Degenerate Vacuum Research Articles

The sources of the A and B degenerate static vacuum fields

We study some known static vacuum solutions of Einstein's equations, namely, the A and B metrics of Ehlers and Kundt. All of them have axial symmetry, so they can be transformed to the Weyl form. In Weyl coordinates log √−g 44 obeys a Laplace equation, and from this a source, calledthe Newtonian image source, can be identified. We use the image sources to give a possible interpretation to the metrics. The procedure is successful in some cases. In others it fails because the Weyl transform does not have reasonable properties at infinity.

Light-front QCD 1+1 coupled to chiral adjoint fermions

We consider SU( N) gauge theory in 1+1 dimensions coupled to chiral fermions in the adjoint representation of the gauge group. With all fields in the adjoint representation the gauge group is actually SU(N) Z N , which possesses nontrivial topology. In particular, there are N distinct topological sectors and the physical vacuum state has a structure analogous to a θ vacuum. We show how this feature is realized in light-front quantization for the case N = 2, using discretization as an infrared regulator. In the discretized form of the theory the nontrivial vacuum structure is associated with the zero momentum mode of the gauge field A +. We find exact expressions for the degenerate vacuum states and the analog of the θ vacuum. The model also possesses a condensate which we calculate. We discuss the difference between this chiral light-front theory and the theories that have previously been considered in the equal-time approach.

Gonihedric 3D Ising actions

We investigate a generalized Ising action containing nearest neighbour, next to nearest neighbour and plaquette terms that has been suggested as a potential string worldsheet discretization on cubic lattices by Savvidy and Wegner. We use both mean field techniques and Monte Carlo simulations to sketch out the phase diagram. The Gonihedric (Savvidy-Wegner) model has a symmetry that allows any plane of spins to be flipped with zero energy cost, which gives a highly degenerate vacuum state. We choose boundary conditions in the simulations that eliminate this degeneracy and allow the definition of a simple ferromagnetic order parameter. This in turn allows us to extract the magnetic critical exponents of the system.

Gauge bosons in superstring theory

Gauge bosons in the Ramond-Ramond sector of four-dimensional models based on the superstring are analyzed. The normalization of degenerate bispinor vacuum states is compared with that of Neveu-Schwarz gauge bosons, an explicit k 0 dependence is shown to be isolated when the polarization vectors are chosen to be in ϵ 0 = 0 gauge; a spin decomposition is derived, and an orthonormal basis for the space of states is defined. Because of the physical state conditions, the bispinors are given as solutions to the Dirac-Ramond equations in the covariant gauge. Aspects of the DKV no-go theorem for non-abelian gauge bosons in this sector are discussed. The on-shell three-point amplitudes involving massless particles of this type are derived in the BRST superghost formalism, and their role in superstring phenomenology is described.

Kinks in finite volume

A (1+1)-dimensional quantum field theory with a degenerate vacuum (in finite volume) can contain particles, known as kinks, which interpolate between different vacua and have non-trivial restrictions on their multi-particle Hilbert space. Assuming such a theory to be integrable, we show how to calculate the multi-kink energy levels in finite volume given its factorizable S-matrix. In massive theories this can be done exactly up to contributions due to off-shell and tunneling effects that fall off exponentially with volume. As a first application we compare our analytical predictions for the kink scattering theories conjectured to describe the sub-leading thermal and magnetic perturbations of the tricritical Ising model with numerical results from the truncated conformal space approach. In particular, for the sub-leading magnetic perturbation our results allow us to decide between the two different S-matrices proposed by Smirnov and Zamolodchikov.

RESTRICTED QUANTUM AFFINE SYMMETRY OF PERTURBED MINIMAL CONFORMAL MODELS

We study the structure of superselection sectors of an arbitrary perturbation of a conformal field theory. We describe how a restriction of the q-deformed sl(2) affine Lie algebra symmetry of the sine-Gordon theory can be used to derive the S-matrices of the Φ(1,3) perturbations of the minimal unitary series. This analysis provides an identification of fields which create the massive kink spectrum. We investigate the ultraviolet limit of the restricted sine-Gordon model, and explain the relation between the restriction and the Fock space cohomology of minimal models. We also comment on the structure of degenerate vacuum states. Deformed Serre relations are proven for arbitrary affine Toda theories, and it is shown in certain cases how relations of the Serre type become fractional spin supersymmetry relations upon restriction.

