scholarly journals Chiralspin Symmetry and Its Implications for QCD

Universe ◽  
2019 ◽  
Vol 5 (1) ◽  
pp. 38 ◽  
Author(s):  
Leonid Glozman
Keyword(s):  
Dirac Operator ◽  
Invariant Theory ◽  
Magnetic Interaction ◽  
Kinetic Term ◽  
Dirac Fermions ◽  
Gauge Invariant ◽  
Zero Modes ◽  
Left Handed ◽  
Electric Interaction ◽  
The Right

In a local gauge-invariant theory with massless Dirac fermions, a symmetry of the Lorentz-invariant fermion charge is larger than a symmetry of the Lagrangian as a whole. While the Dirac Lagrangian exhibits only a chiral symmetry, the fermion charge operator is invariant under a larger symmetry group, S U ( 2 N F ) , that includes chiral transformations as well as S U ( 2 ) C S chiralspin transformations that mix the right- and left-handed components of fermions. Consequently, a symmetry of the electric interaction, which is driven by the charge density, is larger than a symmetry of the magnetic interaction and of the kinetic term. This allows separating in some situations electric and magnetic contributions. In particular, in QCD, the chromo-magnetic interaction contributes only to the near-zero modes of the Dirac operator, while confining chromo-electric interaction contributes to all modes. At high temperatures, above the chiral restoration crossover, QCD exhibits approximate S U ( 2 ) C S and S U ( 2 N F ) symmetries that are incompatible with free deconfined quarks. Consequently, elementary objects in QCD in this regime are quarks with a definite chirality bound by the chromo-electric field, without the chromo-magnetic effects. In this regime, QCD can be described as a stringy fluid.

scholarly journals SU(2NF) symmetry of confinement in QCD and its observation at high temperature.

2018 ◽  
Vol 182 ◽  
pp. 02046 ◽  
Author(s):  
L.Ya. Glozman
Keyword(s):  
High Temperature ◽  
Dirac Operator ◽  
Magnetic Interaction ◽  
High Temperature Phase ◽  
Temperature Phase ◽  
Zero Modes ◽  
Left Handed ◽  
Electric Interaction ◽  
The Right ◽  
Increasing Temperature

In this talk we first overview lattice results that have led to the observation of new SU(2)CS and SU(2NF) symmetries upon artificial truncation of the near-zero modes of the Dirac operator at zero temperatute and at high temperature without any truncation. These symmetries are larger than the chiral symmetry of the QCD Lagrangian and contain chiral symmetries SU(NF)L x SU(NF)R and U(1)A as subgroups. In addition to the standard chiral transformations the SU(2)CS and SU(2NF) transformations mix the right- and left-handed components of the quark fields. It is a symmetry of the confining chromo-electric interaction while the chromo-magnetic interaction manifestly breaks it. Emergence of these symmetries upon truncation of the near-zero modes of the Dirac operator at T=0 means that all effects of the chromo-magnetic interaction are located exclusively in the near-zero modes, while confining chromo-electric interaction is distributed among all modes. Appearance of these symmetries at high T, where the temperature suppresses the near-zero modes, has radical implications because these symmetries are incompatible with the asymptotically free deconfined quarks at increasing temperature. The elementary objects in the high-temperature phase of QCD should be quarks bound by the pure chromo-electric field that is not accompanied by the chromo-magnetic effects.

Three regimes of QCD

2021 ◽  
pp. 2044031
Author(s):  
L. Ya. Glozman
Keyword(s):  
Dirac Operator ◽  
Quark Gluon Plasma ◽  
Degrees Of Freedom ◽  
Magnetic Interaction ◽  
Gluon Plasma ◽  
Magnetic Interactions ◽  
Hadron Spectrum ◽  
Zero Modes ◽  
Electric Interaction ◽  
Hadron Gas

While the QCD Lagrangian as the whole is only chirally symmetric, its electric part has larger chiral-spin [Formula: see text] and [Formula: see text] symmetries. This allows separation of the electric and magnetic interactions in a given reference frame. Artificial truncation of the near-zero modes of the Dirac operator results in the emergence of the [Formula: see text] and [Formula: see text] symmetries in hadron spectrum. This implies that while the confining electric interaction is distributed among all modes of the Dirac operator, the magnetic interaction is located at least predominantly in the near-zero modes. Given this observation one could anticipate that above the pseudocritical temperature, where the near-zero modes of the Dirac operator are suppressed, QCD is [Formula: see text] and [Formula: see text] symmetric, which means absence of deconfinement in this regime. Solution of the [Formula: see text] QCD on the lattice with a chirally symmetric Dirac operator reveals that indeed in the interval [Formula: see text] QCD is approximately [Formula: see text] and [Formula: see text] symmetric which implies that degrees of freedom are chirally symmetric quarks bound by the chromoelectric field into color-singlet objects without the chromomagnetic effects. This regime is referred to as a Stringy Fluid. At larger temperatures this emergent symmetry smoothly disappears and QCD approaches the Quark–Gluon Plasma regime with quasifree quarks. The Hadron Gas, the Stringy Fluid and the Quark–Gluon Plasma differ by symmetries, degrees of freedom and properties.

