Gauge-fixing conditions and natural decompositions of Yang-Mills fields

A general method of constructing canonical decompositions of Yang-Mills fields is presented. The gauge dependence is concentrated to a minimal set of variables which parametrize the group space of the gauge group. The decompositions fall into different classes for different boundary conditions and are characterized by a specific connection to gauge-fixing conditions which are consistent with these boundary conditions. All classes connected to gauge-fixing conditions on the field strength E_aⁱ yield local decompositions generalizing a similar decomposition given by Goldstone and Jackiw for SU(2) Yang-Mills. All classes connected to gauge-fixing conditions. which also involve A_aⁱ yield non-local decompositions in space. Explicit canonical decompositions are given for those classes which are connected to the Coulomb and axial gauges as well as the gauges of the form B_a^b_kE_b^k = 0, where B_a^b_k are constants.     

Gauge invariance of the Euler-Lagrange expressions

We prove, for a Lagrangian density L(g_ij;A _i ⁱ ;A _i ^j ), that the gauge invariance of the Euler-Lagrange expressionsE ⁱ (L) implies the existence of a gauge-invariant scalar densityL ₁, such thatE ⁱ (L) =E ⁱ (L₁). We then prove the uniqueness of the Yang-Mills field equations.     

Hot gluon matter in a constantA 0 background

We compute the effective action of finiteT SU(3) gauge theory in a constant diagonal background fieldA ₀(t,x)=B ₀ ³ T₃+B ₀ ⁸ T₈ in the general covariant background gauge up to terms of orderg ³.B ₀ ^3,8 shield the infrared singularities and the aim is to study whether the minimum of the effective action would determine their values dynamically. We find that the orderg ² term depends explicitly on the gauge fixing parameter ξ. Since the background field screens already at the tree diagram level the interactions of the six non-diagonal gluon fields they do not contribute to the plasmon-likeg ³ term. The two diagonal fieldsA ₀ ³ ,A ₀ ⁸ do, but the electric mass squared they develop will become negative if the background fields are larger than aboutT/g. Hence large background fields make the system unstable.     

Determination of the positions of impurity centers in a dislocation core in a NaCl crystal from magnetoplasticity spectra

The spectra of the mean free paths l(ν) of edge dislocations have been studied in NaCl crystals exposed in the electron paramagnetic resonance scheme to the crossed magnetic fields: the Earth’s field (50 μT) and the pump field (2.5 μT, 5–440 kHz). The spectra have been measured for a series of angles θ = 0°–5° of rotation of the sample around its edge [100] with respect to the Earth’s field. The fine structure of the spectra contains a series of peaks whose resonance frequencies are described by the empirical expression v _i ^± = Asin(θ ± Δθ _i ) ≈ A(θ ± Δθ _i ). The parameters Δθ _i are independent of the angle θ within the experimental errors. Within the model of “frozen” magnetic moments associated with impurity center Ca⁺-Cl⁰, the angles Δθ _i characterize the deviation of the axis of the center from the 〈100〉 direction in the core of a dislocation. These angles can be expressed in terms of the spectra obtained: Δθ _i = (? _i ⁺ ? v _i ^? )/2A. The computer simulation of the edge dislocation core provides the set of the angles Δθ _i close to the measured values. The spin-lattice relaxation time of the center on dislocation has been estimated from the low-frequency edge of the spectrum l(ν) as τ _{s ? l} ～ 10^?4 s.     

Yang-Mills theories in space-like axial and planar gauges

The quantization of Yang-Mills theories according to a canonical procedure is studied first in the axial gauge A₃^a ≡ 0. We show that the perturbative S-matrix cannot be expressed in terms of well-defined distributions in a Hilbert space involving only physical states without conflicting with unitarity. We then resort to the space-like planar gauge and show that it is possible to define a perturbative S-matrix at the price of introducing a set of free ghost fields. The S-matrix is unitary in the subspace of the physically acceptable states on which A₃^a vanish.     

Vacuum copies and perturbation theory in the 't hooft-veltman gauge of QED

The 't Hooft-Veltman gauge condition ?_μA_μ + A_μ² = 0 gives a version of quantum electrodynamics with many similarities to Yang-Mills theory, including the presence of Gribov gauge-fixing ambiguities. We exhibit and discuss some properties of a family of copies of the vacuum, emphasizing their bearing on perturbation theory and the choice of a vacuum state. It is shown that in a general gauge theory, the same perturbation series results from expanding about any gauge-copy of the vacuum.     

