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D. G. C. McKeon

Publications and source records attributed to D. G. C. McKeon.

At least 73 records · Page 4Linked to original sources
arXiv2014

The Canonical Structure of the Superstring Action

We consider the canonical structure of the Green-Schwarz superstring in $9 + 1$ dimensions using the Dirac constraint formalism; it is shown that its structure is similar to that of the superparticle in $2 + 1$ and $3 + 1$ dimensions. A key feature of this structure is that the primary Fermionic constraints can be divided into two groups using field-independent projection operators; if one of these groups is eliminated through use of a Dirac Bracket (DB) then the second group of primary Fermionic constraints becomes first class. (This is what also happens with the superparticle action.) These primary Fermionic first class constraints can be used to find the generator of a local Fermionic gauge symmetry of the action. We also consider the superstring action in other dimensions of space-time to see if the Fermionic gauge symmetry can be made simpler than it is in $2 + 1$, $3 + 1$ and $9 + 1$ dimensions. With a $3 + 3$ dimensional target space, we find that such a simplification occurs. We finally show how in five dimensions there is no first class Fermionic constraint.

hep-th↗
arXiv2013

The Superparticle on the Surface S_2

A superparticle action which is globally supersymmetric in the target space is proposed. The supersymmetry is the supersymmetric extension of the rotation group O(3).

hep-th↗
arXiv2013

The Canonical Structure of the First Order Einstein-Hilbert Action with a Flat Background

It has been shown that the canonical structure of the first order Einstein-Hilbert (1EH) action involves three generations of constraints and that these can be used to find the generator of a gauge transformation which leaves the action invariant; this transformation is a diffeomorphism with field-dependent gauge function while on shell. In this paper we examine the relationship between the canonical structure of this action and that of the first order spin-2 (1S2) action, which is the weak field limit of the Einstein-Hilbert action. We find that the weak field limit of the Possion Brackets (PB) algebra of first class constraints associated with the 1EH action is not that of the 1S2 action.

gr-qc↗
arXiv2013

Treatment of a System with Explicitly Broken Gauge Symmetries

A system in which the free part of the action possesses a gauge symmetry that is not respected by the interacting part presents problems when quantized. We illustrate how the Dirac constraint formalism can be used to address this difficulty by considering an antisymmetric tensor field interacting with a spinor field.

hep-th↗
arXiv2013

On the gauge symmetries of the spinning particle

We reconsider the gauge symmetries of the spinning particle by a direct examination of the Lagrangian using a systematic procedure based on the Noether identities. It proves possible to find a set of local Bosonic and Fermionic gauge transformations that have a simple gauge group structure, which is a true Lie algebra, both for the massless and massive case. This new Fermionic gauge transformation of the "position" and "spin" variables in the action decouples from that of the "einbein" and "gravitino". It is also possible to redefine the fields so that this simple algebra of commutators of the gauge transformations can be derived directly starting from the Lagrangian written in these new variables. We discuss a possible extension of our analysis of this simple model to more complicated cases.

hep-th↗
arXiv2013

Supersymmetric Models on AdS3 and AdS4 Embedding Superspaces

Superspace techniques are used to formulate a supersymmetric model on an AdS3 surface embedded in four dimensions. In this model, the supersymmetry transformation is the "square root" of the transformation generated by the isometry generators of AdS3. Since momentum is not an isometry generator, supersymmetry does not result in equal masses for a Bosonic field and its Fermionic partner. We express this model in terms of coordinates that characterize the AdS3 space. In one coordinate system, it is possible to define a subspace with a Minkowski metric. It becomes possible to infer a model in AdS4 space in which there is a symmetry transformation that relates Bosonic and Fermionic fields. This model is not a consequence of being formulated in superspace and the Fermionic transformation is not the "square root" of an isometry of AdS4.

hep-th↗
arXiv2013

A Massive Non-Abelian Vector Model

The introduction of a Lagrange multiplier field to ensure that the classical equations of motion are satisfied serves to restrict radiative corrections in a model to being only one loop. The consequences of this for a massive non-Abelian vector model are considered.

hep-th↗
arXiv2012

Path Integral Quantization of the First Order Einstein-Hilbert Action from its Canonical Structure

We consider the form of the path integral that follows from canonical quantization and apply it to the first order form of the Einstein-Hilbert action in $d > 2$ dimensions. We show that this is inequivalent to what is obtained from applying the Faddeev-Popov (FP) procedure directly. Due to the presence of tertiary first class constraints, the measure of the path integral is found to have a substantially different structure from what arises in the FP approach. In addition, the presence of second class constraints leads to non-trivial ghosts, which cannot be absorbed into the normalization of the path integral. The measure of the path integral lacks manifest covariance.

