Ghost Fields Research Articles

Nonlinear superfield realisations of extended supersymmetries

A superfield extension of the Volkov-Akulov method of constructing nonlinear realisations of the extended super Poincare symmetry is proposed. The formalism describes a partial supersymmetry breaking, the N=1 supersymmetry remaining unbroken. The case N=2, spontaneously broken down to N=1, is considered in detail. It is shown that in the quadratic approximation the corresponding action contains ghost fields in accordance with the general Witten discussion of supersymmetry breaking. Finally, a nonlinear superfield realisation of N=2 Poincare supersymmetry is considered with three scalar Goldstone superfields describing the U(2)/U(1) sector of the internal symmetry.

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.

Geometric Description of BRS* Transformations for the Fields in P4 Theory

The BRS* transformations for the fields in the gauge theory of the 4-dimensional Poincaré group P4 are derived with the help of the heuristic geometrical approach. There appear three types of ghost fields. Among them, two types correspond to the translational and the additional one to the abelian T4 group. When the simplest form of the Lagrangian is adopted, the theory is shown to be equivalent to Einstein’s theory of gravitation.

Classification of the Yang-Mills anomalies in even and odd dimension

The general solution to the Wess-Zumino consistency equation is constructed. It does not depend on the antighost, nor on the sources, but only on the gauge and ghost fields through the geometrical combination A ̃ = A μ dx μ+c . In dimension d, the anomalies with ghost number g are related to the off-BRS (d+s)-closed exterior forms I( A ̃ , F) , of degree d + g + 1 and at most g-linear in A ̃ .

Geometric Description of BRS Transformation for the Fields in P4 Theory

When the BRS transformation of the vierbein fields are defined as Eq. (26), (26) The changes of the following equations (27)˜(31) are unnecessary. The ghost fields cta defined in Eq. (26) correspond to those in the abelian T4 theory.

Algebraic structure of quantum gravity and the classification of the gravitational anomalies

The BRS equations of quantum gravity and of gauge theories coupled to gravity are established in a formalism which unifies the gauge and ghost fields. This formalism allows one to disentangle the algebra of Lorentz transformations from the local diffeomorphisms. We use it to classify the potential anomalies in the Einstein-Yang-Mills theory. All anomalies which can be written as exterior forms have the structure of usual flat space ABBJ anomalies related to the direct product of the Lorentz group by the Yang-Mills group. The others are related to the ungauged coordinate dilatations. Our results hold true in the presence of torsion.

Some dynamical aspects of compositeness in quantum field theory

The dynamics of composite particles, in particular composite vector bosons, is discussed. An example in two dimensions illustrates the relevance of asymptotic freedom. Several dynamical models in four dimensions are investigated. Negative metric ghost fields, such as occur in theories with non-compact symmetries, may cure some of the problems encountered. Possible applications are discussed.

Anomalies and gauge symmetry

Anomalies are known to have an intrinsic geometrical meaning. Using a formalism where the gauge condition is never made explicit we reanalyze the gauge theory anomaly problem. By requiring simultaneously the BRS and anti-BRS invariances, we do not need to use in our study the gauge dependent anti-ghost equation of motion. Then all equations definining the anomaly are independent of all parameters specifying the lagrangian. Not only does this stress explicitly the geometrical nature of the anomaly problem, but it allows for a single analysis for all possible BRS and anti-BRS invariant gauges, including those with four-ghost interactions. Our method for solving the anomaly equations is as a new sign of the relevance of the formalism in which the ghost components are unified with those of the classical gauge field, the ghost fields playing the role of a “connection” along unphysical directions. We recover the ABJ anomaly directly from the structure of BRS equations, as a straightforward application of the Chern-Weil theorem in some enlarged space. The method can be formally extended to higher space-time dimensions, and a general formula for “anomalies” in any even dimension is given.

