Conserved Noether Currents, Utiyama's Theory of Invariant Variation, and Velocity Dependence in Local Gauge Invariance

The paper discusses the mathematical consequences of the application of derived variables in gauge fields. Physics is aware of several phenomena, which depend first of all on velocities (like e.g., the force caused by charges moving in a magnetic field, or the Lorentz transformation). Applying the property of the second Noether theorem, that allowed generalised variables, this paper extends the article by Al-Kuwari and Taha (1991) with a new conclusion. They concluded that there are no extra conserved currents associated with local gauge invariance. We show, that in a more general case, there are further conserved Noether currents. In its method the paper reconstructs the clue introduced by Utiyama (1956, 1959) and followed by Al-Kuwari and Taha (1991) in the presence of a gauge field that depends on the co-ordinates of the velocity space. In this course we apply certain (but not full) analogies with Mills (1989). We show, that handling the space-time coordinates as implicit variables in the gauge field, reproduces the same results that have been derived in the configuration space (i.e., we do not lose information), while the proposed new treatment gives additional information extending those. The result is an extra conserved Noether current.Comment: 14 page

CRL at Ntcir2

We have developed systems of two types for NTCIR2. One is an enhenced version of the system we developed for NTCIR1 and IREX. It submitted retrieval results for JJ and CC tasks. A variety of parameters were tried with the system. It used such characteristics of newspapers as locational information in the CC tasks. The system got good results for both of the tasks. The other system is a portable system which avoids free parameters as much as possible. The system submitted retrieval results for JJ, JE, EE, EJ, and CC tasks. The system automatically determined the number of top documents and the weight of the original query used in automatic-feedback retrieval. It also determined relevant terms quite robustly. For EJ and JE tasks, it used document expansion to augment the initial queries. It achieved good results, except on the CC tasks.Comment: 11 pages. Computation and Language. This paper describes our results of information retrieval in the NTCIR2 contes

Syntax-Directed Attention for Neural Machine Translation

Attention mechanism, including global attention and local attention, plays a key role in neural machine translation (NMT). Global attention attends to all source words for word prediction. In comparison, local attention selectively looks at fixed-window source words. However, alignment weights for the current target word often decrease to the left and right by linear distance centering on the aligned source position and neglect syntax-directed distance constraints. In this paper, we extend local attention with syntax-distance constraint, to focus on syntactically related source words with the predicted target word, thus learning a more effective context vector for word prediction. Moreover, we further propose a double context NMT architecture, which consists of a global context vector and a syntax-directed context vector over the global attention, to provide more translation performance for NMT from source representation. The experiments on the large-scale Chinese-to-English and English-to-Germen translation tasks show that the proposed approach achieves a substantial and significant improvement over the baseline system.Comment: AAAI2018, revised versio

Confinement, Vacuum Structure: from QCD to Quantum Gravity

A minimal Lorentz gauge gravity model with R^2-type Lagrangian is proposed. In the absence of torsion the model admits a topological phase with unfixed metric. The model possesses a minimal set of dynamical degrees of freedom for the torsion. Remarkably, the torsion has the same number of dynamical of-shell degrees of freedom as the metric tensor. We trace an analogy between the structure of the quantum chromodynamics and the structure of possible theory of quantum gravity.Comment: 7 pages; reduced version of talk given at IV International Symposium on Symmetries in Subatomic Physics (SSP 2009), plenary session in Honor of Yongmin Cho's 65th Birthday, Taipei, Taiwan, 2-5 June 2009; to appear in "Symmetries in Subatomic Physics", ed. P. Hwang

A geometrical derivation of the Dirac equation

We give a geometrical derivation of the Dirac equation by considering a spin-1/2 particle travelling with the speed of light in a cubic spacetime lattice. The mass of the particle acts to flip the multi-component wavefunction at the lattice sites. Starting with a difference equation for the case of one spatial and one time dimensions, we generalize the approach to higher dimensions. Interactions with external electromagnetic and gravitational fields are also considered. One logical interpretation is that only at the lattice sites is the spin-1/2 particle aware of its mass and the presence of external fields.Comment: 9 pages, LaTeX, version accepted for publication in Phys. Lett.

Angular Momentum and Energy-Momentum Densities as Gauge Currents

If we replace the general spacetime group of diffeomorphisms by transformations taking place in the tangent space, general relativity can be interpreted as a gauge theory, and in particular as a gauge theory for the Lorentz group. In this context, it is shown that the angular momentum and the energy-momentum tensors of a general matter field can be obtained from the invariance of the corresponding action integral under transformations taking place, not in spacetime, but in the tangent space, in which case they can be considered as gauge currents.Comment: RevTeX4, 7 pages, no figures. Presentation changes; version to appear in Phys. Rev.

Twist Symmetry and Gauge Invariance

By applying properly the concept of twist symmetry to the gauge invariant theories, we arrive at the conclusion that previously proposed in the literature noncommutative gauge theories, with the use of $\star$-product, are the correct ones, which possess the twisted Poincar\'e symmetry. At the same time, a recent approach to twisted gauge transformations is in contradiction with the very concept of gauge fields arising as a consequence of {\it local} internal symmetry. Detailed explanations of this fact as well as the origin of the discrepancy between the two approaches are presented.Comment: 10 page