Ghost Fields Research Articles

Chiral bosons through linear constraints.

We study in detail the quantization of a model which apparently describes chiral bosons. The model is based on the idea that the chiral condition could be implemented through a linear constraint. We show that the space of states is of an indefinite metric. We cure this disease by introducing ghost fields in such a way that a Becchi-Rouet-Stora-Tyutin symmetry is generated. A quartet algebra is seen to emerge. The quartet mechanism, then, forces all physical states, except the vacuum, to have a zero norm.

Infrared regularization of quantum gravity

The problem of a smooth massless limit of massive spin-2 field theory is re-examined in the light of modern advances in the understanding of the role of ghosts in gauge theories. It seems that some progress in this direction would be required for a satisfactory formulation of the infrared problem in quantum gravity, and it is more than likely that the infrared difficulties are related to the lack of renormalizability in the ultraviolet. Our definition of smoothness is more restrictive than earlier versions. With the help of auxiliary ghost fields with spin-1 and 0 one can avoid all singularities at zero mass, in the Lagrangian and in the propagators. The number of degrees of freedom is preserved, separately in the physical and in the ghost sectors. The massless limit contains one free one-particle mode of each of the helicities ±2, ±1 and 0. The free Lagrangian is invariant under vectorial as well as under scalar BRST tranformations. Interactions can be introduced consistently to low order in the coupling, but we have not succeeded in constructing the complete nonlinear Lagrangian.

On the universal bundle for gravity

We construct a supergravity type theory based on a superspace whose odd directions consist of a vector, together with a scalar representing a topological BRST shift symmetry. As such, the resulting theory is a theory of topological gravity. The gravitino is interpreted as a ghost field for this shift symmetry and plays the usual role of gauge field for local supersymmetry. Our construction is within the bundle of frames approach to superspace where covariant torsion constraints are analyzed, and we find that the resulting theory contains additional fields which are not present in existing theories of topological gravity. In particular, a minimal solution exists which contains a BRST invariant scalar field. Vector supergravity presents a field theoretic model of a universal bundle for gravity, and we show how the vector supersymmetry operator can be used to generate a hierachy of observables.

Formula omitted] noncritical strings

The “volume” of the diffeomorphism group of a surface depends on the metric on the surface, a dependence distinct from that of the Faddeev-Popov determinant. Assuming such a dependence can be consistently described by a natural extension of the ansatz of David, and Distler and Kawai, an anomalous mixing between the conformal factor and the bosonized ghost field above c = 1 results. Consequences for the physics of strings above c = 1 are indicated.

Coherent Anomaly Method Calculationon the Cluster Variation Method. II.Critical Exponents of Bond Percolation Model

The critical exponents of the bond percolation model are calculated in the D (=2, 3,···)-dimensional simple cubic lattice on the basis of Suzuki's coherent anomaly method (CAM) by making use of a series of the pair, the square-cactus and the square approximations of the cluster variation method (CVM) in the s -state Potts model. These simple approximations give reasonable values of critical exponents α, β, γ and ν in comparison with ones estimated by other methods. It is also shown that the results of the pair and the square-cactus approximations can be derived as exact results of the bond percolation model on the Bethe and the square-cactus lattice, respectively, in the presence of ghost field without recourse to the s →1 limit of the s -state Potts model.

Percolation Critical Exponents Under the Triangle Condition

For independent percolation models, it is shown that if the diagrammatic "triangle condition" is satisfied, then the critical exponents $\delta$ and $\hat\beta$ exist and take their mean-field values, generalizing the criterion introduced in 1984 by Aizenman and Newman for the mean-field value of $\gamma$ in nonoriented percolation. The results apply to a broad class of nonoriented, as well as oriented, weakly homogeneous models, in which the range of the connecting bonds need not be bounded. For the nonoriented case, the condition reduces to the finiteness at the critical point of $\nabla \equiv \sum_{x,y}\tau(0,x)\tau(x,y)\tau(y,0)$ [with $\tau(u,\nu)$ the probability that the site $u$ is connected to $\nu$], which was recently established by Hara and Slade for models with sufficiently spread out connections in $d > 6$ dimensions. Our analysis proceeds through the derivation of complementary differential inequalities for the percolation order parameter $M(\beta,h)$--whose value at $h = 0+$ yields the percolation density, with $\beta$ parametrizing the bond, or site, occupation probabilities and with $h, h \geq 0$, a "ghost field." The conclusion is that under the triangle condition, in the vicinity of the critical point $(\beta_c,0), M(\beta,0+) \approx (\beta - \beta_c)^{\hat\beta}_+$ and $M(\beta_c,h) \approx h^{1/\delta}$, with $\hat \beta = 1$ and $\delta = 2$.

