Quantum Gauge Field Theory Research Articles

Unbounded representations of symmetry groups in gauge quantum field theory. I. Confinement and differentiation

Symmetry groups and especially the covariance (substitution rules) of the basic fields in a gauge quantum field theory of the Wightman–Gårding type are investigated. By means of the continuity properties hidden in the substitution rules it is shown that every unbounded form–isometric representation U of a Lie group has a form-skew-symmetric differential ∂U with dense domain in the unphysical Hilbert space. Necessary and sufficient conditions for the existence of the closures of U and ∂U as well as for the isometry of U are derived. It is proved that a class of representations of the translation group enforces a relativistic confinement mechanism, by which some or all basic fields are confined but certain mixed products of them are not.

Confinement of quarks and gluons in gauge quantum field theory

A SU(3)-gauge quantum field theory with a quark triplet, an antiquark triplet, and a self-conjugate gluon octet as basic fields is investigated. In virtue of a nontrivial coupling between the representation of the translation group and the SU(3)-color charge of the basic fields it is proved: (i) The basic quark, antiquark, and gluon fields are confined. (ii) Every state vector of the physical Hilbert space is a SU(3)-color singlet state. (iii) Poincaré invariance holds in the physical Hilbert space. These results rest on a nonstandard transformation law of the basic fields with respect to translations. Its meaning within the frame of classical Lagrangian field theory for chromodynamics is investigated.

Remarks about the nilpotent symmetries of quantum gauge field theories

A conjugation symmetric representation of Becchi–Rouet–Stora (BRS) and anti-BRS operations is presented which differs from the usual versions by terms cubic in the ghost fields. Some consequences of requiring quantum gauge field theories to be invariant under both BRS and anti-BRS transformations are examined.

Physical charged sectors in quantum electrodynamics. II. The charge operator

AbstractThe properties of Maxwell type equations and the related problem of approximation of physical charged states are studied in the framework of axiomatic gauge quantum field theory. The charge operator and the physical charged sectors of quantum electrodynamics are constructed under a set of hypotheses which can be verified in perturbation theory and are supported by some nonperturbative arguments.

Planar rotor: Theθ-vacuum structure, and some approximate methods in quantum mechanics

The quantum planar rotor is chosen as a model to test different approximate techniques, emphasizing the analogies between this simple system and the non-Abelian quantum gauge field theories (instantons, $\ensuremath{\theta}$ vacuum, etc.). In particular, variational and perturbative methods, path-integral techniques, and Monte Carlo simulations are applied. It is pointed out that the maximal destructive interference between instantons takes place in the $\ensuremath{\theta}$-vacuum realization of the interacting rotor system with $\ensuremath{\theta}=\frac{1}{2}$, where the tunneling effects are shown to be severely diminished.

Energy eigenvalues for spin from isospin in a gauge theory

In aSU2 quantum gauge field theory, with isospin symmetry broken spontaneously by a triplet of scalar mesons, the energy eigenvalues associated with the spin degrees of freedom arising from conversion of the isospin degrees of freedom are calculated.

Superfield formulation of skew-symmetric tensor gauge field theories

The Abelian gauge quantum field theories of skew-symmetric tensor fields are reviewed in the fremework of the superfield formalism previously proposed. The BRS invariance properties of those theories and the role of the secondary ghosts are discussed.

Local and covariant gauge quantum field theories. Cluster property, superselection rules, and the infrared problem

General structure properties of local and covariant gauge quantum field theories are investigated and a generalized cluster property is proved. Necessary and sufficient conditions are given for the failure of the cluster property which is strictly related to "quark" confinement. The deep relation between superselection rules and the infrared problems is discussed.

Spontaneous symmetry breaking in local gauge quantum field theory; the Higgs mechanism

Spontaneous symmetry breakings in indefinite metric quantum field theories are analyzed and a generalization of the Goldstone theorem is proved. The case of local gauge quantum field theories is discussed in detail and a characterization is given of the occurrence of the Higgs mechanism versus the Goldstone mechanism. The Higgs phenomenon is explained on general grounds without the introduction of the so-called Higgs fields. The basic property is the relation between the local internal symmetry group and the local group of gauge transformations of the second kind. Spontaneous symmetry breaking ofc-number gauge transformations of the second kind is shown to always occur if there are charged local fields. The implications about the absence of mass gap in the Wightman functions and the occurrence of massless particles associated with the unbroken generators in the Higgs phenomenon are discussed.

Spin from Isospin in a Gauge Theory

We show that in an SU(2) quantum gauge field theory, with isospin symmetry broken spontaneously by a triplet of scalar mesons, isospinor degrees of freedom are converted into spin degrees of freedom in the field of a magnetic monopole.