scholarly journals On the gauge-invariant path-integral measure for the overlap Weyl fermions in 16 of SO(10)

2019 ◽  
Vol 2019 (11) ◽  
Author(s):  
Yoshio Kikukawa
Keyword(s):  
Path Integral ◽  
Boundary Phase ◽  
Basic Question ◽  
Spinor Representation ◽  
Gauge Invariant ◽  
Fermion Model ◽  
Left Handed ◽  
Integral Measure ◽  
The Right ◽  
Weyl Fermions

Abstract We consider the lattice formulation of SO(10) chiral gauge theory with left-handed Weyl fermions in the 16-dimensional spinor representation ($\underline{16}$) within the framework of the overlap fermion/Ginsparg–Wilson relation. We define a manifestly gauge-invariant path-integral measure for the left-handed Weyl field using all the components of the Dirac field, but the right-handed part of it is just saturated completely by inserting a suitable product of the SO(10)-invariant ’t Hooft vertices in terms of the right-handed field. The definition of the measure applies to all possible topological sectors of admissible link fields. The measure possesses all required transformation properties under lattice symmetries and the induced effective action is CP invariant. The global U(1) symmetry of the left-handed field is anomalous due to the non-trivial transformation of the measure, while that of the right-handed field is explicitly broken by the ’t Hooft vertices. There remains the issue of smoothness and locality in the gauge-field dependence of the Weyl fermion measure, but the question is well defined and the necessary and sufficient condition for this property is formulated in terms of the correlation functions of the right-handed auxiliary fields. In the weak gauge-coupling limit at least, all the auxiliary fields have short-range correlations and the question can be addressed further by Monte Carlo methods without encountering the sign problem. We also discuss the relations of our formulation to other approaches/proposals to decouple the species doubling/mirror degrees of freedom. These include the Eichten–Preskill model, the mirror-fermion model with overlap fermions, the domain-wall fermion model with the boundary Eichten–Preskill term, 4D topological insulator/superconductor with a gapped boundary phase, and the recent studies on the PMS phase/“mass without symmetry breaking”. We clarify the similarities and differences in the technical details and show that our proposal is a unified and well defined testing ground for that basic question.

scholarly journals THE DIRAC FIELD IN TAUB–NUT BACKGROUND

2001 ◽  
Vol 16 (10) ◽  
pp. 1743-1758 ◽  
Author(s):  
ION I. COTĂESCU ◽  
MIHAI VISINESCU
Keyword(s):  
Invariant Theory ◽  
Gordon Equation ◽  
Dirac Field ◽  
Dirac Fermions ◽  
Large Collection ◽  
Scalar Theory ◽  
Gauge Invariant ◽  
Commuting Operators ◽  
Klein Gordon ◽  
Kaluza Klein

We investigate the SO (4,1) gauge-invariant theory of the Dirac fermions in the external field of the Kaluza–Klein monopole, pointing out that the quantum modes can be recovered from a Klein–Gordon equation analogous to the Schrödinger equation in the Taub–NUT background. Moreover, we show that there is a large collection of observables that can be directly derived from those of the scalar theory. These offer many possibilities of choosing complete sets of commuting operators which determine the quantum modes. In addition there are some spin-like and Dirac-type operators involving the covariantly constant Killing–Yano tensors of the hyper-Kähler Taub–NUT space. The energy eigenspinors of the central modes in spherical coordinates are completely evaluated in explicit, closed form.

Определение ведущей руки в судебно-медицинской практике с помощью стоматологического индекса КПУ

2020 ◽  
pp. 46-48
Keyword(s):  
Dental Caries ◽  
Forensic Medicine ◽  
Left Handed ◽  
Forensic Practice ◽  
The World ◽  
Medical Identification ◽  
The Right

In current forensic medicine practice, the need for the development of new, scientifically based approaches and methods of forensic medical identification is still very important. The number of left-handed people in the world varies from 5 to 30 %, and it can be useful in forensic practice. The possibility of establishing a dominating hand based on the intensity of dental caries (CFE - CARIES-FILLIN-EXTRACTION index) was studied. Taking into consideration the intensity of caries damage to the teeth on the right and left sides of right-handed, left-handed and ambidextras people, we offered and calculated the CFE difference index: «CFE on the right – CFE on the left». Significant differences in the CFE indexes can help to determine what hand has been predominant and it might be useful for forensic specialists.

