arXiv subjects

D. G. C. McKeon

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

At least 55 records · Page 3Linked to original sources

arXiv2018

Radiative Corrections in 2+1 Dimensional Supergravity

Supergravity in 2+1 dimensions has a set of first class constraints that result in two Bosonic and one Fermionic gauge invariances. When one uses Faddeev-Popov quantization, these gauge invariances result in four Fermionic scalar ghosts and two Bosonic Majorana spinor ghosts. The BRST invariance of the effective Lagrangian is found. As an example of a radiative correction, we compute the phase of the one-loop effective action in the presence of a background spin connection, and show that it vanishes. This indicates that unlike a spinor coupled to a gauge field in 2 + 1 dimensions, there is no dynamical generation of a topological mass in this model. An additional example of how a BRST invariant invariant effective action can arise in a gauge theory is provided in an appendix where the BRST invariant effective action for the classical Palatini action in 1+1 dimensions is examined.

gr-qc↗

arXiv2017

Quantizing the Palatini action using a transverse traceless propagator

We consider the first order form of the Einstein-Hilbert action and quantize it using the path integral. Two gauge fixing conditions are imposed so that the graviton propagator is both traceless and transverse. It is shown that these two gauge conditions result in two complex Fermionic vector ghost fields and one real Bosonic vector ghost field. All Feynman diagrams to any order in perturbation theory can be constructed from two real Bosonic fields, two Fermionic ghost fields and one real Bosonic ghost field that propagate. These five fields interact through just five three point vertices and one four point vertex.

hep-th↗

arXiv2017

Renormalization Group Summation with Heavy Fields

The summation of logarithmic contributions to perturbative radiative corrections in physical processes through use of the renormalization group equation has proved to be a useful way of enhancing the information one can obtain from explicit calculation. However, it has proved difficult to perform this summation when massive fields are present. In this note we point out that if the masses involved are quite large, the decoupling theorem of Symanzik and of Appelquist and Carazzone can be used to make the summation of logarithms possible.

hep-ph↗

arXiv2017

Perturbative Calculations with the First Order Form of Gauge Theories

The first and second order form of gauge theories are classically equivalent; we consider the consequence of quantizing the first order form using the Faddeev-Popov approach. Both the Yang-Mills and the Einstein-Hilbert actions are considered. An advantage of this approach is that the interaction vertices are quite simple, being independent of momenta. It is necessary however to consider the propagator for two fields (including a mixed propagator). We derive the Feynman rules for both models and consider the one loop correction for the thermal energy momentum tensor.

hep-th↗

arXiv2017

The Effectve Potential in Massless Theories

The effective potential V in a massless self-coupled scalar theory and massless scalar electrodynamics is considered. Both the MS and Coleman-Weinberg renormalization schemes are examined. The renormalization scheme dependence of V is determined. Upon summing all of the logarithmic contributions to V, it is shown that the implicit and explicit dependence on the renormalization scale μ cancels. In addition, if there is spontaneous symmetry breaking, then the dependence on the background field Φ cancels, leaving V flat but with non-perturbative contributions. The quartic scalar coupling in the Coleman-Weinberg renormalization scheme consequently vanishes.

hep-th↗

arXiv2017

Renormalization Scheme Dependence and Renormalization Group Summation

We consider logarithmic contributions to the free energy, instanton effective action and Laplace sum rules in QCD that are a consequence of radiative corrections. Upon summing these contributions by using the renormalization group, all dependence on the renormalization scale parameter $μ$ cancels. The renormalization scheme dependence in these processes is examined, and a renormalization scheme is found in which the effect of higher order radiative corrections is absorbed by the behaviour of the running coupling.

hep-ph↗

arXiv2017

Renormalization Scheme Dependence and the Renormalization Group Beta Function

The renormalization that relates a coupling "a" associated with a distinct renormalization group beta function in a given theory is considered. Dimensional regularization and mass independent renormalization schemes are used in this discussion. It is shown how the renormalization $a^*=a+x_2a^2$ is related to a change in the mass scale $μ$ that is induced by renormalization. It is argued that the infrared fixed point is to be a determined in a renormalization scheme in which the series expansion for a physical quantity $R$ terminates.

