scholarly journals GAUGE-INVARIANT FIELDS IN THE TEMPORAL GAUGE, COULOMB-GAUGE FIELDS, AND THE GRIBOV AMBIGUITY

2001 ◽  
Vol 16 (16) ◽  
pp. 2789-2815 ◽  
Author(s):  
KURT HALLER
Keyword(s):  
Physical State ◽  
Equations Of Motion ◽  
Coulomb Gauge ◽  
Gauge Fields ◽  
Gauge Invariant ◽  
Equal Time ◽  
Temporal Gauge ◽  
Equal Time Commutation ◽  
Gribov Ambiguity ◽  
Gribov Copies

We examine the relation between Coulomb-gauge fields and the gauge-invariant fields constructed in the temporal gauge for two-color QCD by comparing a variety of properties, including their equal-time commutation rules and those of their conjugate chromoelectric fields. We also express the temporal-gauge Hamiltonian in terms of gauge-invariant fields and show that it can be interpreted as a sum of the Coulomb-gauge Hamiltonian and another part that is important for determining the equations of motion of temporal-gauge fields, but that can never affect the time evolution of "physical" state vectors. We also discuss multiplicities of gauge-invariant temporal-gauge fields that belong to different topological sectors and that, in a previous work, were shown to be based on the same underlying gauge-dependent temporal-gauge fields. We argue that these multiplicities of gauge-invariant fields are manifestations of the Gribov ambiguity. We show that the differential equation that bases the multiplicities of gauge-invariant fields on their underlying gauge-dependent temporal-gauge fields has nonlinearities identical to those of the "Gribov" equation, which demonstrates the nonuniqueness of Coulomb-gauge fields. These multiplicities of gauge-invariant fields — and, hence, Gribov copies — appear in the temporal gauge, but only with the imposition of Gauss' law and the implementation of gauge invariance; they do not arise when the theory is represented in terms of gauge-dependent fields and Gauss' law is left unimplemented.

A CALCULATION OF THE MAGNETIC MOMENT OF THE Δ++

1993 ◽  
Vol 08 (34) ◽  
pp. 3283-3290
Author(s):  
MILTON DEAN SLAUGHTER
Keyword(s):  
Quark Model ◽  
Magnetic Moment ◽  
Broken Symmetry ◽  
Flavor Symmetry ◽  
Perturbative Calculation ◽  
Gauge Invariant ◽  
Equal Time ◽  
Asymptotic Level ◽  
Equal Time Commutation ◽  
Static Quark

A fully relativistic, gauge-invariant, and non-perturbative calculation of the Δ++ magnetic moment, μΔ++, is made using equal-time commutation relations (ETCRs) and the dynamical concepts of asymptotic SU F(2) flavor symmetry and asymptotic level realization. Physical masses of the Δ and nucleon are used in this broken symmetry calculation. It is found that μΔ++=2.04μp, where μp is the proton magnetic moment. This result is very similar to that obtained by using SU(6) ⊗ O(3) symmetry or the static quark model.

scholarly journals Tensor gauge condition and tensor field decomposition

2015 ◽  
Vol 30 (35) ◽  
pp. 1550192
Author(s):  
Ben-Chao Zhu ◽  
Xiang-Song Chen
Keyword(s):  
Vector Field ◽  
Tensor Field ◽  
Equations Of Motion ◽  
Gauge Condition ◽  
Coulomb Gauge ◽  
Metric Tensor ◽  
Gauge Invariant ◽  
Pure Gauge ◽  
Gauge Fixing ◽  
Gauge Conditions

We discuss various proposals of separating a tensor field into pure-gauge and gauge-invariant components. Such tensor field decomposition is intimately related to the effort of identifying the real gravitational degrees of freedom out of the metric tensor in Einstein’s general relativity. We show that as for a vector field, the tensor field decomposition has exact correspondence to and can be derived from the gauge-fixing approach. The complication for the tensor field, however, is that there are infinitely many complete gauge conditions in contrast to the uniqueness of Coulomb gauge for a vector field. The cause of such complication, as we reveal, is the emergence of a peculiar gauge-invariant pure-gauge construction for any gauge field of spin [Formula: see text]. We make an extensive exploration of the complete tensor gauge conditions and their corresponding tensor field decompositions, regarding mathematical structures, equations of motion for the fields and nonlinear properties. Apparently, no single choice is superior in all aspects, due to an awkward fact that no gauge-fixing can reduce a tensor field to be purely dynamical (i.e. transverse and traceless), as can the Coulomb gauge in a vector case.

