Supersymmetry algebra in N = 1 chiral supergravity

We consider the supersymmetry (SUSY) transformations in the chiral Lagrangian for $N = 1$ supergravity (SUGRA) with the complex tetrad following the method used in the usual $N = 1$ SUGRA, and present the explicit form of the SUSY trasformations in the first-order form. The SUSY transformations are generated by two independent Majorana spinor parameters, which are apparently different from the constrained parameters employed in the method of the 2-form gravity. We also calculate the commutator algebra of the SUSY transformations on-shell.Comment: 10 pages, late

Anisotropy of Doppler spectral parameters in the VHF radar observations at MU and White Sands

International audienceSignificant differences are found between the mean spectral widths from beams in the meridional plane and in the zonal plane at both the MU and the White Sands VHF radars. The spectral width in the beam directed perpendicular to the prevailing wind is greater than that in the beam parallel to the wind. The magnitudes of the differences in spectral width show a linear relationship with wind speed, with the greatest differences at the greatest wind speeds. The differences in spectral width show a positive correlation with the differences in backscattered power. The anisotropy in backscattered power is well-known and is usually attributed to aspect sensitivity effects. However, the anisotropy in spectral width does not appear to be due to the same mechanism, and while several hypotheses to account for this are considered, including finite range-volume effects, effects from the tilting of isentropic layers, and anisotropic turbulence effects, it is seen that each of these suggestions has its shortcomings

On Einstein-Hilbert type action of superon-graviton model(SGM)

The fundamental action of superon-graviton model(SGM) of Einstein-Hilbert type for space-time and matter is written down explicitly in terms of the fields of the graviton and superons by using the affine connection formalism and the spin connection formalism. Some characteristic structures including some hidden symmetries of the gravitational coupling of superons are manifested (in two dimensional space-time) with some details of the calculations. SGM cosmology is discussed briefly.Comment: 20 pages, Latex, some more discussions and new references adde

On confined fractional charges: a simple model

We address the question whether features known from quantum chromodynamics (QCD) can possibly also show up in solid-state physics. It is shown that spinless fermions of charge $e$ on a checkerboard lattice with nearest-neighbor repulsion provide for a simple model of confined fractional charges. After defining a proper vacuum the system supports excitations with charges $\pm e/2$ attached to the ends of strings. There is a constant confining force acting between the fractional charges. It results from a reduction of vacuum fluctuations and a polarization of the vacuum in the vicinity of the connecting strings.Comment: 5 pages, 3 figure

Canonical formulation of N = 2 supergravity in terms of the Ashtekar variable

We reconstruct the Ashtekar's canonical formulation of N = 2 supergravity (SUGRA) starting from the N = 2 chiral Lagrangian derived by closely following the method employed in the usual SUGRA. In order to get the full graded algebra of the Gauss, U(1) gauge and right-handed supersymmetry (SUSY) constraints, we extend the internal, global O(2) invariance to local one by introducing a cosmological constant to the chiral Lagrangian. The resultant Lagrangian does not contain any auxiliary fields in contrast with the 2-form SUGRA and the SUSY transformation parameters are not constrained at all. We derive the canonical formulation of the N = 2 theory in such a manner as the relation with the usual SUGRA be explicit at least in classical level, and show that the algebra of the Gauss, U(1) gauge and right-handed SUSY constraints form the graded algebra, G^2SU(2)(Osp(2,2)). Furthermore, we introduce the graded variables associated with the G^2SU(2)(Osp(2,2)) algebra and we rewrite the canonical constraints in a simple form in terms of these variables. We quantize the theory in the graded-connection representation and discuss the solutions of quantum constraints.Comment: 19 pages, Latex, corrected some typos and added a referenc

N = 3 chiral supergravity compatible with the reality condition and higher N chiral Lagrangian density