Explicit evaluation of group-invariant measure as by-product of path integration over Yang–Mills fields

A method is presented for explicitly evaluating the invariant measure over a Lie group, for any parametrization in which a generic group element is written as a product of exponentials of elements of the Lie algebra. The measure is expressed as a transition amplitude associated with the quantum mechanical evolution operator of the ‘‘ghost fields’’ which appear in the path integral over Yang–Mills fields. As an illustration of the method, the measure is evaluated in two cases: (i) in canonical coordinates, for an arbitrary Lie group which admits them; (ii) in terms of Euler angles, for the group of rotations in three-dimensional space.

Yang-Mills theories in space-like axial and planar gauges

The quantization of Yang-Mills theories according to a canonical procedure is studied first in the axial gauge A 3 a ≡ 0. We show that the perturbative S-matrix cannot be expressed in terms of well-defined distributions in a Hilbert space involving only physical states without conflicting with unitarity. We then resort to the space-like planar gauge and show that it is possible to define a perturbative S-matrix at the price of introducing a set of free ghost fields. The S-matrix is unitary in the subspace of the physically acceptable states on which A 3 a vanish.

Finite-temperature quantum field theory in Minkowski space

We formulate finite-temperature quantum field theories in Minkowski space (real time) using Feynman path integrals. We show that at non-zero temperature a new field arises which plays the role of a ghost field and is necessary for unambiguous Feynman rules. Consequently, the finite-temperature Lagrangian is different from the zero-temperature one and a new, discrete Z 2 symmetry arises. We discuss the functional formalism and spontaneous symmetry breakdown at finite temperature and also the possibility of spontaneous breakdown of the (thermal) Z 2 symmetry.

Proper-time gauge in the quantum theory of gravitation

The proper-time gauge appears to be the simplest one consistent with the invariance properties of the gravitational action. It also permits one to implement in a direct manner the requirement of causality in the quantum theory of gravitation. In this paper the measure for the path integral over gravitational fields in the proper-time gauge is explicitly worked out. The corresponding propagation amplitude results after the following steps: (i) evaluating the amplitude for a transition between two three-geometries for which one specifies the relative pointwise proper-time separation and relative spatial coordinate system, (ii) integrating over all positive proper-time separations with a logarithmic measure, (iii) averaging over all possible choices of the relative coordinate system. (An explicit expression for the measure over the diffeomorphism group in terms of a set of ghost fields emerges from the path integral.)

Gauge fields, BRS symmetry and the Casimir effect

The canonical quantization of the photon field in covariant gauge is studied in the presence of static boundaries, on which the field satisfies either “bag” or superconductor boundary conditions. The inclusion of the Fadeev-Popov ghost fields is found to be essential for agreement with Coulomb gauge calculations of the Casimir energy.

One-loop renormalisation of superfield Yang-Mills theories

We calculate the one-loop ultraviolet and infrared divergences in superfield Yang-Mills theories to fourth order in the gauge field. The ultraviolet divergences require a non-linear field renormalisation, and graphs with external ghost fields show that a non-linear renormalisation of the gauge-fixing function is also needed. These observations are confirmed by calculations incorporating matter fields, which are used to extend the result to all orders for the special case of SU(2). On the other hand the infrared divergences, which occur in general gauges, are apparently impossible to remove in any acceptable way.

Program Gas Well Build-Up Testsa Field Case Illustration Of Solution Through The Use Of Combined Techniques

