scholarly journals A generally relativistic gauge classification of the Dirac fields

2016 ◽  
Vol 13 (06) ◽  
pp. 1650078 ◽  
Author(s):  
Luca Fabbri
Keyword(s):  
Axial Vector ◽  
Supplementary Information ◽  
Dirac Field ◽  
Field Equations ◽  
Momentum Vector ◽  
Nonrelativistic Approximation ◽  
Gauge Transformations ◽  
Dirac Fields

We consider generally relativistic gauge transformations for the spinorial fields finding two mutually exclusive but together exhaustive classes in which fermions are placed adding supplementary information to the results obtained by Lounesto, and identifying quantities analogous to the momentum vector and the Pauli–Lubanski axial vector. We discuss how our results are similar to those obtained by Wigner by taking into account the system of Dirac field equations. We will investigate the consequences for the dynamics and in particular we shall address the problem of getting the nonrelativistic approximation in a consistent way. We are going to comment on extensions.

scholarly journals Torsion gravity for Dirac fields

2017 ◽  
Vol 14 (03) ◽  
pp. 1750037 ◽  
Author(s):  
Luca Fabbri
Keyword(s):  
Matter Field ◽  
Dirac Field ◽  
Field Equations ◽  
Dirac Fields

In this paper, we will take into account the most complete background with torsion and curvature, providing the most exhaustive coupling for the Dirac field, we will discuss the integrability of the interaction of the matter field and the reduction of the matter field equations.

Green function formulation of the Dirac field in curved space

1966 ◽  
Vol 294 (1439) ◽  
pp. 437-448 ◽  
Keyword(s):  
Green Function ◽  
Dirac Field ◽  
Green Functions ◽  
Field Equations ◽  
Curved Space ◽  
Particle Field ◽  
Function Formulation ◽  
Essential Idea ◽  
Mass Field

A Green function formulation of the Dirac field in curved space is considered in the cases where the mass is constant and where it is regarded as a direct particle field in the manner of Hoyle & Narlikar (1964 c ). This description is equivalent to, and in some ways more satisfactory than, that given in terms of a suitable Lagrangian, in which the Dirac or the mass field is regarded as independent of the geometry. The essential idea is to define the Dirac or the mass field in terms of certain Green functions and sources so that the field equations are satisfied identically, and then to obtain the contribution of these fields to the metric field equations from the variation of a suitable action that is defined in terms of the Green functions and sources.

scholarly journals A confining quark model and new gauge symmetry

2014 ◽  
Vol 29 (22) ◽  
pp. 1450120 ◽  
Author(s):  
Jong-Ping Hsu
Keyword(s):  
Gauge Symmetry ◽  
Quark Model ◽  
Power Counting ◽  
Gauge Fields ◽  
Linear Potential ◽  
Field Equations ◽  
Color Charge ◽  
Gauge Bosons ◽  
Gauge Transformations ◽  
Empirical Potentials

We discuss a confining model for quark–antiquark system with a new color SU3 gauge symmetry. New gauge transformations involve non-integrable phase factors and lead to the fourth-order gauge field equations and a linear potential. The massless gauge bosons have non-definite energies, which are not observable because they are permanently confined in quark systems by the linear potential. We use the empirical potentials of charmonium to determine the coupling strength of the color charge gs and find [Formula: see text]. The rules for Feynman diagrams involve propagators with poles of order 2 associated with new gauge fields. The confining quark model may be renormalizable by power counting and compatible with perturbation theory.

Algebraic Classification of Field Equations

2012 ◽  
pp. 465-536
Author(s):  
Anadijiban Das ◽  
Andrew DeBenedictis
Keyword(s):  
Field Equations ◽  
Algebraic Classification

Higher-order Markov models for metagenomic sequence classification

2020 ◽  
Vol 36 (14) ◽  
pp. 4130-4136
Author(s):  
David J Burks ◽  
Rajeev K Azad
Keyword(s):  
Dna Sequences ◽  
Markov Models ◽  
Fragment Size ◽  
Higher Order ◽  
Training Data ◽  
Supplementary Information ◽  
Local Alignment ◽  
Metagenomic Sequence ◽  
Higher Order Models

Abstract Motivation Alignment-free, stochastic models derived from k-mer distributions representing reference genome sequences have a rich history in the classification of DNA sequences. In particular, the variants of Markov models have previously been used extensively. Higher-order Markov models have been used with caution, perhaps sparingly, primarily because of the lack of enough training data and computational power. Advances in sequencing technology and computation have enabled exploitation of the predictive power of higher-order models. We, therefore, revisited higher-order Markov models and assessed their performance in classifying metagenomic sequences. Results Comparative assessment of higher-order models (HOMs, 9th order or higher) with interpolated Markov model, interpolated context model and lower-order models (8th order or lower) was performed on metagenomic datasets constructed using sequenced prokaryotic genomes. Our results show that HOMs outperform other models in classifying metagenomic fragments as short as 100 nt at all taxonomic ranks, and at lower ranks when the fragment size was increased to 250 nt. HOMs were also found to be significantly more accurate than local alignment which is widely relied upon for taxonomic classification of metagenomic sequences. A novel software implementation written in C++ performs classification faster than the existing Markovian metagenomic classifiers and can therefore be used as a standalone classifier or in conjunction with existing taxonomic classifiers for more robust classification of metagenomic sequences. Availability and implementation The software has been made available at https://github.com/djburks/SMM. Contact [email protected] Supplementary information Supplementary data are available at Bioinformatics online.

scholarly journals Extracting topological information from momentum space propagators

