Invariant four-vectors underE(3, 1) and some of its subgroups

Necessary and sufficient conditions ofinvariance on four-vectors under the Poincaré group E(3, 1) and its subgroups are exploited. As an example the Euclidean group in three dimensions and its subgroups are explicitly considered. Their invariant “potentials” are systematically derived.     

Electromagnetic fields with symmetry

In this paper, a study of the connected subgroups of the Poincaré group which can be seen as invariance groups of electromagnetic fields (they will be called CEPS) and of their corresponding invariant fields is reported.It appears that the dimension of such symmetry groups is less than or equal to six. A method of determination of fields invariant under a Poincaré subgroup is proposed and applied to the characterization of all the electromagnetic fields invariant under each six- and five-dimensional CEPS. Moreover, it can be shown that each connected Poincaré subgroup of dimension less than or equal to four is either a CEPS or a subgroup of a CEPS.     

Poincaré-Invariant Coupled-Channel Models for Meson Photoproduction

A general procedure for constructing Poincaré-invariant mass operators in a helicity basis is presented. The procedure is developed in the framework of the instant form of relativistic quantum mechanics, but it can be easily extended to other forms. The method is used to extend a previously developed Poincaré-invariant coupled-channel model for the pion-nucleon system to include a photon-nucleon channel. This makes it possible to carry out calculations on photoproduction from nucleons that satisfy exactly the requirements of special relativity. Methods are given for deriving potentials that couple the photon-nucleon channel to the pion-nucleon channel. These potentials are invariant under gauge transformations of the photon's polarization vector. Amplitudes obtained by solving the Lippmann-Schwinger equations that arise from the Poincaré-invariant mass operators satisfy unitarity, and hence Watson's theorem for photoproduction amplitudes. The methods presented can also be used to develop models for the photoproduction of and mesons, as well as vector mesons. Received April 14, 1997; revised September 24, 1997; accepted for publication October 15, 1997     

Supergravity as a gauge theory of supersymmetry

In a new approach to supergravity we consider the gauge theory of the 14-dimensional supersymmetry group. The theory is constructed from 14×4 gauge fields, 4 gauge fields being associated with each of the 14 generators of supersymmetry. The gauge fields corresponding to the 10 generators of the Poincaré subgroup are those normally associated with general relativity, and the gauge fields corresponding to the 4 generators of supersymmetry transformations are identified with a Rarita-Schwinger spinor. The transformation laws of the gauge fields and the Lagrangian of lowest degree are uniquely constructed from the supersymmetry algebra. The resulting action is shown to be invariant under these gauge transformations if the translation associated field strength vanishes. It is shown that the second-order form of the action, which is the same as that previously proposed, is invariant without constraint.     

Multiplets of linearized SO(2) supergravity

A set of fields for SO(2) supergravity theories is presented on which the gauge algebra closes at the linearized level. The Poincaré Lagrangian and three higher-order invariants are constructed. One of them, an extension of the Weyl Lagrangian, is manifestly invariant under chiral U(2) transformations. Several aspects of our results are discussed, like the particle content of the various Lagrangians and the ghost interactions that occur in the quantised Poincaré action.     

Field theories with an infinite number of conservation laws and Bäcklund transformations in two dimensions

Field theories in two dimensions are generated from the integrability condition of a linear system which possesses Poincaré and internal symmetries. From matrix solutions of this system we get (i) an infinite set of non-local conserved currents and (ii) a family of one-parameter Bäcklund transformations. A large class of models is covered here, as the non-linear sigma, the SU(n) ? SU(n) and the non-abelian gauge invariant projector models.     

A new symmetry group of real self-dual Yang-Mills theory

A new infinite parameter symmetry group is found for real self-dual Yang-Mills theory in four euclidean dimensions. Whereas the gauge potentials transform under a group including local gauge transformations and Kac-Moody-like transformations, the gauge invariant object tr P exp(∮A·dξ) is seen to carry a representation of the Kac-Moody symmetry. Four-dimensional Polyakov loop-space currents restricted to the self-dual sector are constructed from this algebra.     

Manifest gauge and Poincaré covariance

Manifest gauge invariance is known to be incompatible with manifest Poincaré covariance (Strocchi's theorem). By extending the notion of gauge invariance to that of gauge covariance, we circumvent that incompatibility, at least for free electromagnetic potentials. In the new formulation the potentials, A_G, for all permissible gauges G. act on a common Hilbert space. This formulation is shown to be inequivalent to the more conventional ones. (In particular, the Coulomb gauge is now inaccessible.) The abstract gauges G are represented by c-number potentials V_G, which play a central role in the theory. Even without interaction, they obey a field equation with a source, and thus they anticipate the existence of electric charges.     

NONEQUIVALENT SU(2) GAUGE POTENTIALS UNDER EQUAL FIELD STRENTHS AND SOURCES

This paper analyses some common physical characteristics of the gauge field strengths and sources with unequivalent potentials and expresses it in geometrical terms. The eigen-directions of these fields and sources form twistfree curve congrence, which has orthogonal hypersurfaces. The field is Abelianlizable (frequently, even trival) on each hypersurface, i.e. there exists Higgs field, which is invariant under translation along each hypersurface. The gauge field and sources are not altered during the variation of potentials, generated by the gauge rotation around Higgs fields with equal angles on each individual hypersurface but with unequal angles on different hypersurfaces.     

