Diagonalization of multicomponent wave equations with a Born-Oppenheimer example

A general method to decouple multicomponent linear wave equations is presented. First, the Weyl calculus is used to transform operator relations into relations between c-number valued matrices. Then it is shown that the symbol representing the wave operator can be diagonalized systematically up to arbitrary order in an appropriate expansion parameter. After transforming the symbols back to operators, the original problem is reduced to solving a set of linear uncoupled scalar wave equations. The procedure is exemplified for a particle with a Born-Oppenheimer-type Hamiltonian valid through second order in h. The resulting effective scalar Hamiltonians are seen to contain an additional velocity-dependent potential. This contribution has not been reported in recent studies investigating the adiabatic motion of a neutral particle moving in an inhomogeneous magnetic field. Finally, the relation of the general method to standard quantum-mechanical perturbation theory is discussed

From sensorimotor dependencies to perceptual practices: making enactivism social

Proponents of enactivism should be interested in exploring what notion of action best captures the type of action-perception link that the view proposes, such that it covers all the aspects in which our doings constitute and are constituted by our perceiving. This article proposes and defends the thesis that the notion of sensorimotor dependencies is insufficient to account for the reality of human perception, and that the central enactive notion should be that of perceptual practices. Sensorimotor enactivism is insufficient because it has no traction on socially dependent perceptions, which are essential to the role and significance of perception in our lives. Since the social dimension is a central desideratum in a theory of human perception, enactivism needs a notion that accounts for such an aspect. This article sketches the main features of the Wittgenstein-inspired notion of perceptual practices as the central notion to understand perception. Perception, I claim, is properly understood as woven into a type of social practices that includes food, dance, dress, music, etc. More specifically, perceptual practices are the enactment of culturally structured, normatively rich techniques of commerce of meaningful multi- and inter-modal perceptible material. I argue that perceptual practices explain three central features of socially dependent perception: attentional focus, aspects’ saliency, and modal-specific harmony-like relations

Analytical theory for the initial mass function: III time dependence and star formation rate

The present paper extends our previous theory of the stellar initial mass function (IMF) by including the time-dependence, and by including the impact of magnetic field. The predicted mass spectra are similar to the time independent ones with slightly shallower slopes at large masses and peak locations shifted toward smaller masses by a factor of a few. Assuming that star-forming clumps follow Larson type relations, we obtain core mass functions in good agreement with the observationally derived IMF, in particular when taking into account the thermodynamics of the gas. The time-dependent theory directly yields an analytical expression for the star formation rate (SFR) at cloud scales. The SFR values agree well with the observational determinations of various Galactic molecular clouds. Furthermore, we show that the SFR does not simply depend linearly on density, as sometimes claimed in the literature, but depends also strongly on the clump mass/size, which yields the observed scatter. We stress, however, that {\it any} SFR theory depends, explicitly or implicitly, on very uncertain assumptions like clump boundaries or the mass of the most massive stars that can form in a given clump, making the final determinations uncertain by a factor of a few. Finally, we derive a fully time-dependent model for the IMF by considering a clump, or a distribution of clumps accreting at a constant rate and thus whose physical properties evolve with time. In spite of its simplicity, this model reproduces reasonably well various features observed in numerical simulations of converging flows. Based on this general theory, we present a paradigm for star formation and the IMF.Comment: accepted for publication in Ap

On supergravity solutions of space-like Dp-branes

Recently the time dependent solutions of type II supergravities in $d = 10$, with the metric having the symmetry $ISO(p+1) \times SO(8-p, 1)$ have been given by two groups (Chen-Gal'tsov-Gutperle (CGG), [hep-th/0204071] and Kruczenski-Myers-Peet (KMP), [hep-th/0204144]). The supergravity solutions correspond to space-like D$p$-branes in type II string theory. While the CGG solution is a four parameter solution, the KMP solution is a three parameter solution and so in general they are different. This difference can be attributed to the fact that unlike the CGG solution, KMP uses a specific boundary condition for the metric and the dilaton field. It is shown that when we impose the boundary conditions used in the KMP solution to the CGG solution then both become three parameter solutions and they map to each other under a coordinate transformation along with a Hodge duality of the field strength. We also give the relations between the parameters characterizing the two solutions.Comment: 14 pages, LaTeX, v2: minor corrections and a reference adde

Survey of Two-Time Physics

Two-time physics (2T) is a general reformulation of one-time physics (1T) that displays previously unnoticed hidden symmetries in 1T dynamical systems and establishes previously unknown duality type relations among them. This may play a role in displaying the symmetries and constructing the dynamics of little understood systems, such as M-theory. 2T physics describes various 1T dynamical systems as different d-dimensional ``holographic'' views of the same 2T system in $d+2$ dimensions. The ``holography'' is due to gauge symmetries that tend to reduce the number of effective dimensions. Different 1T evolutions (i.e. different Hamiltonians) emerge from the same 2T theory when gauge fixing is done with different embeddings of d dimensions inside d+2 dimensions. Thus, in the 2T setting, the distinguished 1T which we call ``time'' is a gauge dependent concept. The 2T action has also a global SO(d,2) symmetry in flat spacetime, or a more general d+2 symmetry in curved spacetime, under which all dimensions are on an equal footing. This symmetry is observable in many 1T systems, but it remained unknown until discovered in the 2T formalism. 2T physics has mainly been developed in the context of particles, including spin and supersymmetry, but some advances have also been made with strings and p-branes, and insights for M-theory have already emerged. In the case of particles, there exists a general worldline formulation with background fields, as well as a field theory formulation, both described in terms of fields that depend on d+2 coordinates. The Standard Model of particle physics can be regarded as a gauge fixed form of a 2T theory in 4+2 dimensions. These facts already provide evidence for a new type of higher dimensional unification.Comment: Latex, 22 pages, 1 figur