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
Fabrizio Canfora ◽  
David Dudal ◽  
Alex Giacomini ◽  
Igor F. Justo ◽  
Pablo Pais ◽  
...  
Keyword(s):  
Gauge Invariance ◽  
Momentum Space ◽  
Chiral Symmetry Breaking ◽  
Topological Invariant ◽  
Analytic Structure ◽  
Topological Information ◽  
Gauge Transformations ◽  
Small Gauge ◽  
Topological Number

Abstract A new topological invariant quantity, sensitive to the analytic structure of both fermionic and bosonic propagators, is proposed. The gauge invariance of our construct is guaranteed for at least small gauge transformations. A generalization compatible with the presence of complex poles is introduced and applied to the classification of propagators typically emerging from non-perturbative considerations. We present partial evidence that the topological number can be used to detect chiral symmetry breaking or deconfinement.

scholarly journals ON THE HAMILTONIAN FORMULATION OF THE EINSTEIN–HILBERT ACTION IN TWO DIMENSIONS

2006 ◽  
Vol 21 (11) ◽  
pp. 899-905 ◽  
Author(s):  
N. KIRIUSHCHEVA ◽  
S. V. KUZMIN
Keyword(s):  
Hamiltonian Formulation ◽  
Two Dimensions ◽  
General Covariance ◽  
Sufficient Condition ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Metric Tensor ◽  
Gauge Transformations ◽  
Total Divergence ◽  
Hilbert Action

It is shown that if general covariance is to be preserved (i.e. a coordinate system is not fixed) the well-known triviality of the Einstein field equations in two dimensions is not a sufficient condition for the Einstein–Hilbert action to be a total divergence. Consequently, a Hamiltonian formulation is possible without any modification of the two-dimensional Einstein–Hilbert action. We find the resulting constraints and the corresponding gauge transformations of the metric tensor.

scholarly journals Metric-Affine Geometries with Spherical Symmetry

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 453 ◽  
Author(s):  
Manuel Hohmann
Keyword(s):  
Spherical Symmetry ◽  
Rotation Group ◽  
Spin Connection ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Comprehensive Overview ◽  
Pure Rotation ◽  
Affine Geometries ◽  
Spherically Symmetric Metric

We provide a comprehensive overview of metric-affine geometries with spherical symmetry, which may be used in order to solve the field equations for generic gravity theories which employ these geometries as their field variables. We discuss the most general class of such geometries, which we display both in the metric-Palatini formulation and in the tetrad/spin connection formulation, and show its characteristic properties: torsion, curvature and nonmetricity. We then use these properties to derive a classification of all possible subclasses of spherically symmetric metric-affine geometries, depending on which of the aforementioned quantities are vanishing or non-vanishing. We discuss both the cases of the pure rotation group SO ( 3 ) , which has been previously studied in the literature, and extend these previous results to the full orthogonal group O ( 3 ) , which also includes reflections. As an example for a potential physical application of the results we present here, we study circular orbits arising from autoparallel motion. Finally, we mention how these results can be extended to cosmological symmetry.

scholarly journals Learning transferable deep convolutional neural networks for the classification of bacterial virulence factors

2020 ◽  
Vol 36 (12) ◽  
pp. 3693-3702 ◽  
Author(s):  
Dandan Zheng ◽  
Guansong Pang ◽  
Bo Liu ◽  
Lihong Chen ◽  
Jian Yang
Keyword(s):  
Virulence Factors ◽  
State Of The Art ◽  
Binary Classification ◽  
Network Models ◽  
Bacterial Virulence ◽  
Supplementary Information ◽  
Deep Convolutional Neural Networks ◽  
Neural Network Models ◽  
Auxiliary Data

Abstract Motivation Identification of virulence factors (VFs) is critical to the elucidation of bacterial pathogenesis and prevention of related infectious diseases. Current computational methods for VF prediction focus on binary classification or involve only several class(es) of VFs with sufficient samples. However, thousands of VF classes are present in real-world scenarios, and many of them only have a very limited number of samples available. Results We first construct a large VF dataset, covering 3446 VF classes with 160 495 sequences, and then propose deep convolutional neural network models for VF classification. We show that (i) for common VF classes with sufficient samples, our models can achieve state-of-the-art performance with an overall accuracy of 0.9831 and an F1-score of 0.9803; (ii) for uncommon VF classes with limited samples, our models can learn transferable features from auxiliary data and achieve good performance with accuracy ranging from 0.9277 to 0.9512 and F1-score ranging from 0.9168 to 0.9446 when combined with different predefined features, outperforming traditional classifiers by 1–13% in accuracy and by 1–16% in F1-score. Availability and implementation All of our datasets are made publicly available at http://www.mgc.ac.cn/VFNet/, and the source code of our models is publicly available at https://github.com/zhengdd0422/VFNet. Supplementary information Supplementary data are available at Bioinformatics online.

scholarly journals Torsion gravity for Dirac particles

2017 ◽  
Vol 14 (09) ◽  
pp. 1750127 ◽  
Author(s):  
Luca Fabbri
Keyword(s):  
Spinor Field ◽  
Rest Frame ◽  
Axial Vector ◽  
Dirac Field ◽  
Dirac Particles

In this paper, we consider torsion gravity in the case of Dirac field, and by going into the rest frame, we study what happens when a uniform precession as well as a phase is taken into account for the spinor field; we discuss how partially conserved axial-vector currents and torsion-spin attractive potentials justify negative Takabayashi angle and energy smaller than mass: because in this instance the module goes to zero exponentially fast, we obtain stable and localized matter distributions suitable to be regarded as a description of particles.

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