Faddeev-Popov Ghost Fields Research Articles

Field redefinition invariant Lagrange multiplier formalism with gauge symmetries

It has been shown that by using a Lagrange multiplier field to ensure that the classical equations of motion are satisfied, radiative effects beyond one-loop order are eliminated. It has also been shown that through the contribution of some additional ghost fields, the effective action becomes form invariant under a redefinition of field variables, and furthermore, the usual one-loop results coincide with the quantum corrections obtained from this effective action. In this paper, we consider the consequences of a gauge invariance being present in the classical action. The resulting gauge transformations for the Lagrange multiplier field as well as for the additional ghost fields are found. These gauge transformations result in a set of Faddeev–Popov ghost fields arising in the effective action. If the gauge algebra is closed, we find the Becci–Rouet–Stora–Tyutin (BRST) transformations that leave the effective action invariant.

Analysis of unitarity in conformal quantum gravity

We perform a canonical quantization of Weyl’s conformal gravity by means of the covariant operator formalism and investigate the unitarity of the resulting quantum theory. After reducing the originally fourth-order theory to second-order in time derivatives via the introduction of an auxiliary tensor field, we identify the full Fock space of quantum states under a Becchi–Rouet–Stora–Tyutin (BRST) construction that includes Faddeev–Popov ghost fields corresponding to Weyl transformations. This second-order formulation allows the formal tools of operator-based quantum field theory to be applied to quadratic gravity for the first time. Using the Kugo–Ojima quartet mechanism, we identify the physical subspace of quantum states and find that the subspace containing the transverse spin-2 states comes equipped with an indefinite inner product metric and a one-particle Hamiltonian that possesses only a single eigenstate. We construct the Lehmann–Symanzik–Zimmermann (LSZ) reduction formula for the S-matrix in this spin-2 subspace and find that unitarity is violated in scattering events. The explicit way in which this violation occurs represents a new view on the ghost-problem in quadratic theories of quantum gravity.

Quantum Yang-Mills theory in de Sitter ambient space formalism

We present the quantum Yang-Mills theory in the four-dimensional de Sitter ambient space formalism. In accordance with the SU(3) gauge symmetry the interaction Lagrangian is formulated in terms of interacting color charged fields in curved space-time. The gauge-invariant field equations are obtained in an independent coordinate description, and their corresponding color conserved currents are computed. It is shown that the Faddeev-Popov ghost fields appear similarly to their Minkowskian counterparts. We obtain that the free ghost fields are massless minimally coupled scalar fields. The problems of the vacuum state, namely the breaking of de Sitter invariance, and the appearance of infrared divergence in its quantization procedure, are discussed. The existence of an axiomatic quantum Yang-Mills theory within the framework of the Krein space quantization is examined. The infrared divergence regularization of the interaction between the gauge vector fields and the ghost fields is studied in the one-loop approximation. Two different regularization methods are discussed: cut-off regularization and Krein space regularization. A mass term for the gauge vector fields is obtained, which may explain the mass gap and the color confinement problems at the quantum level in de Sitter background. The large curvature limit at the early universe or inflationary epoch is considered.

Perturbative Yang–Mills theory without Faddeev–Popov ghost fields

A modified Faddeev–Popov path integral density for the quantization of Yang–Mills theory in the Feynman gauge is discussed, where contributions of the Faddeev–Popov ghost fields are replaced by multi-point gauge field interactions. An explicit calculation to O(g2) shows the equivalence of the usual Faddeev–Popov scheme and its modified version.

BRST STRUCTURE OF NONLINEAR SUPERALGEBRAS

In this paper we analyze the structure of the BRST charge of nonlinear superalgebras. We consider quadratic nonlinear superalgebras where a commutator (in terms of (super-)Poisson brackets) of the generators is a quadratic polynomial of the generators. We find the explicit form of the BRST charge up to cubic order in Faddeev–Popov ghost fields for arbitrary quadratic nonlinear superalgebras. We point out the existence of constraints on structure constants of the superalgebra when the nilpotent BRST charge is quadratic in Faddeev–Popov ghost fields. The general results are illustrated by simple examples of superalgebras.

The antighost equation in N = 1 super-Yang-Mills theories

The antighost equation valid for usual gauge theories in the Landau gauge, is generalized to the case of N = 1 supersymmetric gauge theories in a supersymmetric version of the Landau gauge. This equation, which expresses the nonrenormalization of the Faddeev-Popov ghost field, plays an important role in the proof of the nonrenormalization theorems for the chiral anomalies.

