Nonperturbative Fermion-Boson Vertex Function in Gauge Theories

The nonperturbative fermion-boson vertex function in four-dimensional Abelian gauge theories is self-consistently and exactly derived in terms of a complete set of normal (longitudinal) and transverse Ward-Takahashi relations for the The nonperturbative fermion-boson vertex function in four-dimensional Abelian gauge theories is self-consistently and exactly derived in terms of a complete set of normal(longitudinal) and transverse Ward-Takahashi relations for the fermion-boson and the axial-vector vertices in the case of massless fermion, in which the possible quantum anomalies and perturbative corrections are taken into account simultaneously. We find that this nonperturbative fermion-boson vertex function is expressed nonperturbatively in terms of the full fermion propagator and contains the contributions of the transverse axial anomaly and perturbative corrections. The result that the transverse axial anomaly contributes to the nonperturbative fermion-boson vertex arises from the coupling between the fermion-boson and the axial-vector vertices through the transverse Ward-Takahashi relations for them and is a consequence of gauge invariance.Comment: 11 pages, RevTa

Transverse Ward-Takahashi Relation for the Fermion-Boson Vertex Function in 4-dimensional QED

I present a general expression of the transverse Ward-Takahashi relation for the fermion-boson vertex function in momentum space in 4-dimensional QED, from which the corresponding one-loop expression is derived straightforwardly. Then I deduce carefully this transverse Ward-Takahashi relation to one-loop order in d-dimensions, with $d = 4 + \epsilon$. The result shows that this relation in d-dimensions has the same form as one given in 4-dimensions and there is no need for an additional piece proportional to $(d-4)$ to include for this relation to hold in 4-dimensions. This result is confirmed by an explicit computation of terms in this transverse WT relation to one-loop order. I also make some comments on the paper given by Pennington and Williams who checked the transverse Ward-Takahashi relation at one loop order in d-dimensions.Comment: 15 page

Full Fermion-Boson Vertex Function Derived in terms of the Ward-Takahashi Relations in Abelian Gauge Theory

I present an approach to derive the full fermion-boson vertex function in four-dimensional Abelian gauge theory in terms of a set of normal (longitudinal) and transverse Ward-Takahashi relations for the fermion-boson and axial-vector vertices in momentum space in the case of massless fermion. Such a derived fermion-boson vertex function should be satisfied both perturbatively and non-perturbatively. I show that, by an explicit computation, such a derived full fermion-boson vertex function to one-loop order leads to the same result as one obtained in perturbation theory.Comment: 12 page

Identical Relations among Transverse Parts of Variant Green Functions and the Full Vertices in Gauge Theories

The identical relations among the transverse parts of variant vertex functions are derived by computing the curl of the time-ordered products of three-point Green functions involving the vector, the axial-vector and the tensor current operators, respectively. These transverse relations are coupled each other. Combining these transverse relations with the normal (longitudinal) Ward-Takahashi identities forms a complete set of constraint relations for three-point vertex functions. As a consequence, the full vector, the full axial-vector and the full tensor vertex functions in the momentum space are exactly obtained.Comment: 12 pages, revte

Quark Contributions to the Proton Spin and Tensor Charge

I calculate the quark contributions to the axial and tensor charges and the spin structure of the proton. The result indicates that the valence current quark spins carry 1/3 of the proton spin, the total contribution of quark spins to the proton spin satisfies $\Delta \Sigma = 1/3 + \Delta \Sigma_{sea} \le 1/3$, and the quarks (their spin plus orbital contributions) contribute about one half of the proton spin at scale of 1 $GeV$. The valence current quark contributions to the proton tensor charge are also obtained.Comment: RevTeX file, 8 pages, no figur

Transverse Symmetry Transformations and the Quark-Gluon Vertex Function in QCD

The transverse symmetry transformations associated with the normal symmetry transformations in gauge theories are introduced, which at first are used to reproduce the transverse Ward-Takahashi identities in the Abelian theory QED. Then the transverse symmetry transformations associated with the BRST symmetry and chiral transformations in the non-Abelian theory QCD are used to derive the transverse Slavnov-Taylor identities for the vector and axial-vector quark-gluon vertices, respectively. Based on the set of normal and transverse Slavnov-Taylor identities, an expression of the quark-gluon vertex function is derived, which describes the constraints on the structure of the quark-gluon vertex imposed from the underlying gauge symmetry of QCD alone. Its role in the study of the Dyson-Schwinger equation for the quark propagator in QCD is discussed.Comment: 13 pages, no figur

Drag-Tracking Guidance for Entry Vehicles Without Drag Rate Measurement

A robust entry guidance law without drag rate measurement is designed for drag-tracking in this paper. The bank angle is regarded as the control variable. First, a state feedback guidance law (bank angle magnitude) that requires the drag and its rate as feedback information is designed to make the drag-tracking error be input-to-state stable (ISS) with respect to uncertainties. Then a high gain observer is utilized to estimate the drag rate which is difficult for a vehicle to measure accurately in practice. Stability analysis as well as simulation results show the efficiency of the presented approach.Comment: 23 pages, 11 figure

Entropy of a nonuniformly rectilinearly accelerating black hole

Adopting thin film brick-wall model, we calculate the entropy of a nonuniformly rectilinearly accelerating non-stationary black hole expressed by Kinnersley metric. Because the black hole is accelerated, the event horizon is axisymmetric. The different points of horizon surface may have different temperature. We calculate the temperature and the entropy density at every point of the horizon at first, then we obtain the total entropy through integration, which is proportional to the aera of event horizon as the same as the stationary black holes. It is shown that the black hole entropy may be regarded as the entropy of quantum fields just on the surface of event horizon

mvn2vec: Preservation and Collaboration in Multi-View Network Embedding

Multi-view networks are broadly present in real-world applications. In the meantime, network embedding has emerged as an effective representation learning approach for networked data. Therefore, we are motivated to study the problem of multi-view network embedding with a focus on the optimization objectives that are specific and important in embedding this type of network. In our practice of embedding real-world multi-view networks, we explicitly identify two such objectives, which we refer to as preservation and collaboration. The in-depth analysis of these two objectives is discussed throughout this paper. In addition, the mvn2vec algorithms are proposed to (i) study how varied extent of preservation and collaboration can impact embedding learning and (ii) explore the feasibility of achieving better embedding quality by modeling them simultaneously. With experiments on a series of synthetic datasets, a large-scale internal Snapchat dataset, and two public datasets, we confirm the validity and importance of preservation and collaboration as two objectives for multi-view network embedding. These experiments further demonstrate that better embedding can be obtained by simultaneously modeling the two objectives, while not over-complicating the model or requiring additional supervision. The code and the processed datasets are available at http://yushi2.web.engr.illinois.edu/

Shadow of complex fixed point: Approximate conformality of Q>4 Potts model

We study the famous example of weakly first order phase transitions in the 1+1D quantum Q-state Potts model at Q>4. We numerically show that these weakly first order transitions have approximately conformal invariance. Specifically, we find entanglement entropy on considerably large system sizes fits perfectly with the universal scaling law of this quantity in the conformal field theories (CFTs). This supports that the weakly first order transitions is proximate to complex fixed points, which are described by recent conjectured complex CFTs. Moreover, the central charge extracted from this fitting is close to the real part of the complex central charge of these complex CFTs. We also study the conformal towers and the drifting behaviors of these conformal data (e.g., central charge and scaling dimensions).Comment: published versio