between copper-oxygen layers mediated by in-plane plasmons. The strength of the interaction is determined by the c-axis geometry and by the ab-plane optical properties. Without making reference to any particular in-plane mechanism of superconductivity, we show that the interlayer interaction favors spontaneous appearance of the superconductivity in the layers. At a qualitative level the model describes correctly the dependence of the transition temperature on the interlayer distance, and on the number of adjacent layers in multilayered homologous compounds. Moreover, the model has a potential to explain (i) a mismatch between the optimal doping levels for critical temperature and superconducting density and (ii) a universal scaling relation between the dc-conductivity, the superfluid density, and the superconducting transition temperature.Comment: 4.4 pages, 2 figures; v2 matches the published version (clarifying remarks and references are added

Integrals over Products of Distributions and Coordinate Independence of Zero-Temperature Path Integrals

In perturbative calculations of quantum-statistical zero-temperature path integrals in curvilinear coordinates one encounters Feynman diagrams involving multiple temporal integrals over products of distributions, which are mathematically undefined. In addition, there are terms proportional to powers of Dirac delta-functions at the origin coming from the measure of path integration. We give simple rules for integrating products of distributions in such a way that the results ensure coordinate independence of the path integrals. The rules are derived by using equations of motion and partial integration, while keeping track of certain minimal features originating in the unique definition of all singular integrals in $1 - \epsilon$ dimensions. Our rules yield the same results as the much more cumbersome calculations in 1- epsilon dimensions where the limit epsilon --> 0 is taken at the end. They also agree with the rules found in an independent treatment on a finite time interval.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper (including all PS fonts) at http://www.physik.fu-berlin.de/~kleinert/33