BRST QUANTIZATION OF GAUGE THEORIES ON THE HYPERSPHERE

Drummond and Shore have shown that the most convenient gauge fixing term for gauge theories on a hypersphere is not a perfect square. We show how BRST quantization can be used to generate this gauge fixing term. This involves the introduction of two ghost fields, ci and [Formula: see text], the second of which is an anticommuting vector field. In the Abelian case, only the radial component of [Formula: see text] enters the effective Lagrangian; this is true in the non-Abelian case only if the gauge field is tangential to the hypersphere.

Reparametrization of paths in manifolds

We discuss some aspects of the construction of the principal fiber bundleEiI→EiI/Aut(I), whereEiI is the space of free and injective paths in an arbitrary topological spaceE, and Aut(I) is the group of automorphisms of the interval. The connection with quantum mechanics in the path integral formalism is presented, and it is qualitatively shown the naturalness of the ghost fields.

On lattice chiral gauge theories

We consider the Smit-Swift-Aoki formulation of a lattice chiral gauge theory, in which the Wilson and other non-invariant terms in the action are made gauge-invariant by the coupling with a non-linear auxiliary scalar field, Ω. We show that Ω decouples from the physical states only if appropriate parameters are tuned so as to satisfy a set of BRST identities. In addition, barring unforeseen cancellations, explicit ghost fields are necessary to ensure decoupling. Thus, for these theories to give rise to the correct continuum limit, the requirements discussed in our previous work have to be satisfied. Similar considerations apply to schemes with mirror fermions. Finally, we discuss simpler cases with a global chiral symmetry and show that the theory becomes free at decoupling. Recent numerical simulations agree with our considerations.

Landau gauge and finiteness

General properties of the Landau gauge are discussed by means of a functional differential equation which holds to all orders of perturbation theory and which allows, in particular, to establish the nonrenormalization of the ghost field c as well as of the composite field Tr c 3. The same equation also yields the finiteness of the three-dimensional Chern-Simons model.

Off-shell amplitudes with physical, auxiliary and Faddeev-Popov ghost fields in covariantized light-cone string field theory

We compute the off-shell tree amplitudes involving physical, auxiliary and second-quantized Faddeev-Popov ghost fields for covariantized light-cone string field theory, using off-shell conformal methods. On-shell agreement with the dual-resonance model is shown.

Semirigid supergravity.

We formulate two-dimensional topological gravity starting from local N=2 superconformal geometry. The theory is free from the very beginning. The usual ``twisting'' of the N=2 algebra emerges from symmetry breaking when we expand about a nonzero value for one of the ghost fields. The mysterious linear term in the supercurrent emerges automatically, as does a full superfield formalism for the whole system including ghosts. We analyze the moduli space of the ``semirigid'' super Riemann surfaces associated with this theory, including their allowed degenerations.

A new characterization of BRS-invariant theories with a simple non-abelian gauge group

For a deeper understanding of the gauge and BRS symmetry it is important to know how non-abelian gauge theories are embedded in general non-invariant models. In order to make this problem accessible to a mathematical analysis the most general renormalizable model with interacting vector and ghost fields is restricted to be invariant under rigid transformations of a simple Lie group, here specifically SU( N). By means of the reduction of couplings it is shown that the non-abelian BRS theories in linear gauge can be characterized within this class of models by the property to be renormalizable and to depend only on one interaction coupling. Analyzing the stability one finds that the BRS solution is completely unstable, i.e. the symmetry is realized in a non-trivial way.

The ß-functions of a general non-symmetric model involving vector fields

The ß-functions of a general non-symmetric model with vector and ghost fields, which is renormalizable by power counting, are calculated in one-loop approximation. Because the BRS-symmetric theory without matter fields is embedded, one gets in a special case the renormalization group coefficients of the gauge parameters in general non-linear gauges, which serve also as a stringent check for the correctness of the ß-functions.