Topological interpretation of electric charge and the Aharonov-Bohm effect in 2+1 dimensions.

We present a low-energy Lagrangian of planar QED written in terms of the local field V(x), which is the order-parameter field for the Higgs-Coulomb phase transition. In this theory, the electric charge is topological and is quantized on the classical level.$---- The relevant homotopy group is ${\mathrm{\ensuremath{\Pi}}}_{1}$(scrM)=scrZ, where scrM=${\mathit{scrS}}^{1}$ is the manifold of degenerate vacuum states in the Coulomb phase. This vacuum degeneracy is due to spontaneous breaking of a global U(1) symmetry generated by magnetic flux. The electrically charged particles are topological defects of the field V(x). The Aharonov-Bohm effect is understood without use of gauge potential and is a consequence of the extended nature of the charged particles.

Massive soliton stars

The structure of nontopological solutions of Einstein field equations as proposed by Friedberg, Lee, and Pang (1987) is examined. This analysis incorporates finite temperature effects and pair creation. Quarks are assumed to be the only species that exist in interior of soliton stars. The possibility of primordial creation of soliton stars in the incomplete decay of the degenerate vacuum in early universe is explored. Because of dominance of pair creation inside soliton stars, the luminosity of soliton stars is not determined by its radiative transfer characteristics, and the surface temperature of soliton stars can be the same as its interior temperature. It is possible that soliton stars are intense X-ray radiators at large distances. Soliton stars are nearly 100 percent efficient energy converters, converting the rest energy of baryons entering the interior into radiation. It is possible that a sizable number of baryons may also be trapped inside soliton stars during early epochs of the universe. In addition, if soliton stars exist they could assume the role played by massive black holes in galactic centers.

Bulk viscous cosmological model

Robertson—Walker cosmological models with bulkviscosity are investigated explicitly with equation of statep=(γ-1)e. In particular, the physical nature of the extreme cases, i.e., degenerate vacuum bulkviscous fluid model and bulkviscous stiff fluid model are studied in detail.

Expanding algebraically degenerate vacuum spaces with homothetic motions

Halford and Kerr [3] and Halford [4] discuss metrics which arise as solutions of Einstein's vacuum field equations and which have an algebraically degenerate Weyl tensor and an expanding repeated principal null direction. A number of the metrics which are explicitly listed appeared to be new. Here all of these explicit metrics are identified, either as well-known metrics or as particular cases of known metrics with arbitrary functions when these functions take various specific forms. Corrections are made to a number of results in these two papers. An overview of the status of homothetic motions in expanding algebraically degenerate vacuum spacetimes is also given.

Dynamically selected vacuum field configuration in massless QED.

Using the Euclidean functional-integral formalism an effective bilocal action is derived for massless quantum electrodynamics (QED). The vacuum field equation is obtained from this action and it is shown that the dynamically selected vacuum field configuration in massless QED is a class of degenerate, nontrivial field configurations related to each other through a one-parameter Abelian chiral transformation. The existence of a chirally degenerate vacuum establishes that the chiral symmetry manifest in the action of massless QED becomes a hidden symmetry when a particular choice of the vacuum configuration is made. Thus it is established that chiral symmetry is spontaneously broken in the vacuum of massless QED.

Soliton bag models of hadrons from QCD.

Several phenomenological models of hadrons are derived from quantum chromodynamics (QCD). Functional-integral methods are used to obtain an approximate bilocal-field representation of the QCD generating functional. The degenerate vacuum configurations of the action for the bilocal fields have a rich topological structure arising from the dynamically broken chiral symmetry. Restricting the bilocal-field fluctuations to those of local fields results in a local-field bosonization of QCD, from which we obtain values for several meson parameters. A nontopological-soliton ansatz for hadronic states leads to a generalized bag-model action which as special cases contains the chiral-bag-model action and the MIT-bag-model action. All parameters in these actions are calculable and in particular the MIT bag constant is calculated. This work extends our previous calculation of the bag constant.