We obtain N = 3 chiral supergravity (SUGRA) compatible with the reality condition by applying the prescription of constructing the chiral Lagrangian density from the usual SUGRA. The $N = 3$ chiral Lagrangian density in first-order form, which leads to the Ashtekar's canonical formulation, is determined so that it reproduces the second-order Lagrangian density of the usual SUGRA especially by adding appropriate four-fermion contact terms. We show that the four-fermion contact terms added in the first-order chiral Lagrangian density are the non-minimal terms required from the invariance under first-order supersymmetry transformations. We also discuss the case of higher N theories, especially for N = 4 and N = 8.Comment: 20 pages, Latex, some more discussions and new references added, some typos corrected, accepted for publication in Physical Review

Non-resonant inelastic x-ray scattering involving excitonic excitations

In a recent publication Larson \textit{et al.} reported remarkably clear $d$-$d$ excitations for NiO and CoO measured with x-ray energies well below the transition metal $K$ edge. In this letter we demonstrate that we can obtain an accurate quantitative description based on a local many body approach. We find that the magnitude of $\vec{q}$ can be tuned for maximum sensitivity for dipole, quadrupole, etc. excitations. We also find that the direction of $\vec{q}$ with respect to the crystal axes can be used as an equivalent to polarization similar to electron energy loss spectroscopy, allowing for a determination of the local symmetry of the initial and final state based on selection rules. This method is more generally applicable and combined with the high resolution available, could be a powerful tool for the study of local distortions and symmetries in transition metal compounds including also buried interfaces

Minimal Off-Shell Version of N = 1 Chiral Supergravity

We construct the minimal off-shell formulation of N = 1 chiral supergravity (SUGRA) introducing a complex antisymmetric tensor field $B_{\mu \nu}$ and a complex axial-vector field $A_{\mu}$ as auxiliary fields. The resulting algebra of the right- and left-handed supersymmetry (SUSY) transformations closes off shell and generates chiral gauge transforamtions and vector gauge transformations in addition to the transformations which appear in the case without auxiliary fields.Comment: 9 pages, late

Episodic Visual Hallucinations, Inference and Free Energy

\ua9 2024 by the authors. Understandings of how visual hallucinations appear have been highly influenced by generative approaches, in particular Friston’s Active Inference conceptualization. Their core proposition is that these phenomena occur when hallucinatory expectations outweigh actual sensory data. This imbalance occurs as the brain seeks to minimize informational free energy, a measure of the distance between predicted and actual sensory data in a stationary open system. We review this approach in the light of old and new information on the role of environmental factors in episodic hallucinations. In particular, we highlight the possible relationship of specific visual triggers to the onset and offset of some episodes. We use an analogy from phase transitions in physics to explore factors which might account for intermittent shifts between veridical and hallucinatory vision. In these triggered forms of hallucinations, we suggest that there is a transient disturbance in the normal one-to-one correspondence between a real object and the counterpart perception such that this correspondence becomes between the real object and a hallucination. Generative models propose that a lack of information transfer from the environment to the brain is one of the key features of hallucinations. In contrast, we submit that specific information transfer is required at onset and offset in these cases. We propose that this transient one-to-one correspondence between environment and hallucination is mediated more by aberrant discriminative than by generative inference. Discriminative inference can be conceptualized as a process for maximizing shared information between the environment and perception within a self-organizing nonstationary system. We suggest that generative inference plays the greater role in established hallucinations and in the persistence of individual hallucinatory episodes. We further explore whether thermodynamic free energy may be an additional factor in why hallucinations are temporary. Future empirical research could productively concentrate on three areas. Firstly, subjective perceptual changes and parallel variations in brain function during specific transitions between veridical and hallucinatory vision to inform models of how episodes occur. Secondly, systematic investigation of the links between environment and hallucination episodes to probe the role of information transfer in triggering transitions between veridical and hallucinatory vision. Finally, changes in hallucinatory episodes over time to elucidate the role of learning on phenomenology. These empirical data will allow the potential roles of different forms of inference in the stages of hallucinatory episodes to be elucidated