hep-th↗
arXiv2012

A Canonical Analysis of the Massless Superparticle

The canonical structure of the action for a massless superparticle is considered in d = 2 + 1 and d = 3 + 1 dimensions. This is done by examining the contribution to the action of each of the components of the spinor θ present; no attempt is made to maintain manifest covariance. Upon using the Dirac Bracket to eliminate the second class constraints arising from the canonical momenta associated with half of these components, we find that the remaining components have canonical momenta that are all first class constraints. From these first class constraints, it is possible to derive the generator of half of the local Fermionic κ-symmetry of Siegel; which half is contingent upon the choice of which half of the momenta associated with the components of θ are taken to be second class constraints. The algebra of the generator of this Fermionic symmetry transformation is examined.

hep-th↗
arXiv2012

On Determining the Running Coupling from the Effective Action

The conformal anomaly has provided an expression for the effective action of gauge theories in the presence of a strong background field in terms of the running coupling constant. We exploit this result to find a novel expansion for the running coupling.

hep-th↗
arXiv2012

Canonical Analysis of a System with Fermionic Gauge Symmetry

A non-Abelian gauge field with a topological action is coupled to a spin 3/2 Majorana spinor. The symmetries of this model are analyzed using the Dirac constraint formalism. These symmetries include a Fermionic symmetry and the algebra of these symmetries closes; it is not the algebra of supergravity. The action is invariant without the need to introduce auxiliary fields.

hep-th↗
arXiv2012

Non-Trivial Ghosts and Second Class Constraints

In a model in which a vector gauge field $W_μ^a$ is coupled to an antisymmetric tensor field $ϕ_{μν}^a$ possessing a pseudoscalar mass, it has been shown that all physical degrees of freedom reside in the vector field. Upon quantizing this model using the Faddeev-Popov procedure, explicit calculation of the two-point functions $<ϕϕ>$ and $ $ at one-loop order seems to have yielded the puzzling result that the effective action generated by radiative effects has more physical degrees of freedom than the original classical action. In this paper we point out that this is not in fact a real effect, but rather appears to be a consequence of having ignored a "ghost" field arising from the contribution to the measure in the path integral arising from the presence of non-trivial second-class constraints. These ghost fields couple to the fields $W_μ^a$ and $ϕ_{μν}^a$, which makes them distinct from other models involving ghosts arising from second-class constraints (such as massive Yang-Mills (YM) models) that have been considered, as in these other models such ghosts decouple. As an alternative to dealing with second class constraints, we consider introducing a "Stueckelberg field" to eliminate second-class constraints in favour of first-class constraints and examine if it is possible to then use the Faddeev-Popov quantization procedure. In the Proca model, introduction of the Stueckelberg vector is equivalent to the Batalin-Fradkin-Tyutin (BFT) approach to converting second-class constraints to being first class through the introduction of new variables. However, introduction of a Stueckelberg vector is not equivalent to the BFT approach for the vector-tensor model. In an appendix, the BFT procedure is applied to the pure tensor model and a novel gauge invariance is found.

hep-th↗
arXiv2012

Generators of Local Supersymmetry Transformation from First Class Constraints

We show how the generator of local supersymmetry transformations can be found from Fermionic first class constraints. This is done by adapting the approaches of Henneaux, Teit- elboim and Zanelli and of Castellani that has been used to find the generator of gauge trans- formations from Bosonic first class constraints. We illustrate how a supersymmetric gauge generator can be found by considering the spinning particle. The invariances that we find are not those presented in the original discussion of the spinning particle.

hep-th↗
arXiv2011

Covariant Gauge Fixing and Canonical Quantization

Theories that contain first class constraints possess gauge invariance which results in the necessity of altering the measure in the associated quantum mechanical path integral. If the path integral is derived from the canonical structure of the theory, then the choice of gauge conditions used in constructing Faddeev's measure cannot be covariant. This shortcoming is normally overcome either by using the "Faddeev-Popov" quantization procedure, or by the approach of Batalin-Fradkin-Fradkina-Vilkovisky, and then demonstrating that these approaches are equivalent to the path integral constructed from the canonical approach with Faddeev's measure. We propose in this paper an alternate way of defining the measure for the path integral when it is constructed using the canonical procedure for theories containing first class constraints and that this new approach can be used in conjunction with covariant gauges. This procedure follows the Faddeev-Popov approach, but rather than working with the form of the gauge transformation in configuration space, it employs the generator of the gauge transformation in phase space. We demonstrate this approach to the path integral by applying it to Yang-Mills theory, a spin-two field and the first order Einstein-Hilbert action in two dimensions. The problems associated with defining the measure for theories containing second-class constraints and ones in which there are fewer secondary first class constraints than primary first class constraints are discussed.

hep-th↗
arXiv2011

An Analysis of the First Order Form of Gauge Theories

The first order form of a Maxwell theory and U(1) gauge theory in which a gauge invariant mass term appears is analyzed using the Dirac procedure. The form of the gauge transformation which leaves the action invariant is derived from the constraints present. A non-Abelian generalization is similarly analyzed. This first order three dimensional massive gauge theory is rewritten in terms of two interacting vector fields. The constraint structure when using light-cone coordinates is considered. The relationship between first and second order forms of the two-dimensional Einstein-Hilbert action is explored where a Lagrange multiplier is used to ensure their equivalence.

hep-th↗