Gauge Ambiguity Research Articles

Gauge dependence of effective gravitational field. II. Pointlike measuring device

The role of the measurement process in resolving the gauge ambiguity of the effective gravitational potential is reexamined. The motion of a classical pointlike particle in the field of an arbitrary linear source and in the field of another pointlike particle is investigated. It is shown that in both cases the value of the gravitational field read off from the one-loop effective action of the testing particle depends on the Feynman weighting parameter. The found dependence is essential in that it persists in the expression for the gravitational potential. This result disproves the general conjecture about the gauge independence of the effective equations of motion of classical pointlike particles.

Hamiltonian formulations of Yang–Mills theory and gauge ambiguity in quantization

A general formulation of the Hamiltonian in non-Abelian Yang–Mills theory is given. The subject of gauge-fixing ambiguity is investigated. It is shown how this type of degeneracy affects the Faddeev–Popov prescription for the corresponding path-integral formulation at the quantum level. A method for treating this problem is developed. The ideas are implemented by quantizing the theory in the axial gauge. PACS Nos.: 11.10Ef, 11.15-q, 11.15Tk

The maximal abelian gauge, monopoles, and vortices in SU(3) lattice gauge theory

We report on calculations of the heavy quark potential in SU(3) lattice gauge theory. Full SU(3) results are compared to three cases which involve gauge-fixing and projection. All of these start from the maximal abelian gauge (MAG), in its simplest form. The first case is abelian projection to U(1)× U(1). The second keeps only the abelian fields of monopoles in the MAG. The third involves an additional gauge-fixing to the indirect maximal center gauge (IMCG), followed by center projection to Z(3). At one gauge fixing/configuration, the string tensions calculated from MAG U(1)× U(1), MAG monopoles, and IMCG Z(3) are all less than the full SU(3) string tension. The projected string tensions further decrease, by approximately 10%, when account is taken of gauge ambiguities. Comparison is made with corresponding results for SU(2). It is emphasized that the formulation of the MAG is more subtle for SU(3) than for SU(2), and that the low string tensions may be caused by the simple MAG form used. A generalized MAG for SU(3) is formulated.

On certain quasi-local spin-angular momentum expressions for large spheres near the null infinity

The recently suggested quasi-local spin-angular momentum expressions, based on the Bramson superpotential and on the holomorphic or anti-holomorphic spinor fields, are calculated for large spheres near the future null infinity of asymptotically flat Einstein–Maxwell spacetimes. It is shown that although the expression based on the anti-holomorphic spinors is finite and unambiguously defined only in the centre-of-mass frame (i.e. it diverges in general), the corresponding Pauli–Lubanski spin is always finite, free of gauge ambiguities and is built only from the gravitational data. Thus it defines a gravitational spin expression at the future null infinity. The construction based on the holomorphic spinors diverges in the presence of outgoing gravitational radiation. For stationary spacetimes both constructions reduce to the ‘standard’ expression.

Gauge invariance in non–relativistic electrodynamics

A novel Hamiltonian scheme for non–relativistic quantum electrodynamics in which the gauge arbitrariness of the field potential is kept explicit is used to study the gauge–dependence properties of various versions of perturbation theory when resonance and line–broadening effects are admitted. Time–dependent perturbation theory is shown to have severe gauge–dependence problems unless ad hoc modifications are made. A time–independent formulation of S –matrix theory is then studied. Far from resonance, the S –matrix is gauge invariant in all orders of perturbation theory due to a very precise cancellation of gauge–dependent terms which requires, among other things, complete sets of intermediate states; energy conservation also has a crucial role. However, an obvious separation of the S –matrix into a resonant (pole) and non–resonant background leads to incomplete cancellation of the gauge–dependent terms. The introduction of the Heitler damping matrix into an integral equation for the T –matrix leads to a gauge–invariant result. This provides the basis for a gauge invariant S –matrix theory of atoms and molecules interacting with electromagnetic radiation that encompasses resonance and damping effects.