Construction of physical states in Yang-Mills theory: The time-like gauge

We construct physical states in pure Yang-Mills theory in the time-like gauge A_α⁰ = 0. We also construct a complete basis in the physical subspace of Hilbert space. Comparison is made with a recent paper by Eylon.     

Deperturbation study of the 0–1 band of the d3Πi-b3Πr transition of the SiO molecule

The structure of the (0–1) band of the d³Π_i-b³Π_r system of SiO has been photographed under high resolution with a chemiluminescent flame source, and a rotational analysis has been carried out. All theoretically predicted 27 branches of the d³Π_i-b³Π_r transition have been identified. The upper-state level is shown to be perturbed by the v = 23 level of the A¹Π state. Due to mixing of the A¹Π with the d³Π, the (23-1) band of the A¹Π-b³Π_r transition has also been observed. The deperturbed molecular constants of the d³Π_i and A¹Π levels have been evaluated.     

Ghost-free non-Abelian gauge theory: renormalization and gauge-invariance

Although it has been known for a long time that the special case n^μA_μ = 0 for an axial gauge of a vector field A_μ, characterized by a direction n_μ, is free from the peculiar loop complications inherent in all other known gauges of non-Abelian gauge theories, practical use of this ghost-free gauge has often met with some reserve. The reasons were always difficulties in the development of the theoretical formalism, all of which can be traced back to a singularity at n^μp_μ = 0 where p is some four-momentum. This paper, which is a sequel to an earlier one by one of the authors, is intended to show that within the functional integration formalism a consistent field theory can be developed. Here we first prove the gauge invariance of the renormalized theory, allowing for the presence of an arbitrary number of scalar and fermion fields with spontaneous symmetry breaking. Then it is shown that all on-shell elements for the physical S-matrix between properly selected physical sources are independent of n_μ (gauge invariant) and so are the renormalized masses.     

Absorption spectrum of the (2, 1) band in the AПi-XΣ system of CS cation

The spectrum of CS⁺ cation was recorded in the 12,235-12,600 cm⁻¹ region by employing optical heterodyne velocity modulation absorption spectroscopy. In combination with simultaneous measurement of optical heterodyne concentration modulation absorption spectroscopy, the spectral lines of CS⁺ blended with the neutral CS lines were identified and extracted from the observed spectra. One hundred and eighty-two spectral lines of CS⁺ were assigned to the (2, 1) band in the A²П_i-X²Σ⁺ system and the improved molecular constants of the upper level (υ = 2) in the A²П_i state were derived by nonlinear least squares fitting.     

On the problem of whether the transition probability plays a role in describing secondary-photon yields

The yields of secondary photons, i.e. photons emitted from sputtered excited states, have been described variously as being proportional to either P(?_i) b_fi or P(?_i) v_fiA_fi. Here P( the function giving the probability of a sputtered particle having excitation energy ?_i, b_fi is the branching ratio, v_fi is the photon frequency, and A_fi is the transition probability. In an attempt to clarify the role of A_fi we have compared experimental yields from bombarded Li, Zn, Cd, Sc, and Ti with tabulated plasma yields and obtained results which suggest that A_fi does not enter, in the case of secondary photons, as a simple multiplier of P(?_i). This is not really surprising, as secondary photons are emitted by isolated atoms whereas the use of the factor A(_fi) assumes thermodynamic equilibrium during decay, as in a plasma. In further experiments, yields were measured versus distance in front of the target. Introducing the decay rate constant, γ_i = ΣA_fi, one finds that for γ_i exceeding 0.4 × 10⁸ s^?1 the signals fall by a factor of 10 within 1.5 mm, for γi of (0.02?0.2) × 10⁸ s^?1 they fall by such a factor within 3–10 mm, and for γi of (0.0004–0.004) × 10⁸ s^?1 significant decay occurs beyond the reach of the detector. This shows that A_fi does indeed play a role in describing photon yields whenever γ_i is sufficiently small, namely in the somewhat complicated relation describing the spatial distribution of the photon emission. Nevertheless, in most situations the use of A_fi is unjustified.     

Rotational analysis of the A2Πi → X2Πr band system of the sulfur monoxide cation,SO+

Six bands in the 0-v″ progression and three bands in the 1-v″ progression of the A²Π_i → X²Π_r visible system of SO⁺ have been recorded photoelectrically and rotationally assigned. Molecular constants for v′ = 0 and 1 in the A state and for v″ = 4–9 in the X state have been obtained using direct fitting and merging techniques.     