hep-ph↗

arXiv2017

Symplectic Analysis of the Two Dimensional Palatini Action

The symplectic analysis, initiated by Faddeev and Jackiw, is applied to the first order (Palatini) form of the Einstein-Hilbert action in 1 + 1 dimensions. The constraints that arise are shown to result in the same gauge transformations that follow from the first class constraints occurring when the Dirac constraint formalism is applied to this action. Problems associated with gauge fixing are discussed.

hep-th↗

arXiv2017

The Effective Potential in Non-Conformal Gauge Theories

By using the renormalization group (RG) equation it has proved possible to sum logarithmic corrections to quantities that arise due to quantum effects in field theories. In particular, the effective potential V in the Standard Model in the limit that there are no massive parameters in the classical action (the "conformal limit") has been subject to this analysis, as has the effective potential in a scalar theory with a quartic self coupling and in massless scalar electrodynamics. Having multiple coupling constants and/or mass parameters in the initial action complicates this analysis, as then several mass scales arise. We show how to address this problem by considering the effective potential in scalar electrodynamics when the scalar field has a tree level mass term. In addition to summing logarithmic corrections by using the RG equation, we also consider the consequences of the condition V'(v)=0 where v is the vacuum expectation value of the scalar. If V is expanded in powers of the logarithms that arise, then it proves possible to show that either v is zero or that V is independent of the scalar. (That is, either there is no spontaneous symmetry breaking or the vacuum expectation value is not determined by minimizing V as V is "flat".)

hep-th↗

arXiv2016

Dual symmetry in a generalized Maxwell theory

We examine Podolsky's electrodynamics, which is noninvariant under the usual duality transformation. We deduce a generalization of Hodge's star duality, which leads to a dual gauge field and restores to a certain extent the dual symmetry. The model becomes fully dual symmetric asymptotically when it reduces to the Maxwell theory. We argue that this strict dual symmetry directly implies the existence of the basic invariants of the electromagnetic fields.

hep-th↗

arXiv2016

Renormalization Scheme Dependence in a QCD Cross Section

The zero to four loop contribution to the cross section $R_{e^{+}e^{-}}$ for $e^{+}e^{-} \longrightarrow$ hadrons, when combined with the renormalization group equation, allows for summation of all leading-log ($LL$), next-to-leading-log $(NLL) \ldots N^3LL$ perturbative contributions. It is also shown how all logarithmic contributions to $R_{e^{+}e^{-}}$ can be summed and that $R_{e^{+}e^{-}}$ can be expressed in terms of the log independent contributions, and once this is done the running coupling $a$ is evaluated at a point independent of the renormalization scale $μ$. All explicit dependence of $R_{e^{+}e^{-}}$ on $μ$ cancels against its implicit dependence on $μ$ through the running coupling $a$ so that the ambiguity associated with the value of $μ$ is shown to disappear. The renormalization scheme dependency of the "summed" cross section $R_{e^{+}e^{-}}$ is examined in three distinct renormalization schemes. In each case, $R_{e^{+}e^{-}}$ is expressible in terms of renormalization scheme independent parameters $τ_i$ and is explicitly and implicitly independent of the renormalization scale $μ$. Two of the forms are then compared graphically both with each other and with the purely perturbative results and the $RG$-summed $N^3LL$ results.

hep-ph↗

arXiv2016

Light Front Quantization with the Light Cone Gauge

The Dirac procedure for dealing with constraints is applied to the quantization of gauge theories on the light front. The light cone gauge is used in conjunction with the first class constraints that arise and the resulting Dirac brackets are found. These gauge conditions are not used to eliminate degrees of freedom from the action prior to applying the Dirac constraint procedure. This approach is illustrated by considering Yang-Mills theory and the superparticle in a 2 + 1 dimensional target space.

hep-th↗

arXiv2016

Renormalization Group Summation of Laplace QCD Sum Rules for Scalar Gluon Currents

