N = 4 Yang-Mills theory on the light cone

The 10-dimensional supersymmetric Yang-Mills theory is constructed in the light-cone gauge. When the theory is dimensionally reduced to four dimensions it is shown that the corresponding N = 4 theory is conveniently described in terms of a scalar superfield. This formalism avoids the problem of auxiliary fields but is Lorentz invariant only on the mass shell. Similar formalisms in terms of scalar superfields are also sketched for the other supersymmetric Yang-Mills as well as for N = 8 supergravity.     

High spin spectroscopy in odd-odd 170Lu

High-spin states in doubly odd ¹⁷⁰Lu have been studied through the ¹⁶⁰Gd(¹⁴N, 4nγ) fusion-evaporation reaction at a beam energy of 68 MeV. γγ-coincidences, Eγ,Iγ and angular distribution are measured. For the first time a high-spin level scheme consisting of three rotational structures is proposed. In the πh_9/2Θvp_3/2 yrast band, the (ab) neutron crossing occurs at a rotational frequency of ≈0.27 MeV. This is indicative of the partial disappearance of the blocking effect of the odd neutron. Another signature-split πh_9/2Θvi13/2 band exhibits normal signature-dependence and delayed (bc) neutron crossing is anticipated to occur at h?ω > 0.39 MeV in this structure.     

Hamiltonian treatment of the spherically symmetric einstein-Yang-Mills system

A canonical formalism of the dynamics of interacting spherically symmetric Yang-Mills and gravitational fields is presented. The work is based on Dirac's technique for constrained hamiltonian systems. The gauge freedom of the Yang-Mills field is treated in the same footing with the coordinate transformation freedom of the gravitational field. In particular, the fixation of coordinates and the fixation of the internal gauge are achieved by totally similar techniques. Two classes of spherically symmetric motions are considered: (i) the class for which the Yang-Mills potentials themselves are spherically symmetric (“manifest spherical symmetry”). In this case the results are valid for an arbitrary gauge group; and (ii) the class for which, in the SO(3) gauge group, a rotation in physical space is compensated by a rotation of equal magnitude but opposite direction in isospin space (“spherical symmetry up to a gauge transformation”). For manifest spherical symmetry the problem amounts to effectively dealing with an abelian gauge group and the most general solution of the field equations turns out to be the Reissner-Nordström metric with a Coulomb field. For spherical symmetry up to a gauge transformation the problem is more interesting. the formalism contains then, besides the gravitational variables, three pairs of functions of the radial coordinate that describe the degrees of freedom of the Yang-Mills field. Two pairs of these functions can be combined into a complex field ψ and its conjugate. The hamiltonian is then invariant under r-dependent rotations in the complex ψ-plane. The third degree of freedom plays the role of a compensating field associated with this invariance under localized U(l) rotations. The compensating field can always be brought to zero by a gauge transformation. After this is done the gauge is completely fixed but the problem remains invariant under position independent rotations in the ψ plane. Static solutions of the field equations in this gauge are of the form ψ(r) = (r) exp (iΘ) with Θ independent of position. The particular case Θ = 0 corresponds to the Wu-Yang ansatz. A nontrivial static solution can be found in closed form. The Yang-Mills field is of the generalized Wu-Yang type with an extra electric term, and the metric is the Reissner-Nordström one. It is pointed out that a Higgs field can be easily introduced in the formalism. The addition of the Higgs field does not destroy the invariance of the Hamiltonian under r-dependent rotations in the ψ-plane. The conserved quantity associated with the invariance under ψ → exp (i(const))ψ coincides with the electric charge as defined by 't Hooft in a more general context.     

A method to compare quark and gluon jets in $$e^ + e^ - \to q\bar qg$$ hadronisation

The conserved charges of non-abelian gauge theories are systematically investigated in the framework of the manifestly-covariant canonical formalism. An internal-symmetry superalgebra consisting of 4n+5 generators is found in the Landaugauge case of the Yang-Mills theory, wheren denotes the dimension of the gauge group. Likewise, a superalgebra consisting of 4×6+5 generators is found in the internal-Lorentz (local-Lorentz) part of the vierbein formalism of quantum gravity. It is pointed out that there is a complete parallelism between both superalgebras.     

