Renormalizability of generalized quantum electrodynamics

In this work we present the study of the renormalizability of the Generalized Quantum Electrodynamics ($GQED_{4}$). We begin the article by reviewing the on-shell renormalization scheme applied to $GQED_{4}$. Thereafter, we calculate the explicit expressions for all the counter-terms at one-loop approximation and discuss the infrared behavior of the theory as well. Next, we explore some properties of the effective coupling of the theory which would give an indictment of the validity regime of theory: $m^{2} \leq k^{2} < m_{P}^{2}$. Afterwards, we make use of experimental data from the electron anomalous magnetic moment to set possible values for the theory free parameter through the one-loop contribution of Podolsky mass-dependent term to Pauli's form factor $F_{2}(q^{2})$.Comment: 9 page

Semiclassical theory for small displacements

Characteristic functions contain complete information about all the moments of a classical distribution and the same holds for the Fourier transform of the Wigner function: a quantum characteristic function, or the chord function. However, knowledge of a finite number of moments does not allow for accurate determination of the chord function. For pure states this provides the overlap of the state with all its possible rigid translations (or displacements). We here present a semiclassical approximation of the chord function for large Bohr-quantized states, which is accurate right up to a caustic, beyond which the chord function becomes evanescent. It is verified to pick out blind spots, which are displacements for zero overlaps. These occur even for translations within a Planck area of the origin. We derive a simple approximation for the closest blind spots, depending on the Schroedinger covariance matrix, which is verified for Bohr-quantized states.Comment: 16 pages, 4 figures

Local quantum ergodic conjecture

The Quantum Ergodic Conjecture equates the Wigner function for a typical eigenstate of a classically chaotic Hamiltonian with a delta-function on the energy shell. This ensures the evaluation of classical ergodic expectations of simple observables, in agreement with Shnirelman's theorem, but this putative Wigner function violates several important requirements. Consequently, we transfer the conjecture to the Fourier transform of the Wigner function, that is, the chord function. We show that all the relevant consequences of the usual conjecture require only information contained within a small (Planck) volume around the origin of the phase space of chords: translations in ordinary phase space. Loci of complete orthogonality between a given eigenstate and its nearby translation are quite elusive for the Wigner function, but our local conjecture stipulates that their pattern should be universal for ergodic eigenstates of the same Hamiltonian lying within a classically narrow energy range. Our findings are supported by numerical evidence in a Hamiltonian exhibiting soft chaos. Heavily scarred eigenstates are remarkable counter-examples of the ergodic universal pattern.Comment: 4 figure

Will Oakland Burn Again: Understanding the Fire Hazard in an Urban Park System

Though almost thirty years have passed since the 1991 Tunnel Fire, the wildfire hazard is still present in the Oakland Hills. This study was conducted to determine if the vegetation in the Oakland Hills had reverted back to fuel conditions that contributed to the Tunnel Fire, examine how the fire hazard has changed since 1991, and evaluate planned wildfire mitigation. The goal was to determine how fuel conditions have changed since 1991 and compare potential fire behavior to that of the Tunnel Fire. Additionally, the study examined the effectiveness of the mitigation actions described in the East Bay Regional Park District’s Wildfire Hazard Reduction and Resource Management Plan on lowering extreme fire behavior. Through the use of remote sensing, historical aerial imagery, satellite imagery, and Landsat imagery the 1991 and 2018 fuel conditions were analyzed. ArcGIS Pro and FlamMap 6 were used to compare hectares of fuel and changed in fire behavior between the two year. Mitigation actions were modeled with FlamMap 6 and ArcGIS Pro and fire behavior was compared between untreated conditions and post treatment conditions. The vegetation in the Oakland Hills, in the absence of fire, returned to a mature state, similar to the 1991 conditions. However, there was a reduction in the overall hectares of fuel model 147 in 2018. Modeled fire behavior indicated an overall reduction in extreme fire behavior when comparing 1991 to 2018. This reduction varied on a park level with each park performing differently. When modeled, mitigation was able to lower extreme fire behavior across the landscape but success varied on an individual park basis. In conclusion, should ignition occur presently, under foehn wind conditions, a fire would still exhibit very extreme behavior with a high potential for catastrophic loss, and implantation of planned mitigation measures may be able to lower the degree of extreme fire behavior

The canonical structure of Podolsky's generalized electrodynamics on the Null-Plane

In this work we will develop the canonical structure of Podolsky's generalized electrodynamics on the null-plane. This theory has second-order derivatives in the Lagrangian function and requires a closer study for the definition of the momenta and canonical Hamiltonian of the system. On the null-plane the field equations also demand a different analysis of the initial-boundary value problem and proper conditions must be chosen on the null-planes. We will show that the constraint structure, based on Dirac formalism, presents a set of second-class constraints, which are exclusive of the analysis on the null-plane, and an expected set of first-class constraints that are generators of a U(1) group of gauge transformations. An inspection on the field equations will lead us to the generalized radiation gauge on the null-plane, and Dirac Brackets will be introduced considering the problem of uniqueness of these brackets under the chosen initial-boundary condition of the theory

Are stealth scalar fields stable?

Non-gravitating (stealth) scalar fields associated with Minkowski space in scalar-tensor gravity are examined. Analytical solutions for both non-minimally coupled scalar field theory and for Brans-Dicke gravity are studied and their stability with respect to tensor perturbations is assessed using a covariant and gauge-invariant formalism developed for alternative gravity. For Brans-Dicke solutions, the stability with respect to homogeneous perturbations is also studied. There are regions of parameter space corresponding to stability and other regions corresponding to instability.Comment: 10 pages, 1 table, no figures, to appear in Phys. Rev,