We employ renormalization group (RG) summation techniques to obtain portions of Laplace QCD sum rules for scalar gluon currents beyond the order to which they have been explicitly calculated. The first two of these sum rules are considered in some detail, and it is shown that they have significantly less dependence on the renormalization scale parameter $μ^2$ once the RG summation is used to extend the perturbative results. Using the sum rules, we then compute the bound on the scalar glueball mass and demonstrate that the 3 and 4-Loop perturbative results form lower and upper bounds to their RG summed counterparts. We further demonstrate improved convergence of the RG summed expressions with respect to perturbative results.

hep-ph↗

arXiv2015

Renormalization Scheme Dependence in b->u Semileptonic Decays

After reviewing how the renormalization group equation can be used to sum logarithmic corrections to the decay rate for the semi-leptonic process b->u when using minimal subtraction, we consider renormalization scheme dependence for this calculation when employing this renor- malization scheme. In this calculation, an ambiguity resides in the running strong coupling and in the running b quark mass. The ambiguity usually associated with the renormalization mass scale mu is shown to cancel. It is demonstrated how in one renormalization scheme, there are only leading-log contributions to this decay rate. Another choice of renormalization scheme results in the decay rate being expressed in terms of the two-loop contribution to the beta-function associated with the strong coupling and the one-loop contribution to the anomalous mass dimension as well as a set of renormalization scheme invariant parameters.

hep-ph↗

arXiv2015

Renormalization Scheme Dependence with Renormalization Group Summation

We consider all radiative corrections to the total electron-positron cross section showing how the renormalization group equation can be used to sum the logarithmic contributions in two ways. First of all, one can sum leading-log etc. contributions. A second summation shows how all logarithmic corrections can be expressed in terms of log-independent contributions. Next, using Stevenson's characterization of renormalization scheme, we examine scheme dependence when using the second way of summing logarithms. The renormalization scheme invariants that arise are then related to those of Stevenson. We consider two choices of renormalization scheme, one resulting in two powers of a running coupling, the second in an infinite series in the two loop running constant. We then establish how the coupling constant arising in one renormalization scheme can be expressed as a power series of the coupling in any other scheme. Next we establish how by using different mass scale at each order of perturbation theory, all renormalization scheme dependence can be absorbed into these mass scales when one uses the second way of summing logarithmic corrections. We then employ this approach to renormalization scheme dependency to the effective potential in a scalar model, showing the result that it is independent of the background field is scheme independent. The way in which the "principle of minimal sensitivity" can be applied after summation is then discussed.

hep-th↗

arXiv2015

Ghosts from Ghosts in the BRST Formalism

We show that the Hamiltonian HQ introduced in the course of BRST analysis of a gauge theory may in fact be associated with an action that itself is gauge invariant. This action can then be treated using the BRST formalism. We illustrate this by considering the spinning particle and the first order Einstein-Hilbert action in 1 + 1 dimensions.

hep-th↗

arXiv2015

Multiple Gauge Fixing Conditions

We consider how more than one gauge fixing condition can be accommodated within the Feynman path integral both by extending the Faddeev-Popov procedure and the BV approach. The first order Einstein-Hilbert action in 1 + 1 dimensions and the massless spin- 3/2 action are considered.

hep-th↗

arXiv2014

Multi-scale Renormalization Group Methods for Effective Potentials with Multiple Scalar Fields

Multi-scale renormalization group (RG) methods are reviewed and applied to the analysis of the effective potential for radiative symmetry breaking with multiple scalar fields, allowing an extension of the Gildener & Weinberg (GW) method beyond the weak coupling limit. A model containing two interacting real scalar fields is used to illustrate multi-scale RG methods and the multi-scale RG functions of this model are calculated to one-loop order for the $β$ function and two-loop order for the anomalous mass dimension. The introduction of an extra renormalization scale allows the mapping of the effective potential in this model onto an RG-equivalent form with an O(2) symmetric structure along a particular trajectory in the multiple renormalization-scale space, leading to a simplified form of the effective potential. It is demonstrated that the physical content of the effective potential in the original model, referenced to a single conventional renormalization scale, can be extracted from a particular RG-trajectory that connects to this multi-scale O(2)-symmetric form of the effective potential. Extensions of these multi-scale methods for effective potentials in models containing multiple scalars with $O(M)\times O(N)$ symmetry are also discussed.

hep-ph↗