Electric-Magnetic Dualities in Non-Abelian and Non-Commutative Gauge Theories

Electric-magnetic dualities are equivalence between strong and weak coupling constants. A standard example is the exchange of electric and magnetic fields in an abelian gauge theory. We show three methods to perform electric-magnetic dualities in the case of the non-commutative $U(1)$ gauge theory. The first method is to use covariant field strengths to be the electric and magnetic fields. We find an invariant form of an equation of motion after performing the electric-magnetic duality. The second method is to use the Seiberg-Witten map to rewrite the non-commutative $U(1)$ gauge theory in terms of abelian field strength. The third method is to use the large Neveu Schwarz-Neveu Schwarz (NS-NS) background limit (non-commutativity parameter only has one degree of freedom) to consider the non-commutative $U(1)$ gauge theory or D3-brane. In this limit, we introduce or dualize a new one-form gauge potential to get a D3-brane in a large Ramond-Ramond (R-R) background via field redefinition. We also use perturbation to study the equivalence between two D3-brane theories. Comparison of these methods in the non-commutative $U(1)$ gauge theory gives different physical implications. The comparison reflects the differences between the non-abelian and non-commutative gauge theories in the electric-magnetic dualities. For a complete study, we also extend our studies to the simplest abelian and non-abelian $p$-form gauge theories, and a non-commutative theory with the non-abelian structure.Comment: 55 pages, minor changes, references adde

Dimensional Reduction of the Generalized DBI

We study the generalized Dirac-Born-Infeld (DBI) action, which describes a $q$-brane ending on a $p$-brane with a ($q$+1)-form background. This action has the equivalent descriptions in commutative and non-commutative settings, which can be shown from the generalized metric and Nambu-Sigma model. We mainly discuss the dimensional reduction of the generalized DBI at the massless level on the flat spacetime and constant antisymmetric background in the case of flat spacetime, constant antisymmetric background and the gauge potential vanishes for all time-like components. In the case of $q=2$, we can do the dimensional reduction to get the DBI theory. We also try to extend this theory by including a one-form gauge potential.Comment: 29 pages, minor change

Ethyl 3-{[(3-methyl­anilino)(1H-1,2,4-triazol-1-yl)methyl­idene]amino}-1-benzofuran-2-carboxyl­ate

The crystal structure of the title compound, C21H19N5O3, is stabilized by inter­molecular N—H⋯N and C—H⋯O hydrogen bonds. The mol­ecule contains a planar [maximum deviations = −0.026 (1) and 0.027 (2) Å] benzofuran ring system, which forms dihedral angles of 78.75 (8) and 39.78 (7)° with the benzene and triazole rings, respectively

6-Allyl-3-(6-chloro-3-pyridylmeth­yl)-6,7-dihydro-3H-1,2,3-triazolo[4,5-d]pyrimidin-7-imine

The title compound, C13H12ClN7, crystallizes with two independent mol­ecules in the asymmetric unit, each with similar geometries. The dihedral angles between the triazole and pyrimidine rings are 0.45 (9) and 1.00 (10)° in the two mol­ecules. A number of N—H⋯N hydrogen bonds co-operate with C–H⋯N contacts, forming a supra­molecular array in the ab plane. C—H⋯π inter­actions are also present. One of the vinyl groups was found to be disordered so that the C(H)=CH2 atoms were resolved over two positions with the major component having a site occupancy factor of 0.539 (4)

3-Benzyl-6-isopropyl-5-phen­oxy-3H-1,2,3-triazolo[4,5-d]pyrimidin-7(6H)-one

In the title compound, C20H19N5O2, all atoms of the 1,2,3-triazolo[4,5-d]pyrimidine ring system are essentially coplanar [maximum deviation = 0.015 (2) Å], indicating the existence of a conjugate system in which each carbon and nitrogen atom is sp 2 hybridized and ten π electrons (three from carbon atoms and seven from nitrogen atoms) constitute an aromatic heterocycle. The ring system forms dihedral angles of 68.37 (10) and 71.57 (9)° with the phenyl rings. The crystal packing is stabilized by van der Waals inter­actions and intermolecular C—H⋯π interactions

Integrated Behavior Planning and Motion Control for Autonomous Vehicles with Traffic Rules Compliance

In this article, we propose an optimization-based integrated behavior planning and motion control scheme, which is an interpretable and adaptable urban autonomous driving solution that complies with complex traffic rules while ensuring driving safety. Inherently, to ensure compliance with traffic rules, an innovative design of potential functions (PFs) is presented to characterize various traffic rules related to traffic lights, traversable and non-traversable traffic line markings, etc. These PFs are further incorporated as part of the model predictive control (MPC) formulation. In this sense, high-level behavior planning is attained implicitly along with motion control as an integrated architecture, facilitating flexible maneuvers with safety guarantees. Due to the well-designed objective function of the MPC scheme, our integrated behavior planning and motion control scheme is competent for various urban driving scenarios and able to generate versatile behaviors, such as overtaking with adaptive cruise control, turning in the intersection, and merging in and out of the roundabout. As demonstrated from a series of simulations with challenging scenarios in CARLA, it is noteworthy that the proposed framework admits real-time performance and high generalizability.Comment: 7 pages, 5 figures, accepted for publication in The 2023 IEEE International Conference on Robotics and Biomimetics (ROBIO

3D Theory of Microscopic Instabilities Driven by Space-Charge Forces

Microscopic, or short-wavelength, instabilities are known for drastic reduction of the beam quality and strong amplification of the noise in a beam. Space charge and coherent synchrotron radiation are known to be the leading causes for such instabilities. In this paper we present rigorous 3D theory of such instabilities driven by the space-charge forces. We define the condition when our theory is applicable for an arbitrary accelerator system with 3D coupling. Finally, we derive a linear integral equation describing such instability and identify conditions when it can be reduced to an ordinary second order differential equation.Comment: 38 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:2101.0410