PATH INTEGRALS FOR QUASI-HERMITIAN HAMILTONIANS

2011 ◽  
Vol 20 (05) ◽  
pp. 919-932 ◽  
Author(s):  
R. J. RIVERS
Keyword(s):  
Equations Of Motion ◽  
Path Integrals ◽  
Standard Form ◽  
Functional Integral ◽  
Feynman Diagrams ◽  
Quantum Theories ◽  
Equal Time ◽  
Heisenberg Equations ◽  
Equal Time Commutation ◽  
Heisenberg Equations Of Motion

Inner products in quasi-Hermitian quantum theories, and hence probabilities, are defined through a metric that depends on the details of the Hamiltonians themselves. We shall see that the functional integral for quasi-Hermitian theories, and hence Feynman diagrams, for example, can be calculated without needing to evaluate the metric. The reason turns out be that their derivation is based fundamentally on the Heisenberg equations of motion and the canonical equal-time commutation relations, which retain their standard form. As an application, we show how co-ordinate transformations in the path integral can enable us to recover equivalent Hermitian Hamiltonians.

scholarly journals IV. On the dynamical theory of incompressible viscous fluids and the determination of the criterion

1895 ◽  
Vol 186 ◽  
pp. 123-164 ◽  
Keyword(s):  
Singular Solution ◽  
Physical State ◽  
Theoretical Calculations ◽  
Equations Of Motion ◽  
Dynamical Theory ◽  
Viscous Fluids ◽  
Linear Functions ◽  
Incompressible Viscous Fluids ◽  
Theoretical Results

1. The equations of motion of viscous fluid (obtained by grafting on certain terms to the abstract equations of the Eulerian form so as to adapt these equations to the case of fluids subject to stresses depending in some hypothetical manner on the rates of distortion, which equations Navier seems to have first introduced in 1822, and which were much studied by Cauchy and Poisson) were finally shown by St. Venant and Sir Gabriel Stokes, in 1845, to involve no other assumption than that the stresses, other than that of pressure uniform in all directions, are linear functions of the rates of distortion, with a co-efficient depending on the physical state of the fluid. By obtaining a singular solution of these equations as applied to the case of pendulums in steady periodic motion, Sir G. Stokes was able to compare the theoretical results with the numerous experiments that had been recorded, with the result that the theoretical calculations agreed so closely with the experimental determinations as seemingly to prove the truth of the assumption involved. This was also the result of comparing the flow of water through uniform tubes with the flow calculated from a singular solution of the equations so long as the tubes were small and the velocities slow. On the other hand, these results, both theoretical and practical, were directly at variance with common experience as to the resistance encountered by larger bodies moving with higher velocities through water, or by water moving with greater velocities through larger tubes. This discrepancy Sir G. Stokes considered as probably resulting from eddies which rendered the actual motion other than that to which the singular solution referred and not as disproving the assumption.

scholarly journals GRIBOV PROBLEM FOR GAUGE THEORIES: A PEDAGOGICAL INTRODUCTION

2004 ◽  
Vol 01 (04) ◽  
pp. 423-441 ◽  
Author(s):  
GIAMPIERO ESPOSITO ◽  
DIEGO N. PELLICCIA ◽  
FRANCESCO ZACCARIA
Keyword(s):  
Cross Sections ◽  
Gauge Theories ◽  
Functional Integral ◽  
Point Of View ◽  
Spherically Symmetric ◽  
Abelian Gauge ◽  
Gauge Transformations ◽  
Recent Developments ◽  
Gribov Ambiguity ◽  
Gribov Copies

The functional-integral quantization of non-Abelian gauge theories is affected by the Gribov problem at non-perturbative level: the requirement of preserving the supplementary conditions under gauge transformations leads to a nonlinear differential equation, and the various solutions of such a nonlinear equation represent different gauge configurations known as Gribov copies. Their occurrence (lack of global cross-sections from the point of view of differential geometry) is called Gribov ambiguity, and is here presented within the framework of a global approach to quantum field theory. We first give a simple (standard) example for the SU(2) group and spherically symmetric potentials, then we discuss this phenomenon in general relativity, and recent developments, including lattice calculations.

scholarly journals PHYSICS OF GLUON HELICITY

2014 ◽  
Vol 25 ◽  
pp. 1460028
Author(s):  
XIANGDONG JI ◽  
YONG ZHAO
Keyword(s):  
Matrix Element ◽  
Time Correlation ◽  
Spin Operator ◽  
Large Momentum ◽  
Time Correlation Functions ◽  
Gauge Invariant ◽  
Equal Time ◽  
Polarized Proton ◽  
Gluon Spin ◽  
Gluon Helicity

The total gluon helicity in a polarized proton is shown to be a matrix element of a gauge-invariant but nonlocal, frame-dependent gluon spin operator [Formula: see text] in the large momentum limit. The operator [Formula: see text] is fit for the calculation of the total gluon helicity in lattice QCD. This calculation also implies that parton physics can be studied through the large momentum limit of frame-dependent, equal-time correlation functions of quarks and gluons.

scholarly journals VARIATIONAL PROBLEM FOR THE FRENKEL AND THE BARGMANN–MICHEL–TELEGDI (BMT) EQUATIONS

2013 ◽  
Vol 28 (01) ◽  
pp. 1250234 ◽  
Author(s):  
A. A. DERIGLAZOV
Keyword(s):  
Abelian Group ◽  
Variational Problem ◽  
Classical Theory ◽  
Equations Of Motion ◽  
Lagrangian Formulation ◽  
Gauge Invariant ◽  
Local Symmetries

We propose Lagrangian formulation for the particle with value of spin fixed within the classical theory. The Lagrangian is invariant under non-Abelian group of local symmetries. On this reason, all the initial spin variables turn out to be unobservable quantities. As the gauge-invariant variables for description of spin we can take either the Frenkel tensor or the Bargmann–Michel–Telegdi (BMT) vector. Fixation of spin within the classical theory implies O(ℏ)-corrections to the corresponding equations of motion.

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