Abstract This paper illustrates with a four-well example several problems that can be encountered ill the analysis of pressure buildup data. The subject wells being analyzed are in the Ghost River (Salter) Field in southern Alberta, Canada. They are completed in either single or dual zone low permeability Mississippian carbonate sour gas reservoirs, and in all cases have been given acid fracture stimulations. Of the seven tests analyzed, only one test had complete bottomhole pressure data available. Of the remainder, two had partial bottomhole recorded pressure data and four had only surface-recorded pressure data. Other important points to the evaluation are:—hydrates were encountered throughout much of the testing; as a result, production test flow rates varied considerably in some cases—commingling of production from two zones occurred in some of the tests—changing wellbore temperature effects are evident—only minor amounts of reservoir liquids were produced during testing. Through the combined use of pseudo-pressures, superposition radial flow plots, square root plots, type curves, wellbore storage theory and other techniques, solutions are obtained and interpretations made. FIGURE 1. Field and well location map, Ghost River (Salter). (Available in full paper) Introduction The Ghost River Field (also named the Salter Field by the Alberta Energy Resources Conservation Board) lies in the Alberta Foothills approximately 40 miles west northwest of the city of Calgary, as shown in Figure 1. The field is defined by four gas wells (in Lsd's 4–1–27–8, 4–36–26–8, 6–25–26–8, and 15–24–26–8 W5M), one suspended well, and two dry holes. Three of the subject gas wells (4–36, 6–25, and 15–24) were completed in two zones, being the Mount Head and Turner Valley Sections of the Mississippian Formation. The remaining gas well (4–1) was completed in only the Mount Head Section. A typical well completion is illustrated in Figure 2. Net pays vary from 25 feet in the Mount Head at 4–1 to a total of 243 feet in the two zones at 6–25. Average porosity in each zone is approximately 4%. Wellbore and reservoir parameters for the Ghost Field are listed in Table 1. All wells were acid stimulation fractured. Following the fracturing, production tests with varying rates and test procedures were run. On the discovery well, 4–36–26–8 W5, each zone was completed, fractured and AOF tested separately. However, downhole hydrate formation hampered the individual zone AOF tests. Finally, a commingled Mount Head and Turner Valley test was run in order to get a rate high enough to overcome the hydrate problems. As a result of the difficulties experienced with 4–36, the test procedures on subsequent wells were modified. The Mount Head and Turner Valley zones were commingled from the start, less clean-up flow was used, and more emphasis was placed on obtaining build-up data. Typical early and later flow test procedures are illustrated in Figures 3 and 4, respectively. TABLE 1, Ghost River Field — reservoir data (Available in full paper) A study was undertaken to analyze these tests, with the major objective being to determine values of the reservoir permeability.

Geometrical interpretation of the BRS transformations of quantum gravity

A geometrical interpretation of ghost fields and BRS transformations in the framework of the metric formulation of quantum gravity is proposed without introducing a superspace.

The two quantum symmetries associated with a classical symmetry

Given a classical local symmetry, it is shown how to build two associated quantum symmetries s and s . These generalized BRS and anti-BRS symmetries interchange classical and ghost fields. A direct consequence of the closure and Jacobi identities of the classical algebra are the complete nilpotency relations s 2 = s s+ ss = s 2 = 0 . This nilpotency allows one to derive very simply the correct quantum lagrangian from the classical one without recourse to the Faddeev-Popov construction. A simple formal proof is given, showing that s and s are preserved by renormalization.

Transition amplitude in the quantum theory of the relativistic membrane

Abstract The transition amplitude between two configurations of the n-dimensional relativistic membrane is written explicitly. Its expression contains coupling terms of order 2n in the ghost fields, despite the fact that the algebra of the gauge transformations is closed in the covariant formalism. The inclusion of these additional coupling terms ensures the BRS invariance of the effective action.

Graded fibre bundles and unified field theories

A gauge field theory is constructed in terms of connections over fibre bundles using a supergroup as structure group. Superconnections are imposed to eliminate ghost fields with negative energy but these break the conformal symmetry. The theory can be related to classical theory by use of suitable scaling factors: this leads to specified masses for the Higgs multiplet and the spinor multiplet.

The principle of BRS symmetry: An alternative approach to Yang-Mills theories

Postulating BRS and anti-BRS symmetry of the quantum Yang-Mills lagrangian and of the measure of the functional integral, we prove gauge invariance and renormalizability and recover the classical theory from the quantum one. We also give a heuristic interpretation of the BRS and anti-BRS symmetry. The most general BRS and anti-BRS admissible gauges are linear in the gauge field, but may depend non-linearly on the ghost fields.