A derivation of the Jacobi identity in classical mechanics.
Jacobi identity in classical mechanics
Epstein, S. T.↗
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Supersymmetry and the celestial Jacobi identity
In this paper we study the simplifying effects of supersymmetry on celestial OPEs at both tree and loop level. We find at tree level that theories with unbroken supersymmetry around a stable vacuum have celestial soft current algebras satisfying the Jacobi identity, and we show at one loop that celestial OPEs in these theories have no double poles.
Supersymmetric Gauge Theory↗
Deformed $w_{1+\infty}$ Algebras in the Celestial CFT
We compute the modification of the w 1+∞ algebra of soft graviton, gluon and scalar currents in the celestial CFT due to non-minimal couplings. We find that the Jacobi identity is satisfied only when the spectrum and couplings of the theory obey certain constraints. We comment on the similarities and essential differences of this algebra to W 1+∞ .
97 MATHEMATICS AND COMPUTING↗
Multicollinear singularities in celestial CFT
The purpose of this paper is to study the holomorphic multicollinear limit of (celestial) amplitudes and use it to further investigate the double residue condition for (hard celestial) amplitudes and the celestial operator product expansion. We first set up the notion of holomorphic multicollinear limits of amplitudes and derive the 3-collinear splitting functions for Yang-Mills theory, Einstein gravity, and massless ϕ 3 theory. In particular, we find that in ϕ 3 theory the celestial 3-OPE contains a term with a branch cut. This explicit example confirms that branch cuts can obstruct the double residue condition for hard celestial amplitudes, which is the underlying cause of the celestial Jacobi identities not holding for certain theories. This addresses an ongoing debate in the literature about associativity of the celestial OPEs and concretely demonstrates a new (multi-particle) term in the celestial OPE coming from the multi-particle channel in the amplitudes.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
On effective field theories with celestial duals
We show that associativity of the tree-level OPE in a celestial CFT imposes constraints on the coupling constants of the corresponding bulk theory. These constraints are the same as those derived in [9] from the Jacobi identity of the algebra of soft modes. The constrained theories are interesting as apparently well-defined celestial CFTs with a deformed w 1+∞ symmetry algebra. We explicitly work out the ramifications of these constraints on scattering amplitudes involving gluons, gravitons and scalars in these theories. We find that all four-point amplitudes constructible solely from holomorphic or anti-holomorphic three-point amplitudes vanish on the support of these constraints, which implies that all purely holomorphic or purely anti-holomorphic higher-point amplitudes vanish.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Next-to-$\mathrm{MHV}$ Yang-Mills kinematic algebra
Kinematic numerators of Yang-Mills scattering amplitudes possess a rich Lie algebraic structure that suggest the existence of a hidden infinite-dimensional kinematic algebra. Explicitly realizing such a kinematic algebra is a longstanding open problem that only has had partial success for simple helicity sectors. In past work, we introduced a framework using tensor currents and fusion rules to generate BCJ numerators of a special subsector of NMHV amplitudes in Yang-Mills theory. Here we enlarge the scope and explicitly realize a kinematic algebra for all NMHV amplitudes. Master numerators are obtained directly from the algebraic rules and through commutators and kinematic Jacobi identities other numerators can be generated. Inspecting the output of the algebra, we conjecture a closed-form expression for the master BCJ numerator up to any multiplicity. We also introduce a new method, based on group algebra of the permutation group, to solve for the generalized gauge freedom of BCJ numerators. It uses the recently introduced binary BCJ relations to provide a complete set of NMHV kinematic numerators that consist of pure gauge.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
The topology of the regularized integral surfaces of the 3-body problem.
A method is described by which the integral surface can be modified in such a way that Newton's equations of motion actually give a flow. The process of regularization of vector fields by surgery, as described by the author (1971) is reviewed. The planar 3-body problem and its regularization, and the topology of the integral surfaces are considered. The Lagrange-Jacobi identity is used to show that there exists an isolating block such that any orbit which ends in a triple collision must enter and remain in this block.
Easton, R.↗
Conformal invariance and Hamilton Jacobi theory for dissipative systems
For certain dissipative systems, a comparison can be made between the Hamilton-Jacobi theory and the conformal invariance of action theory. The two concepts are not identical, but the conformal action theory covers the Hamilton-Jacobi theory.
Kiehn, R. M.↗
Ellipsoidal figures of equilibrium - Compressible models
The results of Chandrasekhar (1969) are generalized to polytropes, using a formalism based on ellipsoidal energy variational principle to construct approximate stellar equilibrium solutions and study their stability. After reviewing the energy variational method and describing the approach, several equivalent stability conditions are established and secular vs. dynamical instabilities are discussed. Then, the equilibrium structure equations are derived for isolated, rotating polytropes, and axisymmetric configurations (compressible Maclaurin spheroids) are considered. Particular attention is given to triaxial configurations, either in a state of uniform rotation (generalizing the classical Jacobi ellipsoids) or with internal fluid motions of uniform vorticity (the compressible analogues of Riemann-S ellipsoids) and to the stability of these single star configurations. The compressible generalizations of the Roche and Roche-Riemann problems for a polytrope in orbit about a point-mass companion are solved, and the generalized Darwin problem for two identical polytropes in a binary is considered.
Lai, Dong↗
A high-fidelity residential building occupancy detection dataset
Abstract This paper describes development of a data acquisition system used to capture a range of occupancy related modalities from single-family residences, along with the dataset that was generated. The publicly available dataset includes: grayscale images at 32-by-32 pixels, captured every second; audio files, which have undergone processing to remove personally identifiable information; indoor environmental readings, captured every ten seconds; and ground truth binary occupancy status. The data acquisition system, coined the mobile human presence detection (HPDmobile) system, was deployed in six homes for a minimum duration of one month each, and captured all modalities from at least four different locations concurrently inside each home. The environmental modalities are available as captured, but to preserve the privacy and identity of the occupants, images were downsized and audio files went through a series of processing steps, as described in this paper. This dataset adds to a very small body of existing data, with applications to energy efficiency and indoor environmental quality.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
The nova rate in the elliptical component of NGC 5128
The results are presented of a five year nova survey of NGC 5128 performed with an H-alpha filter at the prime focus of the CTIO 4 m telescope. In all, 16 novae were detected, of which 12 are members of a statistically complete and homogeneous sample unaffected by the absorption lane of the galaxy. When normalized to B luminosity, the nova rate in the elliptical component of NGC 5128 is 2.7 + or - 1.0 times less than that observed in the bulge of M31. However, when normalized in the infrared K bandpass, the two nova rates are identical, and comparable to that measured in the Large Magellanic Cloud. These data suggest that (1) the percentage of binary stars is approximately constant over a large range of star-forming environments, (2) the nova rate in our own galaxy is between 11 and 46/yr, and (3) nova rates are not strongly affected by tidal captures in bright globular clusters.
Ciardullo, Robin↗
Simulation fidelity of a virtual environment display
We assessed the degree to which a virtual environment system produced a faithful simulation of three-dimensional space by investigating the influence of a pitched optic array on the perception of gravity-referenced eye level (GREL). We compared the results with those obtained in a physical environment. In a within-subjects factorial design, 12 subjects indicated GREL while viewing virtual three-dimensional arrays at different static orientations. A physical array biased GREL more than did a geometrically identical virtual pitched array. However, addition of two sets of orthogonal parallel lines (a grid) to the virtual pitched array resulted in as large a bias as that obtained with the physical pitched array. The increased bias was caused by longitudinal, but not the transverse, components of the grid. We discuss implications of our results for spatial orientation models and for designs of virtual displays.
Nemire, Kenneth↗