Lorentz gauge and Gribov ambiguity in the compact lattice U(1) theory

The Gribov ambiguity problem is studied for compact U(1) lattice theory within the Lorentz gauge. In the Coulomb phase, it is shown that apart from double Dirac sheets Gribov copies originate mainly from zero-momentum modes of the gauge fields. The removal of the zero-momentum modes is necessary for reaching the absolute maximum of the Lorentz gauge functional.

Anyonic physical observables and spin phase transition

The quantization of a charged matter system coupled to Chern-Simons gauge fields is analyzed in covariant gauge fixing and gauge invariant, physical anyon operators satisfying fractional statistics are constructed in a symmetric phase, based on Dirac's recipe performed on QED. This method provides us a definite way of identifying physical spectrums free from gauge ambiguity and constructing physical anyon operators under a covariant gauge fixing and we analyze the statistical spin phase transition in a symmetry-broken phase predicted by Wen and Zee. The Higgs mechanism transmutes an anyon satisfying fractional statistics into a canonical boson, a spin 0 Higgs boson, or a topologically massive photon which is a Chern-Simons gauge field absorbed would-be Goldstone boson.

Gauge ambiguities in(e→,e′N→)reactions

We examine the sensitivity of the distorted-wave impulse approximation for single-nucleon electromagnetic knockout from valence orbitals to ambiguities in the one-body current operator. Violations of current conservation are classified as gauge ambiguities, whereas the elements of a particular class of structural differences off shell are labeled Gordon ambiguities. Gauge ambiguities in differential cross sections and longitudinal response functions are found to increase with missing momentum and to become particularly severe for low-${Q}^{2}$ kinematical conditions that are far from quasifree but are sometimes used to investigate correlations. The azimuthal asymmetry may provide a useful experimental means for selecting a gauge. Gordon ambiguities increase with ${Q}^{2}$ and are larger for relativistic than for nonrelativistic approaches. Because ambiguities in the one-body current are at least as large as effects due to correlations and there are additional uncertainties due to two-body currents, final-state interactions, and relativistic distortion, we conclude that is unlikely that information about correlations can be extracted from single-nucleon knockout from valence orbitals at large missing momentum. On the other hand, gauge and Gordon ambiguities and uncertainties in final-state interactions have very little effect upon the helicity-dependent recoil polarization, which can be used to investigate the roles of two-body currents and/or possible medium modifications of the one-body current.

Euclidean Thermal Green Functions of Photons in Generalized Euclidean Rindler Spaces for Any Feynman-Like Gauge

The thermal Euclidean Green functions for Photons propagating in the Rindler wedge are computed by employing an Euclidean approach within any covariant Feynman-like gauge. This is done by generalizing a formula which holds in the Minkowskian case. The coincidence of the found (β = 2π)-Green functions and the corresponding Minkowskian vacuum Green functions is discussed in relation to the remaining static gauge ambiguity already found in previous works. Further generalizations to more complicated manifolds are discussed. Ward identities are verified in the general case.

Canonical quantization of photons in a Rindler wedge

Photons and thermal photons are studied in the Rindler wedge employing Feynman’s gauge and canonical quantization. A Gupta–Bleuler-like formalism is explicitly implemented. Nonthermal Wightman functions and related (Euclidean and Lorentzian) Green functions are explicitly calculated and their complex time analytic structure is carefully analyzed using the Fulling–Ruijsenaars master function. The invariance of the advanced minus retarded fundamental solution is checked and a Ward identity discussed. It is suggested that the KMS condition can be implemented to define thermal states also dealing with unphysical photons. Following this way, thermal Wightman functions and related (Euclidean and Lorentzian) Green functions are built up. Their analytic structure is carefully examined employing a thermal master function as in the nonthermal case and other corresponding properties are discussed. Some subtleties arising dealing with unphysical photons in the presence of the Rindler conical singularity are pointed out. In particular, a one-parameter family of thermal Wightman and Schwinger functions with the same physical content is proved to exist due to a remaining (nontrivial) static gauge ambiguity. A photon version of the Bisognano–Wichmann theorem is investigated in the case of photons propagating in the Rindler Wedge employing Wightman functions. In spite of the found ambiguity in defining Rindler Green functions, the coincidence of (β=2π)-Rindler Wightman functions and Minkowski Wightman functions is proved dealing with test functions related to physical photons and Lorentz photons.