Reformulation of general relativity as a gauge theory

The starting point is a spinor affine space-time. At each point, two-component spinors and a basis in spinor space, called “spin frame,” are introduced. Spinor affine connections are assumed to exist, but their values need not be known. A metric tensor is not introduced. Global and local gauge transformations of spin frames are defined with GL(2) as the gauge group. Gauge potentials B_μ are introduced and corresponding fields F_μν are defined in analogy with the Yang-Mills case. Gravitational field equations are derived from an action principle. Incases of physical interest SL(2, C) is taken as the gauge group, instead of GL(2). In the special case of metric space-times the theory is identical with general relativity in the Newman-Penrose formalism. Linear combinations of B_μ are generalized spin coefficients, and linear combinations of F_μν are generalized Weyl and Ricci tensors and Ricci scalar. The present approach is compared with other formulations of gravitation as a gauge field.     

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.     

SO q (4) quantum mechanics

In this paper we extend our previously discovered exact solution for an SU(2) Yang-Mills-Higgs theory, to the general group SU(N+1). Using the first-order formalism of Bogomolny, an exact, spherically symmetric solution for the gauge and scalar fields is found. This solution is similar to the Schwarzschild solution of general relativity, in that the gauge and scalar fields become infinite on a spherical shell of radiusr ₀=K. However in the Schwarzschild case the singularity at the event horizon is a coordinate singularity while for the present solution the singularity is a true singularity. It is speculated that this solution may give a confinement mechanism for non-Abelian gauge theories, since any particle which carries the SU(N+1) charge would become permanently trapped inside the regionr<r ₀.     

Geometry of multidimensional universes

LetG be a compact group of transformation (global symmetry group) of a manifoldE (multidimensional universe) with all orbits of the same type (one stratum). We studyG invariant metrics onE and show that there is one-to-one correspondence between those metrics and triples (g _μv,A _μ ^ä ,h _αβ), whereg _μv is a (pseudo-) Riemannian metric on the space of orbits (space-time),A _μ ^ä is a Yang-Mills field for the gauge groupN|H, whereN is the normalizer of the isotropy groupH inG, andh _αβ are certain scalar fields characterizing geometry of the orbits (internal spaces). The scalar curvature ofE is expressed in terms of the component fields onM. Examples and model building recipes are also given. The results generalize those of non-abelian Kaluza-Klein theories to the case where internal spaces are not necessarily group manifolds.     

An effective potential for classical Yang-Mills fields as outline for bifurcation on gauge orbit space

Classical Yang-Mills (Y.M.) equations with static external sources are formulated as a Hamiltonian system with gauge symmetry in A₀ = 0 gauge. Using the concept of a “momentum mapping” (J. Marsden and A. Weinstein, Rep. Math. Phys.5 (1974), 121) on symplectic manifolds with symmetry, an analogue of centrifugal potential of a mass point in a spherically symmetric potential is derived. This gives rise to an effective potentialV_eff, whose critical points are rigorously proved to be in one-to-one correspondence with static Y.M. solutions. V_eff additionally depends on the prescribed external source ?, which is as a constant of motion analogous to angular moment of the mass point. Thus bifurcation of static solutions is caused by bifurcation of critical points of V_eff under variation of the external parameter ?. Some closing remarks on dynamics and stability on gauge orbit space are added.     

Tunneling conductance in ferromagnet/Sr2RuO4 junction: Detection of the d-vector direction

When a spin-triplet superconductor is attached to a ferromagnet, the tunneling conductance depends not only on the degree of the spin polarization but also sensitively on the relative angles between the magnetic moment in ferromagnet and the d-vector in spin-triplet superconductor. We study theoretically the tunneling conductance in ferromagnet/triplet superconductors assuming three nodal unitary gap functions, which are promising candidates for the pairing symmetry of Sr₂RuO₄. Our results suggest that the d-vector direction in Sr₂RuO₄ may be detected by performing angular dependent tunneling spectroscopy in this hybrid structure. We also show that these three gap functions can be distinguished by their distinctive conductance spectra.     

Tensor methods for the exceptional group E6

We present a tensor formalism to describe irreducible representations of the exceptional group E₆. Irreducible tensors are characterized by covariant and contravariant indices associated with the irreducible representation 27, and a third (orthogonal-type) index associated with the 78; contractions of these indices with a set of invariant tensors are required to vanish for irreducibility. The formalism is applied to the reduction of Kronecker products of E₆ irreducible representations. As a further illustration of the method, we construct explicitly the Higgs potential for scalar fields in the E₆ representations 27, 78, 351, 351′.     

