Renormalization of the quantum chromodynamics with massive gluons

In our previously published papers, it was proved that the chromodynamics with massive gluons can well be set up on the gauge-invariance principle. The quantization of the chromodynamics was perfectly performed in the both of Hamiltonian and Lagrangian path-integral formalisms by using the Lagrangian undetermined multiplier method. In this paper, It is shown that the quantum theory is invariant with respect to a kind of BRST-transformations. From the BRST-invariance of the theory, the Ward-Takahashi identities satisfied by the generating functionals of full Green functions, connected Green functions and proper vertex functions are successively derived. As an application of the above Ward-Takahashi identities, the Ward-Takahashi identities obeyed by the massive gluon and ghost particle propagators and various proper vertices are derived and based on these identities, the propagators and vertices are perfectly renormalized. Especially, as a result of the renormalization, the Slavnov-Taylor identity satisfied by renormalization constants is natually deduced. To demonstrate the renormalizability of the theory, the one-loop renormalization of the theory is carried out by means of the mass-dependent momentum space subtraction scheme and the renormalization group approach, giving an exact one-loop effective coupling constant and one-loop effective gluon and quark masses which show the asymptotically free behaviors as the same as those given in the quantum chromodynamics with massless gluons.Comment: 34 pages, 12 figure

Oseba: Optimization for Selective Bulk Analysis in Big Data Processing

Selective bulk analyses, such as statistical learning on temporal/spatial data, are fundamental to a wide range of contemporary data analysis. However, with the increasingly larger data-sets, such as weather data and marketing transactions, the data organization/access becomes more challenging in selective bulk data processing with the use of current big data processing frameworks such as Spark or keyvalue stores. In this paper, we propose a method to optimize selective bulk analysis in big data processing and referred to as Oseba. Oseba maintains a super index for the data organization in memory to support fast lookup through targeting the data involved with each selective analysis program. Oseba is able to save memory as well as computation in comparison to the default data processing frameworks

Simplification of protein representation from the contact potentials between residues

Based on the concept of energy landscape a picture of the mismatch between the reduced interaction matrix of residues and the matrix of statistical contact potentials is presented. For the Miyazawa and Jernigan (MJ) matrix, rational groupings of 20 kinds of residues with minimal mismatches under the consideration of local minima and statistics on correlation between the residues are studied. A hierarchical tree of groupings relating to different numbers of groups $N$ is obtained, and a plateau around $N=8\sim 10$ is found, which may represent the basic degree of freedom of the sequence complexity of proteins.Comment: 10 pages, 5 figures, submitted to PR

Renormalization of the SU(2)-symmetric model of hadrodynamics

It is proved that the SU(2)-symmetric model of hadrodynamics can well be set up on the gauge-invariance principle. The quantization of the model can readily be performed in the Lagrangian path-integral formalisms by using the Lagrangian undetermined multiplier method. Furthermore, it is shown that the quantum theory is invariant with respect to a kind of BRST-transformations. From the BRST-symmetry of the theory, the Ward-Takahashi identities satisfied by the generating functionals of full Green functions, connected Green functions and proper vertex functions are successively derived. As an application of the above Ward-Takahashi identities, the Ward-Takahashi identities obeyed by the propagators and various proper vertices are derived. Based on these identities, the propagators and vertices are perfectly renormalized. Especially, as a result of the renormalization, the Slavnov-Taylor identity satisfied by renormalization constants is natually deduced. To demonstrate the renormalizability of the theory, the one-loop renormalization of the theory is carried out by means of the mass-dependent momentum space subtraction and the renormalization group approach, giving an exact one-loop effective coupling constant and one-loop effective nucleon, pion and $\rho -$meson masses

Strings in Noncommutative Spacetime

Free bosonic strings in noncommutative spacetime are investigated. The string spectrum is obtained in terms of light-cone quantization. We construct two different models. In the first model the critical dimension is still required to be 26 while only extreme high energy spectrum is modified by noncommutative effect. In the second model, however, the critical dimension is reduced to be less than 26 while low-energy (massless) spectrum only contains degrees of freedom of our four dimensional physics.Comment: 9 pages, no figure