Quark-Gluon Interactions at High Temperature and Large Distances

Continuum fourdimensional Quantum Chromodynamics (QCD) including quarks in the regime of high temperature and large distances (the HT regime) is studied to all perturbative orders. The imaginary time (τ) formalism is used. Then, as shown in previous works, QCD is described by a new generating functional ZHT, in which quark fields retain their dependences on τ, while gluon and ghost fields are τ-independent. The invariance of ZHT under BRST transformations in the HT regime is exhibited: it closed quark and electric gluon loops in the HT regime are obtained. The electric mass terms in ZHT. Infinite sets of non-abelian Ward identities for the closed quark and electric gluon loops in the HT regime are obtained. The electric mass terms in ZHT are shown to be infrared finite. We prove to all perturbative orders that one can regard as subdominant, and, hence, neglect consistently the contributions of :i) all closed electric gluon loops, ii) all closed quark loops with three or more vertices in diagrams having an even number of electric gluons (or none) in the external lines. In the HT regime, the axial anomalies are obtained: their expressions in terms of τ-independent gluon fields are similar to those for zero temperature. A non-trivial renormalization group (RG) equation in the HT regime, specifically due to the quark-gluon interaction, is presented. A positive beta function is obtained, and it is argued that interactions are not weak in that regime. The RG and the perturbative analysis to all orders appear to indicate that quarks and gluons may be confined in the HT regime (and, in particular in the Early Universe), due to the infrared divergent magnetic gluon sector. Other possibilities are also discussed.

The Contribution of the Vacuum Fluctuation to Casimir Effect

The path integral method is a useful tool which can be used to calculate contribution of ghost field to Casimir effect. But only free field was considered rather than interaction field. In this paper, we consider contribution of the vacuum fluctuation of QED to Casimir effect with the aid of source-field separation and Wick's expansion, and a little additional attractive force can be obtained from this method.

Quantum mechanics of a twisted superparticle

This paper is devoted to the quantization of the ten-dimensional superparticle in the formulation, due to Siegel, in which the local fermionic symmetry is implemented using explicit gauge fields and in which momentum coordinates conjugate to the fermionic superspace coordinates are introduced. Here, a truncation of the complete N = 1 superparticle is considered (the complete superparticle is analysed in a separate paper). This “truncated model” (which was the first modified superparticle considered by Siegel) is shown to be invariant under a “twisted” N = 2 space-time supersymmetry, and a light-cone gauge analysis shows that the physical spectrum is a representation of this algebra which includes negative norm states. The Batalin-Vilkovisky method is used to covariantly quantize the system in two ways, one with an infinite number of ghost fields and one with only a finite number. In both cases, the BRST cohomology is analysed in detail. Our results illustrate certain general features: (i) In a formulation with gauge fields for the fermionic symmetries the invariance can be fixed by imposing gauge conditions on the gauge fields. This results in a free quantum action, without the need for the problematic field redefinitions that arise in earlier formulations in which gauge conditions are imposed on the spinorial coordinates. (ii) There is an interesting pattern for the infinite number of ghost-for-ghosts, which naturally divide into two sets. The first is an infinite sequence of gauge fields while the second is a set of ghosts for the corresponding sequence of gauge invariances. (iii) The infinite set of quantum fields packages into simple infinite-dimensional spinor representations of the supergroup OSp(9, 1 | 2). The cohomology classes are particularly easy to describe in terms of OSp(9, 1 | 2) spinor notation.

The geometry of BRS transformations

where A is the potential field (connection one form) and 1 is the ghost field. We show how these BRS transformations can be interpreted as purely differential geometric objects. We define a general BRS cohomology H q, p of the infinite dimensional Lie algebra g of infinitesimal gauge transformations with respect to an induced representation. As a special case, namely with respect to the adjoint representation, we obtain the classical BRS transformations as coboundary operator

PARTITION FUNCTIONS OF THE SUPERCONFORMAL GHOST THIRRING MODEL

The one-loop partition functions of the superconformal Thirring model for first order b − c and β − γ ghost fields are studied for both closed and open string boundary conditions. Bosonized partition functions are given by formal series which usually diverge because the energy spectrum of the theory is unbounded below as a correlate of nonunitarity. However, the same partition functions are then calculated by path integral methods directly in the fermionic formulation, and well-defined (convergent) integral representations are obtained. A formal series expansion of those integrals reproduces the bosonized partition functions.

Remarks on mathematical structure of BRST theories

A number of rigorous results concerning the mathematical structure of quantum systems with the BRST symmetry are presented. For studying model-independent properties of such systems, a generalization of the Strocchi-Wightman theory is suggested, which is a Wightman type theory in the Krein space with an OpJ*-algebra of physical and ghost fields. It is proved that the BRST charge operatorQ is either bounded with σ(Q)={0} or unbounded with σ(Q)=¢. A number of conditions equivalent to the “no-ghost theorem” (which states that the kernel ofQ is non-negative) are derived.