Covariant gauges at finite temperature

A prescription is presented for real-time finite-temperature perturbation theory in covariant gauges, in which only the two physical degrees of freedom of the gauge-field propagator acquire thermal parts. The propagators for the unphysical degrees of freedom of the gauge field, and for the Faddeev-Popov ghost field, are independent of temperature. This prescription is applied to the calculation of the one-loop gluon self-energy and the two-loop interaction pressure, and is found to be simpler to use than the conventional one.

The polyakov path integral over bordered surfaces

The geometrical approach to the functional integral over Faddeev-Popov ghost fields is developed and applied to construct the BRST extension of the off-shell closed string amplitudes in the constant curvature gauge. In this gauge the overlap path integral for off-shell amplitudes is evaluated. It leads to the nonlocal sewing procedure generating all off-shell amplitudes from the cubic interaction vertex. The general scheme of the reconstruction of a covariant closed string field theory from the off-shell amplitudes is discussed within the path integral framework

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.

Covariant off-shell string amplitudes with auxiliary fields

We employ BRST invariance to explicitly determine the ghost part of the four-point vertex in Witten's open, bosonic, string field theory. This allows the computation of any covariant off-shell four-point amplitude involving physical as well as first-quantized auxiliary or second-quantized Faddeev-Popov ghost fields. We display some examples and complete the proof of associativity of the star product.

On the covariant quantization of the free string:: The conformal structure

We discuss a lagrangian approach to the first quantization of the relativistic string. The conformal properties of the theory are exhibited. We identify the basic fields of the theory, and in particular the Faddeev-Popov ghost fields, as primary conformal fields whose conformal weights are computed.

Background field method in stochastic quantization

The background field approach to non-abelian gauge field theory in stochastic quantization is presented. We discuss on the basis of the Zwanziger-type stochastic gauge fixing, in which we need not introduce the Faddeev-Popov ghost field. We can choose the Zwanziger function, and thus the Langevin equation, to be manifestly covariant under the background gauge transformation. Due to the background gauge covariance, we can easily find a simple Ward identity by which the β-function calculation in stochastic quantization can be greatly simplified. We give the one-loop result of the β-function which is equivalent to the normal one. We also give another β-function, β γ, which will give the relation between the energy scale and the fictitious time scale.

Gauge invariant actions and gauge fixed actions of free superstring field theory

Gauge-fixed covariant actions of free open superstring field theory are re-examined and gauge invariant actions are derived systematically from them. The structure of the gauge-fixed actions is made clear in the course of consistently truncating Faddeev-Popov ghost and Nakanishi-Lautrup string fields.

Ghosts and geometry

We comment on recent attempts to give a geometrical interpretation of the Faddeev-Popov ghost fields.

Geometric description of extended BRS symmetry in superfield formulation

We present here the geometry of the superfield formulation of the extended BRS symmetry. The Faddeev-Popov ghost fields appear as parameters of a gauge transformation in a suitable geometrical structureQ(M S,G S), a fibre bundle constructed over a 4+2 superspaceM S with a suitable supergroupG S as «structure group».

On secondary and higher-generation ghosts

The authors give a simplified discussion of 'secondary' and further Faddeev-Popov ghost fields occurring in covariantly quantised gauge theories with differentially constrained gauge transformations. Several examples of this new phenomenon are presented.

Explicit classical construction of the Faddeev-Popov ghost field

Using explicit co-ordinates, we display the Faddeev-Popov ghost field as the difference between the vertical, globally defined, connection of a principal fibre bundle and the gauge-dependent Yang-Mills field. We identify the Cartan-Maurer fibration conditions with the Becchi-Rouet-Stora equations and define generalized gauge transformations.

Uniqueness connection between charge conjugation and statistics

The charge conjugation properties of bilinear quantum field theories are examined in considerable detail. It is shown that the connection between charge conjugation and statistics is unique. The relation between spin and statistics for a large class of these theories and the statistics of unusual fields such as Faddeev–Popov ghost fields and Gupta’s regularizing fields with negative norm are discussed.

The vanishing norm of Faddeev-Popov ghost fields

It is shown that the charge conjugation properties of relativistic, local gauge theory require that the Faddeev-Popov ghost fields have vanishing norm.

Renormalization of higher-derivative quantum gravity

Gravitational actions which include terms quadratic in the curvature tensor are renormalizable. The necessary Slavnov identities are derived from Becchi-Rouet-Stora (BRS) transformations of the gravitational and Faddeev-Popov ghost fields. In general, non-gauge-invariant divergences do arise, but they may be absorbed by nonlinear renormalizations of the gravitational and ghost fields (and of the BRS transformations). Fortunately, these artifactual divergences may be eliminated by letting the coefficient of the harmonic gauge-fixing term tend to infinity, thus considerably simplifying the renormalization procedure. Coupling to other renormalizable fields may then be handled in a straightforward manner.