Particle paths in small amplitude solitary waves with negative vorticity

We investigate the particle trajectories in solitary waves with vorticity, where the vorticity is assumed to be negative and decrease with depth. We show that the individual particle moves in a similar way as that in the irrotational case if the underlying laminar flow is favorable, that is, the flow is moving in the same direction as the wave propagation throughout the fluid, and show that if the underlying current is not favorable, some particles in a sufficiently small solitary wave move to the opposite direction of wave propagation along a path with a single loop or hump .Comment: 11page

Magnetic field at the center of a vortex: a new criterion for the classification of the superconductors

Magnetic response of a superconductor depends on the thermodynamic stability of vortex in the material. Here we show that the vortex stability has a close relation with the ratio of the magnetic field at the vortex core center to the thermodynamic critical field. This finding provides a new criterion for the classification of the superconductors according to their magnetic responses.Comment: 3 pages, 2 figure

Anomalous Josephson Effect in magnetic Josephson junctions with noncentrosymmetric superconductors

We show that the two-band nature of noncentrosymmetric superconductors leads naturally to an anomalous Josephson current appearing at zero phase difference in a clean noncentrosymmetric superconductor/ferromagnet/noncentrosymmetric superconductor junction. The two-band nature provides two sets of Andreev bound states which carry two supercurrents with different amplitudes. When the magnetization direction of the ferromagnet is suitably chosen, two supercurrents experience opposite phase shifts from the conventional sinusoidal current-phase relation. Then the total Josephson current results in a continuously tunable ground-state phase difference by adjusting the ferromagnet parameters and the triplet-singlet ratio of noncentrosymmetric superconductors. The physics picture and analytical results are given on the basis of the $s$+$p$ wave, while the numerical results are reported on both $s$+$p$ and $d$+$p$ waves. For the $d$+$p$ wave, we find novel states in which the supercurrents are totally carried by continuous propagating states instead of discrete Andreev bound states. Instead of carrying supercurrent, the Andreev bound states which here only appear above the Fermi energy block the supercurrent flowing along the opposite direction. These novel states advance the understaning of the relation between Andreev bound states and the Josephson current. And the ground-state phase difference serves as a tool to determine the triplet-singlet ratio of noncentrosymmetric superconductors.Comment: 10pages, 6figure

Recovering modified Newtonian dynamics by changing inertia

Milgrom's modified Newtonian dynamics (MOND) has done a great job on accounting for the rotation curves of a variety of galaxies by assuming that Newtonian dynamics breaks down for extremely low acceleration typically found in the galactic contexts. This breakdown of Newtonian dynamics may be a result of modified gravity or a manifest of modified inertia. The MOND phenomena are derived here based on three general assumptions: 1) Gravitational mass is conserved; 2) Inverse-square law is applicable at large distance; 3) Inertial mass depends on external gravitational fields. These assumptions not only recover the deep-MOND behaviour, the accelerating expansion of the universe is also a result of these assumptions. Then Lagrangian formulae are developed and it is found that the assumed universal acceleration constant a0 is actually slowly varying by a factor no more than 4. This varying 'constant' is just enough to account for the mass-discrepancy presented in bright clusters

Cosmological Constant as Vacuum Energy Density of Quantum Field Theories on Noncommutative Spacetime

We propose a new approach to understand hierarchy problem for cosmological constant in terms of considering noncommutative nature of space-time. We calculate that vacuum energy density of the noncommutative quantum field theories in nontrivial background, which admits a smaller cosmological constant by introducing an higher noncommutative scale $\mu_{NC}\sim M_p$. The result $\rho_\Lambda\sim 10^{-6}\Lambda_{SUSY}^8M_p^4/\mu_{NC}^8$ yields cosmological constant at the order of current observed value for supersymmetry breaking scale at 10TeV. It is the same as Banks' phenomenological formula for cosmological constant.Comment: 7 pages, no figures, v4, references adde