Quantization of gauge-fields in the fock-schwinger gauge

The gauge conditionx _μ A ^μ =0 produces a theory which is free from Faddeev-Popov ghosts, but whose Green's functions obviously lack translational invariance. We present for the first time a consistent perturbation theory in this gauge. Besdes discussing example howlocal counter-terms in the action suffice for the one-loop renormalization ofS-matrix elements.     

Two-loop free energy for finite temperatureSU(3) gauge theory in a constant external field

A two-loop calculation of the free energy for finite temperatureSU(3) gauge theory in an external fieldA ₀=const is carried out using background Feynman gauge. Nontrivial minima of the free energy are obtained atA ₀{gT forg→0 corresponding to the gauge symmetry breakingSU(3)→U(1)×U(1). Higher order perturbative effects are briefly discussed.     

On the formulation of D = 11 supergravity and the composite nature of its three-form gauge field

The underlying gauge group structure of the D = 11 Cremmer-Julia-Scherk supergravity becomes manifest when its three-form field A₃ is expressed through a set of one-form gauge fields, , , η_1α, and E^a, ψ^α. These are associated with the generators of the elements of a family of enlarged supersymmetry algebras parametrized by a real number s. We study in detail the composite structure of A₃ extending previous results by D’Auria and Fré, stress the equivalence of the above problem to the trivialization of a standard supersymmetry algebra E^(11|32) cohomology four-cocycle on the enlarged superalgebras, and discuss its possible dynamical consequences. To this aim we consider the properties of the first order supergravity action with a composite A₃ field and find the set of extra gauge symmetries that guarantee that the field theoretical degrees of freedom of the theory remain the same as with a fundamental A₃. The extra gauge symmetries are also present in the so-called rheonomic treatment of the first order D = 11 supergravity action when A₃ is composite. Our considerations on the composite structure of A₃ provide one more application of the idea that there exists an extended superspace coordinates/fields correspondence. They also suggest that there is a possible embedding of D = 11 supergravity into a theory defined on the enlarged superspace .     

Vibronic-spin-orbit coupling in octachlorodibenzo-p-dioxin

The dipole moments of vibronic transitions P _0R caused by vibronic-spin-orbit coupling along the coordinates of out-of-plane vibration modes R (to which the most intense vibronic lines of the fine-structure phosphorescence spectrum correspond) were calculated for the ³ B _1u (π π*) → S ₀ electronic transition in an octachlorodibenzo-p-dioxin molecule. The dependence of distribution (P _0R )² over R on the constant of spin-orbit coupling ?_A in different atomic groups (A = C, O, α-Cl, and β-Cl) of the molecule is ascertained. The contribution of these atomic groups (related to ?_A) to the value of P _0R ⁱ for the transitions from various triplet i-sublevels of the electronic state is determined. The obtained results about the different effect of the α-Cl and β-Cl atoms on the vibronic P _0R ⁱ and pure electronic transition dipole moments are discussed in connection with experimental data on the weak influence of the amount of chlorine atoms in polychlorinated dioxins on the phosphorescence decay time.     

Chemical potentials in gauge theories

One-loop calculations of the thermodynamic potential Ω are presented for temperature gauge and non-gauge theories. Prototypical formulae are derived which give Ω as a function of both (i) boson and/or fermion chemical potential, and in the case of gauge theories (ii) the thermal vacuum parameter A₀=const (A_μ is the euclidean gauge potential). From these basic abelian gauge theory formulae, the one-loop contribution to Ω can readily be constructed for Yang-Mills theories, and also for non-gauge theories.     

Quantum inequivalence of different field representations

The gauge theories of antisymmetric tensor potentials A_μν and A_μν? describe 1 and 0 degrees of freedom, respectively. Yet we show the gravitational trace anomalies of A_μν and a scalar field A to be different, and that of A_μν? to be non-vanishing. Corresponding inequivalences also occur in their one-loop counterterms when the spacetime has non-trivial topology. Furthermore, the coupling of A_μν? to gravity provides a gauge principle derivation of the cosmological constant. Possible applications to supergravity are also discussed.     

Topological vortices in chiral gauge theory of graphene

Generation mechanism of energy gaps between conductance and valence bands is at the centre of the study of graphene material. Recently, Chamon, Jackiw et al. proposed a mechanism of using a Kekulé distortion background field φ and its induced gauge potential A_i to generate energy gaps. In this paper, various vortex structures inhering in this model are studied. Regarding φ as a generic background field rather than a fixed Nielson-Oleson type distribution, we have found two new types of vortices on the graphene surface—the velocity field vortices and the monopole-motion induced vortices—from the inner structure of the potential A_i. These vortex structures naturally arise from the motion of the Dirac fermions instead of from the background distortion field.