Domain walls - horizontal epilogue

A horizontal realization of the Peccei-Quinn symmetry together with the presence of B (or B - L) global invariance allow us to solve the domain wall problem without the need for exotic fermions or extra gauge interactions. The intergenerational Yukawa structure dictated by the connectness of the manifold of degenerate vacuum states is analysed.

The form of Killing vectors in expanding ℋℋ spaces

The Killing vector structure of those spaces of complexified general relativity known as expanding hyperheavens is investigated using the methods of spinor calculus. The Killing equations for all left-algebraically degenerate Einstein vacuum spaces are completely integrated. Using the available gauge freedom, the resulting homothetic and isometric Killing vectors are classified in an invariant way according to Petrov–Penrose type. A total of four distinct kinds of isometric Killing vectors and three distinct kinds of homothetic Killing vectors are found. A master Killing vector equation is found which gives the form that the Lie derivative of the metric potential function W must take in order that it admit a given Killing vector.

Mass scales and confinement. A nonperturbative approach

A self-consistent method is used to show that, in the «wrong sign» massless limit, a theory of spinors interacting with massless gluons excludes, in first approximation, the spinor degrees of freedom and sets a mass scale in a gap parameterlike manner. In the lowest order the spectrum will contain bosonic excitations of two different kinds and a vector collective excitation of the fermion background. Although the self-consistent method used leads to a non-Lorentz-invariant infinitely degenerate vacuum, the theory is shown to be consistent with Lorentz invariance at the observational level.

On the covariant description of spontaneously broken symmetry in general field theory

Reducible fieldsA(x) with degenerate vacuum which allow the unitary-symmetry transformationU−1(c)A(x)U(c)=A(x)+c are analysed. We describe the mathematical properties of the « charge integral » related to the conserved current of this spontaneously broken symmetry. Further we discuss the structure of theS-matrix theory in such a generalized field theory as a guide-line for the treatment of more complex examples of spontaneously broken symmetries.

Dynamical symmetry breaking as a bootstrap

This paper is concerned with the bootstrap nature of dynamical symmetry breaking and with the infrared origins of the mass of the electron. We present a general calculational procedure for handling the situation in which a composite operator $\overline{\ensuremath{\Psi}}\ensuremath{\Psi}$ acquires a dynamical vacuum expectation value. We apply our procedure to finite quantum electrodynamics to show how the infrared divergences of the theory self-consistently cause $〈\overline{\ensuremath{\Psi}}\ensuremath{\Psi}〉$ to become nonzero nonperturbatively so that it can provide a scale for a purely dynamical electron mass. Since no Goldstone boson need accompany this spontaneous breakdown, the electron mass bootstraps itself about the ${\ensuremath{\gamma}}_{5}$ degenerate vacuum. The mechanism also yields a new eigenvalue condition for the fine-structure constant. We discuss the deep interplay between the ultraviolet and the infrared, a characteristic feature of dynamical symmetry breaking. We use this interplay to show how to extend the Wilson operator-product expansion to the situation in which there is a degenerate vacuum. We discuss the possibility that the infrared structure of the weak interaction provides a dynamical origin for the Gell-Mann, Oakes, and Renner Hamiltonian. We indicate briefly the possibility that anomalous dimensions can soften a 4-Fermi interaction sufficiently to make it renormalizable.

On the meaning of time-reversal invariance violation

The possible effect of a cosmological background (such as proton-neutron preponderance) on the meaning of time"reversal violation is discussed in the context of the Dürr-Heisenberg degenerate vacuum theory of strangeness.

A new attempt at a unified field theory

It is attempted to construct an improved version of the non-linear spinor field theory originally proposed by the author andHeisenberg. A new perturbation theory dissimilar to the Tamm—Dancoff one is used for the case of degenerate vacuum. Furthermore, a new propagator is introduced and the existence of unitary symmetry is supposed to hold from the very beginning, i.e. essentially a non-linear theory of quarks is proposed.

Is the photon a goldstone particle?

The degenerate vacuum formalism is developed for spin-1 Goldstone particles with an indefinite metric. This formalism eliminates the ambiguities in the early treatments and shows that there is no inconsistency with Poincare invariance. It is argued that if the photon were a Goldstone particle there would be observable consequences, such as apparent angular-momentum nonconservation and violation of the principle of detailed balance.