Narrow Results

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.

A 16-year-old girl complains that she has yet to experience menstruation.

• Is this abnormal?
• What produces menstruation?
• What conditions may explain her complaint?
• What investigations should be performed on her?

The onset of puberty in girls is marked by the beginning of ovarian function in estrogen secretion followed by physical development of breast buds detectable as firm nodules directly beneath the nipples. This occurs between the ages of 10 and 11.5 years old and is known as thelarche. The first menstruation, or menarche, should occur within three years of thelarche. The mean age of menarche is 12.5 years old. Fewer than 10% of girls menstruate before 11 years old and 90% of girls are menstruating by 13.7 years old. Absence of menarche three years after thelarche or after 16 years old is an abnormal delay known as primary amenorrhea. The incidence of primary amenorrhea is less than 1%.

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 explore the connection between the distribution of particles spontaneously produced from an electric field or black hole and the vacuum persistence, twice the imaginary part of the one-loop effective action. Employing the reconstruction conjecture, we find the effective action for the Bose-Einstein or Fermi-Dirac distribution. The Schwinger effect in AdS₂ is computed via the phase-integral method in the static coordinates. The Hawking radiation and Schwinger effect of a charged black hole is rederived and interpreted via the phase-integral. Finally, we discuss the relation between the vacuum persistence and the trace or gravitational anomalies.

This paper introduces an efficient and scalable cloud-based privacy preserving model using a new optimal cryptography scheme for anomaly detection in large-scale sensor data. Our proposed privacy preserving model has maintained a better tradeoff between reliability and scalability of the cloud computing resources by means of detecting anomalies from the encrypted data. Conventional data analysis methods have used complex and large numerical computations for the anomaly detection. Also, a single key used by the symmetric key cryptographic scheme to encrypt and decrypt the data has faced large computational complexity because the multiple users can access the original data simultaneously using this single shared secret key. Hence, a classical public key encryption technique called RSA is adopted to perform encryption and decryption of secure data using different key pairs. Furthermore, the random generation of public keys in RSA is controlled in the proposed cloud-based privacy preserving model through optimizing a public key using a new hybrid local pollination-based grey wolf optimizer (LPGWO) algorithm. For ease of convenience, a single private server handling the organization data within a collaborative public cloud data center when requiring the decryption of secure sensor data are allowed to decrypt the optimal secure data using LPGWO-based RSA optimal cryptographic scheme. The data encrypted using an optimal cryptographic scheme are then encouraged to perform data clustering computations in collaborative public servers of cloud platform using Neutrosophic c-Means Clustering (NCM) algorithm. Hence, this NCM algorithm mainly focuses for data partitioning and classification of anomalies. Experimental validation was conducted using four datasets obtained from Intel laboratory having publicly available sensor data. The experimental outcomes have proved the efficiency of the proposed framework in providing data privacy with high anomaly detection accuracy.

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.

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.

We address some issues of renormalization and symmetries of effective field theories with unstable particles - resonances. We also calculate anomalous contributions in the divergence of the singlet axial current in an effective field theory of massive SU(N) Yang-Mills fields interacting with fermions and discuss their possible relevance to the strong CP problem.

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.

The response of fermionic system to external gauge fields is defined by current–current correlation function Π_μν(q, q₀). Transport properties of different physical quantities are determined by zero energy–momentum limit of it. As it is known close to half-filling the physics of graphene is described by (2+1)-dimensional Dirac theory. In this paper, we calculate current–current correlation function in Dirac theory in a presence of chemical potential η and gap m.

We present a coordinate-invariant approach, based on a Pauli–Villars measure, to the definition of the path integral in two-dimensional conformal field theory. We discuss some advantages of this approach compared to the operator formalism and alternative path integral approaches. We show that our path integral measure is invariant under conformal transformations and field reparametrizations, in contrast to the measure used in the Fujikawa calculation, and we show the agreement, despite different origins, of the conformal anomaly in the two approaches. The natural energy–momentum in the Pauli–Villars approach is a true coordinate-invariant tensor quantity, and we discuss its nontrivial relationship to the corresponding nontensor object arising in the operator formalism, thus providing a novel explanation within a path integral context for the anomalous Ward identities of the latter. We provide a direct calculation of the nontrivial contact terms arising in expectation values of certain energy–momentum products, and we use these to perform a simple consistency check confirming the validity of the change of variables formula for the path integral. Finally, we review the relationship between the conformal anomaly and the energy–momentum two-point functions in our formalism.

