Explicit solution of the (quantum) elliptic Calogero-Sutherland model

We derive explicit formulas for the eigenfunctions and eigenvalues of the elliptic Calogero-Sutherland model as infinite series, to all orders and for arbitrary particle numbers and coupling parameters. The eigenfunctions obtained provide an elliptic deformation of the Jack polynomials. We prove in certain special cases that these series have a finite radius of convergence in the nome $q$ of the elliptic functions, including the two particle (= Lam\'e) case for non-integer coupling parameters.Comment: v1: 17 pages. The solution is given as series in q but only to low order. v2: 30 pages. Results significantly extended. v3: 35 pages. Paper completely revised: the results of v1 and v2 are extended to all order

Renormalization of Non-Commutative Phi^4_4 Field Theory in x Space

In this paper we provide a new proof that the Grosse-Wulkenhaar non-commutative scalar Phi^4_4 theory is renormalizable to all orders in perturbation theory, and extend it to more general models with covariant derivatives. Our proof relies solely on a multiscale analysis in x space. We think this proof is simpler and could be more adapted to the future study of these theories (in particular at the non-perturbative or constructive level).Comment: 32 pages, v2: correction of lemmas 3.1 and 3.2 with no consequence on the main resul

Singular factorizations, self-adjoint extensions, and applications to quantum many-body physics

We study self-adjoint operators defined by factorizing second order differential operators in first order ones. We discuss examples where such factorizations introduce singular interactions into simple quantum mechanical models like the harmonic oscillator or the free particle on the circle. The generalization of these examples to the many-body case yields quantum models of distinguishable and interacting particles in one dimensions which can be solved explicitly and by simple means. Our considerations lead us to a simple method to construct exactly solvable quantum many-body systems of Calogero-Sutherland type.Comment: 17 pages, LaTe

Simulation of stable water isotopes in precipitation over South america: Comparing regional to global circulation models

A simulation of the stable water isotope cycle over South America by the regional circulation model REMOiso is discussed. The performance of the regional model, with a resolution of 0.5° (∼55 km), is compared to simulations by the global circulation model ECHAMiso at two coarser resolutions and evaluated against observations of precipitation and δ18O. Here REMOiso is demonstrated to reproduce reasonably well climatic and isotopic features across South America. This paper explores further insights of δ18O as a climate proxy, based on REMOiso’s improvements as compared to ECHAMiso. In particular, the authors focus on the seasonal variation of the amount effect (δ18O decrease with precipitation amounts) and the anomalous δ18O continental gradient across the Amazon basin, as inferred from the REMOiso, ECHAMiso, and GNIP datasets. The finer resolution of topography in REMOiso enables a detailed analysis of the altitude effect: not only the first, but also the second derivative of δ18O with altitude is considered. It appears that high-altitude grid cells show an isotopic signature similar to Rayleigh distillation, in accordance with experimental studies. Finally, a Lagrangian reference frame is adopted to describe the evolution of δ18O in precipitation along its trajectory, in order to relate the simulation analysis to the fractionation mechanisms. This confirms that the amount effect, via Rayleigh distillation processes, is dominant during the wet season. During the dry season, the δ18O in precipitation is controlled by isotopic reequilibration of rain droplets with surrounding vapor, reflecting the impact of nonfractionating transpiration by the vegetation

Lattice Gauge Theories and the Heisenberg Antiferromagnetic Chain

We study the strongly coupled 2-flavor lattice Schwinger model and the SU(2)-color QCD_2. The strong coupling limit, even with its inherent nonuniversality, makes accurate predictions of the spectrum of the continuum models and provides an intuitive picture of the gauge theory vacuum. The massive excitations of the gauge model are computable in terms of spin-spin correlators of the quantum Heisenberg antiferromagnetic spin-1/2 chain.Comment: Proceedings LATTICE99 (spin models), 3 page

Loop Correlators and Theta States in 2D Yang-Mills Theory

Explicit computations of the partition function and correlation functions of Wilson and Polyakov loop operators in theta-sectors of two dimensional Yang-Mills theory on the line cylinder and torus are presented. Several observations about the correspondence of two dimensional Yang-Mills theory with unitary matrix quantum mechanics are presented. The incorporation of the theta-angle which characterizes the states of two dimensional adjoint QCD is discussed.Comment: 30 pages, Latex, no figure

Gravitational Constant and Torsion

Riemann-Cartan space time $U_{4}$ is considered here. It has been shown that when we link topological Nieh-Yan density with the gravitational constant then we get Einstein-Hilbert Lagrangian as a consequence.Comment: 8 page

A Review of Noncommutative Field Theories

We present a brief review of selected topics in noncommutative field theories ranging from its revival in string theory, its influence on quantum field theories, its possible experimental signatures and ending with some applications in gravity and emergent gravity.Comment: Talk presented at the XIV Mexican School on Particles and Fields, Morelia, Mexico, November 9-11, 2010; 8 pages. V2 reference adde

Exact solution of a 2D interacting fermion model

We study an exactly solvable quantum field theory (QFT) model describing interacting fermions in 2+1 dimensions. This model is motivated by physical arguments suggesting that it provides an effective description of spinless fermions on a square lattice with local hopping and density-density interactions if, close to half filling, the system develops a partial energy gap. The necessary regularization of the QFT model is based on this proposed relation to lattice fermions. We use bosonization methods to diagonalize the Hamiltonian and to compute all correlation functions. We also discuss how, after appropriate multiplicative renormalizations, all short- and long distance cutoffs can be removed. In particular, we prove that the renormalized two-point functions have algebraic decay with non-trivial exponents depending on the interaction strengths, which is a hallmark of Luttinger-liquid behavior.Comment: 59 pages, 3 figures, v2: further references added; additional subsections elaborating mathematical details; additional appendix with details on the relation to lattice fermion