ANALYSIS OF THE COMPETITIVE ACTIVITIES OF THE WORLD STRONGEST BELT WRESTLERS

2020 ◽  
Vol 8 (1) ◽  
pp. 38-45
Author(s):  
Mariya Sedunova ◽  
Liliya Konovalova
Keyword(s):  
Female Athletes ◽  
Group Differences ◽  
Men And Women ◽  
World Championship ◽  
Left Handed ◽  
Competitive Activity ◽  
The World ◽  
The Right ◽  
Competitive Activities ◽  
Distinguishing Features

International potential and consequent greater competition in belt wrestling increase the significance of assessing quantitative and qualitative indicators of competitive activity of the strongest wrestlers in the world. It is important to identify the sport development trends and to search for effective ways and tools for achievement of the sport excellence. Purpose: to reveal the features of efficient competitive activities of the world leading wrestlers on the basis of analysis of group differences in technical and tactical excellence indicators. Materials and methods of research. We analyzed videos of 285 events with participation of 197 wrestlers competing at the Belt Wrestling World Championship 2019 in Kazan. We registered the following indicators of competitive activity: the total and average number of fighting techniques, including techniques executed to the right and to the left side within 4 minutes of combat; number and types of technical actions of competition winners among men and women. Research results and discussion. The paper focuses on the comparative analysis of technical and tactical skills of men and women, the winners of the Belt Wrestling World Championship. The research revealed distinguishing features of the winner’s technical toolkit including the diversity of technical and tactical actions, a balance in the knowledge of the right and left-handed techniques. At the same time, the analysis of technical and tactical actions in women wrestling shows the backlog of female athletes in these components of technical fitness.

The Standard Theory

2017 ◽  
Author(s):  
John Iliopoulos
Keyword(s):  
Gauge Theory ◽  
Invariant Theory ◽  
Standard Theory ◽  
Strong Interactions ◽  
Gauge Invariant ◽  
Electromagnetic Interactions ◽  
Protons And Neutrons ◽  
Free Particles ◽  
Theoretical Predictions ◽  
Theory And Experiment

All ingredients of the previous chapters are combined in order to build a gauge invariant theory of the interactions among the elementary particles. We start with a unified model of the weak and the electromagnetic interactions. The gauge symmetry is spontaneously broken through the BEH mechanism and we identify the resulting BEH boson. Then we describe the theory known as quantum chromodynamics (QCD), a gauge theory of the strong interactions. We present the property of confinement which explains why the quarks and the gluons cannot be extracted out of the protons and neutrons to form free particles. The last section contains a comparison of the theoretical predictions based on this theory with the experimental results. The agreement between theory and experiment is spectacular.

TREE DIAGRAMS IN WITTEN’S SUPERSTRING FIELD THEORY

1989 ◽  
Vol 04 (21) ◽  
pp. 2063-2071
Author(s):  
GEORGE SIOPSIS
Keyword(s):  
Field Theory ◽  
Scattering Amplitudes ◽  
Invariant Theory ◽  
Higher Order ◽  
Contact Term ◽  
Tree Level ◽  
Gauge Invariant

It is shown that the contact term discovered by Wendt is sufficient to ensure finiteness of all tree-level scattering amplitudes in Witten’s field theory of open superstrings. Its inclusion in the action also leads to a gauge-invariant theory. Thus, no additional higher-order counterterms in the action are needed.

scholarly journals Majorana zero modes in impurity-assisted vortex of LiFeAs superconductor

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Lingyuan Kong ◽  
Lu Cao ◽  
Shiyu Zhu ◽  
Michał Papaj ◽  
Guangyang Dai ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Zero Mode ◽  
Scanning Tunneling ◽  
Homogeneous Material ◽  
Dirac Fermions ◽  
Tunneling Microscopy ◽  
Zero Modes ◽  
Topological Quantum ◽  
One Step ◽  
Topological Quantum Computation

AbstractThe iron-based superconductor is emerging as a promising platform for Majorana zero mode, which can be used to implement topological quantum computation. One of the most significant advances of this platform is the appearance of large vortex level spacing that strongly protects Majorana zero mode from other low-lying quasiparticles. Despite the advantages in the context of physics research, the inhomogeneity of various aspects hampers the practical construction of topological qubits in the compounds studied so far. Here we show that the stoichiometric superconductor LiFeAs is a good candidate to overcome this obstacle. By using scanning tunneling microscopy, we discover that the Majorana zero modes, which are absent on the natural clean surface, can appear in vortices influenced by native impurities. Our detailed analysis reveals a new mechanism for the emergence of those Majorana zero modes, i.e. native tuning of bulk Dirac fermions. The discovery of Majorana zero modes in this homogeneous material, with a promise of tunability, offers an ideal material platform for manipulating and braiding Majorana zero modes, pushing one step forward towards topological quantum computation.

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