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.

In the present work we have derived the gravitational anomaly from a fundamentally different perspective: it emerges due to the tunneling of particles (in the present case fermions) across the black hole horizon. The latter effect is in fact the Hawking radiation. We have used the analogy of an early idea^17,18 of visualizing chiral gauge anomaly as an effect of spectral flow of the energy levels, from the negative energy Dirac sea, across zero energy level in the presence of gauge interactions. This was extended to conformal anomaly in Ref. 23. In the present work, we exploit the latter formalism in black hole physics where we interpret crossing the horizon of black hole (the zero energy level) as a spectral flow since it is also accompanied by a change of sign in the energy of the particle. Furthermore, Hawking radiation induces a shrinking of the radius of the horizon^15,16 which reminds us of a similar rearrangement in the Fermi level generated by the spectral flow.^17,18,21 Hence in our formulation the negative energy states below horizon play a similar role as the Dirac sea. We successfully recover the gravitational anomaly.

Anomalous features of models with nonlinear symmetry realization are addressed. It is shown that such models can have anomalous amplitudes breaking of its original symmetry realization. An illustrative example of a simple models with a nonlinear conformal symmetry realization is given. It is argued that the effective action obtained via nonlinear symmetry realization should be used to obtain an anomaly-induced action which is to drive the low-energy dynamics.

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.

We consider the field renormalization group (RG) of two coupled one-spatial dimension (1D) spinless fermion chains under intraforward, interforward, interbackscattering and interumklapp interactions until two-loops order. Up to this order, we demonstrate the quantum confinement in the RG flow, where the interband chiral Fermi points reduce to single chiral Fermi points and the renormalized interaction couplings have Luttinger liquid fixed points. We show that this quasi-1D system is equivalently described in terms of one- and two-color interactions and address the problem of quantum anomaly, inherent to this system, as a direct consequence of coupling 1+1 free Dirac fields to one- and two-color interactions.

The purpose of this study is to examine the effect of topology change on anomaly in the initial universe. G-cobordism is introduced to argue about the topology change accompanied by gauge group. Our results revealed that change of anomalies results from topology change.

In a Hamiltonian approach to anomalies, parity and time-reversal symmetries can be restored by introducing suitable impure (or mixed) states. However, the expectation values of observables such as the Hamiltonian diverges in such impure states. Here, we show that such divergent expectation values can be treated within a renormalization group (RG) framework, leading to a set of β-functions in the moduli space of the operators representing the observables. This leads to well-defined expectation values of the Hamiltonian in a phase where the impure state restores the P and T symmetry. We also show that this RG procedure leads to a mass gap in the spectrum. Such a framework may be relevant for long wavelength descriptions of condensed matter systems such as the quantum spin Hall (QSH) effect.

We discuss a covariant functional integral approach to the quantization of the bosonic string. In contrast to approaches relying on noncovariant operator regularizations, interesting operators here are true tensor objects with classical transformation laws, even on target spaces where the theory has a Weyl anomaly. Since no implicit noncovariant gauge choices are involved in the definition of the operators, the anomaly is clearly separated from the issue of operator renormalization and can be understood in isolation, instead of infecting the latter as in other approaches. Our method is of wider applicability to covariant theories that are not Weyl invariant, but where covariant tensor operators are desired.

After constructing covariantly regularized vertex operators, we define a class of background-independent path integral measures suitable for string quantization. We show how gauge invariance of the path integral implies the usual physical state conditions in a very conceptually clean way. We then discuss the construction of the BRST action from first principles, obtaining some interesting caveats relating to its general covariance. In our approach, the expected BRST related anomalies are encoded somewhat differently from other approaches. We conclude with an unusual but amusing derivation of the value D = 26 of the critical dimension.

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.