Narrow Results

The triangle anomaly in massless and massive QED is investigated by adopting the symmetry-preserving loop regularization method proposed recently in Refs. 1 and 2. The method is realized in the initial dimension of theory without modifying the original Lagrangian, it preserves symmetries under non-Abelian gauge and Poincaré transformations in spite of the existence of two intrinsic mass scales M_c and μ_s which actually play the roles of UV- and IR-cutoff respectively. The axial-vector–vector-vector (AVV) triangle diagrams in massless and massive QED are evaluated explicitly by using the loop regularization. It is shown that when the momentum k of external state is soft with , m² (m is the mass of loop fermions) and M_c → ∞, both massless and massive QED become anomaly free. The triangle anomaly is found to appear as quantum corrections in the case that m², and M_c → ∞. Especially, it is justified that in the massless QED with μ_s = 0 and M_c → ∞, the triangle anomaly naturally exists as quantum effects in the axial-vector current when the ambiguity caused by the trace of gamma matrices with γ₅ is eliminated by simply using the definition of γ₅. It is explicitly demonstrated how the Ward identity anomaly of currents depends on the treatment for the trace of gamma matrices, which enables us to make a clarification whether the ambiguity of triangle anomaly is caused by the regularization scheme in the perturbation calculations or by the trace of gamma matrices with γ₅. For comparison, an explicit calculation based on the Pauli–Villars regularization and dimensional regularization is carried out and the possible ambiguities of Ward identity anomalies caused from these two regularization schemes are carefully discussed, which include the ambiguities induced by the treatment of the trace of gamma matrices with γ₅ and the action of the external momentum on the amplitude before the direct calculation of the AVV diagram.

Analysis of flows in crowd videos is a remarkable topic with practical implementations in many different areas. In this paper, we present a wide overview of this topic along with our own approach to this problem. Our approach treats the difficulty of crowd flow analysis by distinguishing single versus multiple flows in a scene. Spatiotemporal features of two consecutive frames are extracted by optical flows to create a three-dimensional tensor, which retains appearance and velocity information. Tensor’s upper left minor matrix captures intensity structure. A normalized continuous rank-increase measure for each frame is calculated by a generalized interlacing property of the eigenvalues of these matrices. In essence, measure values put through the knowledge of existing flows. Yet they do not go into effect desirably due to optical flow estimation error and some other factors. A proper set of the degree of polynomial fitting functions decodes their existence. But how can we estimate that set? Its detailed study is performed. Zero flow, single flow, multiple flows, and interesting events are detected as frame basis using thresholds on the polynomial fitting measure values. Plausible mean outputs of recall rate (88.9%), precision rate (86.7%), area under the receiver operating characteristic curve (98.9%), and accuracy (92.9%) reported from conducted experiments on PETS2009 and UMN benchmark datasets make clear and visible that our method gains high-quality results to detect flows and events in crowd videos in terms of both robustness and potency.

We study the cohomological physics of fivebranes in type II and heterotic string theory. We give an interpretation of the one-loop term in type IIA, which involves the first and second Pontrjagin classes of spacetime, in terms of obstructions to having bundles with certain structure groups. Using a generalization of the Green–Schwarz anomaly cancellation in heterotic string theory which demands the target space to have a String structure, we observe that the "magnetic dual" version of the anomaly cancellation condition can be read as a higher analog of String structure, which we call Fivebrane structure. This involves lifts of orthogonal and unitary structures through higher connected covers which are not just 3- but even 7-connected. We discuss the topological obstructions to the existence of Fivebrane structures. The dual version of the anomaly cancellation points to a relation of string and Fivebrane structures under electric-magnetic duality.

We report a case of Linburg-Comstock syndrome, which is characterized with anomalous tendon slips connecting flexor pollicis longus (FPL) to the flexor digitorum profundus (FDP), usually at the index finger. The present patient started to be a carpenter and was suffering from his disability of flexing the thumb and the index finger independently when he handled the screws in his work. We surgically removed the tendinous connection of the FPL tendon and the index FDP tendon. After surgery, he could work as a carpenter without any difficulty. Surgical disconnection was effective treatment. Dynamic high-resolution ultrasound and three dimensions of computed tomography of the left distal forearm were helpful to confirm the diagnosis.

We explicitly express the spectral determinant of Friedrichs Dirichlet Laplacians on the 2-dimensional hyperbolic (Gaussian curvature -1) cones in terms of the cone angle and the geodesic radius of the boundary.

The universal behavior of Hawking radiation is originated in the conformal symmetries of matter fields near the black hole horizon. We explain the origin of this universality based on (1) the gravitational anomaly and its higher-spin generalizations and (2) conformal transformation properties of fluxes.

The index theorems relate the gauge field and metric on a manifold to the solution of the Dirac equation on it. In the standard approach, the Dirac operator must be massless to make the chirality operator well defined. In physics, however, the index theorem appears as a consequence of chiral anomaly, which is an explicit breaking of the symmetry. It is then natural to ask if we can understand the index theorems in a massive fermion system which does not have chiral symmetry. In this review, we discuss how to reformulate the chiral anomaly and index theorems with massive Dirac operators, where we find nontrivial mathematical relations between massless and massive fermions. A special focus is placed on the Atiyah–Patodi–Singer index, whose original formulation requires a physicist-unfriendly boundary condition, while the corresponding massive domain-wall fermion reformulation does not. The massive formulation provides a natural understanding of the anomaly inflow between the bulk and edge in particle and condensed matter physics.

Based on the path integral formalism, we rederive and extend the transverse Ward–Takahashi identities (which were first derived by Yasushi Takahashi) for the vector and the axial vector currents and simultaneously discuss the possible quantum anomaly for them. Subsequently, we propose a new scheme for writing down and solving the Schwinger–Dyson equation in which the transverse Ward–Takahashi identity together with the usual (longitudinal) Ward–Takahashi identity are applied to specify the fermion–boson vertex function. Within this framework, we give an example of exactly soluble truncated Schwinger–Dyson equation for the fermion propagator in an Abelian gauge theory in arbitrary dimension when the bare fermion mass is zero. It is especially shown that in two dimensions, it becomes the exact and closed Schwinger–Dyson equation which can be exactly solved.

Gauge theory and anomalies which arise under quantization of these theories are formulated using differential geometric methods. The Wess–Zumino conditions are developed and some other relevant geometric properties of anomalies are mentioned. An elementary derivation of the non-Abelian anomaly in 2n dimensions is presented using this formalism.

Lifetime-standing psychosocial effects of congenital hand anomalies are inevitable in patients who have not received a comprehensive treatment with appropriate timing and approach. Herein, two adult cases of untreated thumb polydactyly are presented. Both of them had hands with striking appearance and late consequent psychosocial problems.

We develop a general regulated volume expansion for the volume of a manifold with boundary whose measure is suitably singular along a separating hypersurface. The expansion is shown to have a regulator independent anomaly term and a renormalized volume term given by the primitive of an associated anomaly operator. These results apply to a wide range of structures. We detail applications in the setting of measures derived from a conformally singular metric. In particular, we show that the anomaly generates invariant ($Q$-curvature, transgression)-type pairs for hypersurfaces with boundary. For the special case of anomalies coming from the volume enclosed by a minimal hypersurface ending on the boundary of a Poincaré–Einstein structure, this result recovers Branson’s $Q$-curvature and corresponding transgression. When the singular metric solves a boundary version of the constant scalar curvature Yamabe problem, the anomaly gives generalized Willmore energy functionals for hypersurfaces with boundary. Our approach yields computational algorithms for all the above quantities, and we give explicit results for surfaces embedded in 3-manifolds.