On Three Magnetic Relativistic Schr?dinger Operators and Imaginary-Time Path Integrals

Three magnetic relativistic Schr?dinger operators are considered corresponding to the classical relativistic Hamiltonian symbol with magnetic vector and electric scalar potentials. We discuss their difference in general and their coincidence in the case of constant magnetic fields, as well as whether they are covariant under gauge transformation. Then results are surveyed on path integral representations for their respective imaginary-time relativistic Schr?dinger equations, i.e. heat equations, by means of the probability path space measure coming from the Lévy process concerned.     

RIEMANNIAN STRUCTURE ON GAUGE GROUP AND METRIC COMPATIBLE YANG-MILLS THEORY

A gauge theory with gauge potentials that are compatible with right invariant metric of the gauge group is presented. It is shown that in the metric compatible torsion free gauge theory, gauge potentials can acquire the mass, without introducing the tliggs field. A plane-wave exact solution in vacuum is obtained.     

Quantenphysikalischer Ursprung der Eichidee

The Quantum Physical Origin of the Gauge Idea To consider quantum physics as an interplay of creation and annihilation processes has the consequence that gauge field theories are not only possible but necessary. Since the complex conjugate phase factors of each pair of fermion creators and annihilators can be arbitrary chosen, quantum field theories must be completely phase invariant. Unfortunately, even globally the Dirac equation for systems of free fermions is not phase invariant. The Dirac matrices are namely transformed, if we multiply the spinor components by different constant phase factors. The Dirac equations before and after the transformation are however physically equivalent. We may therefore say: Systems of free fermions will be completely described, only if we consider the class of all equivalent Dirac equations. Since Dirac's commutation relations are unitarily invariant, the class equivalent Dirac equations is invariant under all transformations of the group U 4. Unitary diagonal matrices yield arbitrary phase transformations. Hence, gauge fields of the group U 4 are compatible with the postulate of general phase invariance. These gauge file are so similar to the QED that we may speak of an “extended quantum electrodynamics”, EQE. Here, we will show that EQE exists. The invariant subgroup U 1 U 4 yields QED. The complementary subgroup SU 4 includes four subgroups SU 3, there subgroups O 4, and six subgroups SU 2. The latter ones may yield three pairs of quarks and three pairs of leptons, where the quarks form a group SU 3. More than two times three pairs of elementary fermions does not exist in in EQE Probably, EQE is different from the United EQD and QCD. However, it should be a promising version of a field theory in elementary particle physics, because it follows from an existing symmetry of the empirically wel founded Dirac theory. EQE is therefore free from hypothesis in the Newtonian sense of the word. Whatever it will finally mean, it cannot be rejected, since phase invariance must be required. The invention of new symmetries and the acception of a bie number of independent spinor components is dispensable or must be postponed at least.     

On symmetric gauge fields

The subgroups of the symmetry group of the gauge invariant Lagrangian are studied. For given subgroupG theG-invariant gauge fields are listed.     

Realisation of a Lorentz algebra in Lorentz violating theory

A Lorentz non-invariant higher derivative effective action in flat spacetime, characterised by a constant vector, can be made invariant under infinitesimal Lorentz transformations by restricting the allowed field configurations. These restricted fields are defined as functions of the background vector in such a way that background dependence of the dynamics of the physical system is no longer manifest. We show here that they also provide a field basis for the realisation of a Lorentz algebra and allow the construction of a Poincaré invariant symplectic two-form on the covariant phase space of the theory.     

Abelian Extensions of the Group of Diffeomorphisms of a Torus

In this Letter we construct Abelian extensions of the group of diffecomorphisms of a torus. We consider the Jacobian map, which is a crossed homomorphism from the group of diffeomorphisms into a toroidal gauge group. A pull-back under this map of an invariant central 2-cocycle on a gauge group turns out to be an Abelian cocycle on the group of diffeomorphisms. In the case of a circle we get an interpretation of the Virasoro–Bott cocycle as a pull-back of the Heisenberg cocycle. We also give an Abelian generalization of the Virasoro–Bott cocycle to the case of a manifold with a volume form.     

Constituent quarks from QCD

Starting from the observation that colour charge is only well defined on gauge invariant states, we construct perturbatively gauge invariant, dynamical dressings for individual quarks. Explicit calculations show that an infra-red finite mass-shell renormalisation of the gauge invariant, dressed propagator is possible and, further, that operator product effects, which generate a running mass, may be included in a gauge invariant way in the propagator. We explain how these fields may be combined to form hadrons and show how the interquark potential can now be directly calculated. The onset of confinement is identified with an obstruction to building a non-perturbative dressing. We propose several methods to extract the hadronic scale from the interquark potential. Various extensions are discussed.     

Reissner--Nordström-de--Sitter-type Solution by a Gauge Theory of Gravity

We use the theory based on a gravitational gauge group （Wu＇s model） to obtain a spherical symmetric solution of the field equations for the gravitational potential on a Minkowski spacetime. The gauge group, the gauge covariant derivative, the strength tensor of the gauge feld, the gauge invariant Lagrangean with the cosmological constant, the field equations of the gauge potentiaIs with a gravitational energy-momentum tensor as well as with a tensor of the field of a point like source are determined. Finally, a Reissner-Nordstrom-de Sitter-type metric on the gauge group space is obtained.