Complexification of gauge theories

For the case of a first-class constrained system with equivariant momentum map, we study the conditions under which the double process of reducing to the constraint surface and dividing out by the group of gauge transformations G is equivalent to the single process of dividing out the initial phase space by the complexification G_C of G. For the particular case of a phase space action that is the lift of a configuration space action, conditions are found under which, in finite dimensions, the physical phase space of a gauge system with first-class constraints is diffeomorphic to a manifold imbedded in the physical configuration space of the complexified gauge system. Similar conditions are shown to hold for the infinite-dimensional example of Yang-Mills theories. As a physical application we discuss the adequateness of using holomorphic Wilson loop variables as (generalized) global coordinates on the physical phase space of Yang-Mills theory.     

Quantum Symmetries in the Maxwell–Chern–Simons Theory Coupled to Scalar Fields

The Maxwell-Chern-Simons gauge theory coupled to a complex scalar field is quantized in the Becchi-Rouet-Stora-Tyutin (BRST) path integral formalism. On the basis of the symmetries of a constrained canonical (Hamiltonian) system, we get the quantal conserved angular momentum of the system under the global symmetry transformation. It is shown that fractional spin also appears at the quantum level. The canonical Ward identities for this system are derived under local gauge transformation.     

Conformal symmetry breaking and mass generation

We consider an extension of the supersymmetry formalism in order to include gauge fields. We construct a fiber bundle P(M ₄×{θ}, G) over the superspace with the gauge group as the structural group. We obtain the equations of interacting pure Yang-Mills and massless Higgs fields, considering these fields as the components of the same gauge field. Moreover, by fixing a gauge we generate a mass as a result of the supersymmetry breaking. Supported by Instituto Nacional de Investigacao Cientifica (Lisboa).     

The symmetries in the Maxwell－Chern－Simons theory coupled to matter fields

The Maxwell－Chern－Simons gauge theory coupled to a complex scalar field is quantized in the Becchi－Rouet－Stora－Tyutin path integral formalism. Based on the symmetries of a constrained canonical (Hamiltonian) system, we obtain the quantal conserved angular momentum of the system under the global symmetry transformation. It is shown that fractional spin also appears at the quantum level. The canonical Ward identities for this system are derived under local gauge transformation.     

S Q E D 4 and Q E D 4 on the Null-Plane

We study the scalar electrodynamics (S Q E D ₄) and the spinor electrodynamics (Q E D ₄) in the null-plane formalism. We follow Dirac’s technique for constrained systems to analyze the constraint structure in both theories in detail. We impose the appropriate boundary conditions on the fields to fix the hidden subset first class constraints that generate improper gauge transformations and obtain a unique inverse of the second-class constraint matrix. Finally, choosing the null-plane gauge condition, we determine the generalized Dirac brackets of the independent dynamical variables, which via the correspondence principle give the (anti)-commutators for posterior quantization.     

Contribution of the inhomogeneous waves in angular-spectrum representations

Angular-spectrum representations of wave fields separate naturally into two parts, V_h(R,t) containing only homogeneous plane waves and V_i(R,t) containing only inhomogeneous plane waves. Some properties of V_i(R,t) are presented here. We conclude that, for some problems, V_i(R,t) has several unphysical properties, and that under certain specified conditions, V_i(R,t) can not be neglected compared to V_h(R,t), even far from the sources of the field.     

Topological ϴ-sectors in canonically quantized gravity

It is shown that in canonical quantization of general relativity on a closed, orientable three-manifold Σ, the diffeomorphism group Diff Σ of Σ gives rise to n- and ?sectors analogous to the well-known Yang-Mills results. There is also a “Gribov effect” which precludes the choice of a non-singular gauge for Diff Σ.     

CANONICAL QUANTIZATION OF GAUGE FIELDS(Ⅱ)——SPONTANEOUSLY BROKEN GAUGE FIELDS

In R_ξ gauges a SU（2）spontaneonly broken gauge theory is qnantized within the canonical formalism,and the gauge compensating term is derived.