Test of asymptotic freedom and scaling hypothesis in the 2d O(3) sigma model

The 7--particle form factors of the fundamental spin field of the O(3) nonlinear $\sigma$--model are constructed. We calculate the corresponding contribution to the spin--spin correlation function, and compare with predictions from the spectral density scaling hypothesis. The resulting approximation to the spin--spin correlation function agrees well with that computed in renormalized (asymptotically free) perturbation theory in the expected energy range. Further we observe simple lower and upper bounds for the sum of the absolute square of the form factors which may be of use for analytic estimates.Comment: 14 pages, 3 figures, late

An exact solution of the Currie-Hill equations in 1 + 1 dimensional Minkowski space

We present an exact two-particle solution of the Currie-Hill equations of Predictive Relativistic Mechanics in $1 + 1$ dimensional Minkowski space. The instantaneous accelerations are given in terms of elementary functions depending on the relative particle position and velocities. The general solution of the equations of motion is given and by studying the global phase space of this system it is shown that this is a subspace of the full kinematic phase space.Comment: 13 pages, LaTeX. arXiv admin note: text overlap with arXiv:1402.699

Illusionism's discontent

Frankish positions his view, illusionism about qualia (a.k.a. eliminativist physicalism), in opposition to what he calls radical realism (dualism and neutral monism) and conservative realism (a.k.a. non-eliminativist physicalism). Against radical realism, he upholds physicalism. But he goes along with key premises of the Gap Arguments for radical realism, namely, 1) that epistemic/explanatory gaps exist between the physical and the phenomenal, and 2) that every truth should be perspicuously explicable from the fundamental truth about the world; and he concludes that because physicalism is true, there could be no phenomenal truths, and no qualia. I think he is wrong to accept 2); and even if he was right to accept it, the more plausible response would be not to deny the existence of qualia but to deny physicalism. In either case, denying the existence of qualia is the wrong answer. I present a physicalist realist alterative that refutes premise 2 of the Gap Argument; I also make a general case against the scientism that accompanies Frankish’s metaphysics

Structure functions of the 2d O(n) non-linear sigma models

We investigate structure functions in the 2-dimensional (asymptotically free) non-linear O(n) sigma-models using the non-perturbative S-matrix bootstrap program. In particular the exact small (Bjorken) x behavior is derived. Structure functions in the special case of the n=3 model are accurately computed over the whole x range for $-q^2/M^2<10^5$, and some moments are compared with results from renormalized perturbation theory. Some results concerning the structure functions in the 1/n approximation are also presented.Comment: 57 pages, 5 figures, 3 table

Inhomogeneities on all scales at a phase transition altered by disorder

We have done a finite-size scaling study of a continuous phase transition altered by the quenched bond disorder, investigating systems at quasicritical temperatures of each disorder realization by using the equilibriumlike invaded cluster algorithm. Our results indicate that in order to access the thermal critical exponent $y_\tau$, it is necessary to average the free energy at quasicritical temperatures of each disorder configuration. Despite the thermal fluctuations on the scale of the system at the transition point, we find that spatial inhomogeneities form in the system and become more pronounced as the size of the system increases. This leads to different exponents describing rescaling of the fluctuations of observables in disorder and thermodynamic ensembles.Comment: 11 pages, 4 figure

Two-particle wave function in four dimensional Ising model

An exploratory study of two-particle wave function is carried out with a four dimensional simple model. The wave functions not only for two-particle ground and first excited states but also for an unstable state are calculated from three- and four-point functions using the diagonalization method suggested by L\"uscher and Wolff. The scattering phase shift is evaluated from these wave functions.Comment: Poster presented at Lattice2004(spectrum), Fermilab, June 21-26, 200

W-Algebra Symmetries of Generalised Drinfel'd-Sokolov Hierarchies

Using the zero-curvature formulation, it is shown that W-algebra transformations are symmetries of corresponding generalised Drinfel'd-Sokolov hierarchies. This result is illustrated with the examples of the KdV and Boussinesque hierarchies, and the hierarchy associated to the Polyakov-Bershadsky W-algebra.Comment: 13 page