Thermal Wightman functions and renormalized stress tensors in the Rindler wedge

The Wightman functions in the Rindler portion of Minkowski space-time are presented for any value of the temperature and for massless spin fields up to s = 1 and the renormalized stress tensor relative to Minkowski vacuum is discussed. A gauge ambiguity in the vector case is pointed out.

ON OPERATOR CONSTRUCTION OF FUNCTIONAL INTEGRAL IN NON-ABELIAN GAUGE THEORY

Here we suggest a gauge-invariant and relativistic-covariant operator canonical construction of the path integral that is useful for considering the problems whose solutions in conventional approaches depend on the gauge choice. We consider the fermionic Green function, gauge ambiguities and infrared behaviour of non-Abelian theories. We show that the “constructive” approach not only solves such an old problem as a correct definition of analytical properties of the fermionic Green functions but also leads to a new picture of colour confinement based on the phenomenon of destructive interference of phase factors arising in the construction of physical variables.

Investigation of gauge ambiguity by means of the theory of harmonic maps

For non-Abelian gauge theory with the groups G = SU(2), SO(4), and SU(3) and dimensions n = 2 and n = 4 of space functional and (in the case of G = SU(3)) finite-dimensional families of potentials A/sub ..mu../ = g/sup -1/delta/sub ..mu..g/ satisfying the condition delta/sub ..mu../A/sub ..mu../ = 0 are found explicitly. The dimension of intersection of the orbit A/sub ..mu../ = g/sup -1/delta/sub ..mu../g and the surface delta/sub ..mu../A/sub ..mu../ = 0 is discussed.

Topology of the gauge condition and new confinement phases in non-abelian gauge theories

The gauge-fixing constraint in a gauge field theory is crucial for understanding both short-distance and long-distance behavior of non-abelian gauge field theories. We define what we call “non-propagating” gauge conditions such as the unitary gauge and “approximately non-propagating” or renormalizable gauge conditions, and study their topological properties. By first fixing the non-abelian part of the gauge ambiguity we find that SU( N) gauge theories can be written in the form of abelian gauge theories with N − 1 fold multiplicity enriched with magnetic monopoles with certain magnetic charge combinations. Their electric chargesare governed by the instanton angle θ. If θ is continuously varied from 0 to 2π and a confinement mode is assumed for some θ, then at least one phase-transition must occur. We speculate on the possibility of new phases: e.g., “oblique confinement,” where θ ⋍ π, and explain some peculiar features of this mode. In principle there may be infinitely many such modes, all separated by phase transition boundaries.

Relation between nonlinear models and gauge ambiguities

We show that the solutions of a class of nonlinear models also generate gauge ambiguities in the vacuum sector of Yang-Mills theories. Our results extend known connections between gauge ambiguities and certain nonlinear σ-models, and clarify the underlying group theory. For many nonlinear models, we also give a simple, intrinsic parametrization of physical fields (which have values in a homogeneous space of a group).

The CP N−1 model with unconstrained variables

The CP N−1 model is investigated in terms of unconstrained variables in both the lagrangian and hamiltonian formulations. The presence of a gauge ambiguity is intimately related with confinement and the appearance of a dynamically generated vector field. Various aspects of the spectrum of states in the large- N limit are investigated.

Gauge ambiguities, zero modes and classification of field size

The occurrence of zero modes for copies of the pure vacuum is studied in Coulomb and Landau gauges. We propose a precise criterion to distinguish small and large fields. An example of a zero mode that reflects symmetries of the generalized Gribov equation is noted.

Consequences of gauge ambiguities

Gribov's prescription for removing the Coulomb gauge ambiguities is applied to the Weinberg-Salam model. We find that (a) it does not provide a current-current weak interaction and (b) confinement of intermediate vector bosons is indicated. We introduce a general functional form factor to handle the gauge ambiguities. Generalizing this procedure to include a functional form factor for the fermion fields as well implies a dynamical mass generation.

On the gauge invariance of transition probabilities

It is emphasized that if one specifies the experimental arrangement in physical terms then there can be no gauge ambiguity of the corresponding exact theoretical predictions.

On the question of gauge ambiguity

On the question of gauge ambiguity