arXiv subjects

D. G. C. McKeon

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

At least 91 records · Page 5Linked to original sources

arXiv2011

Canonical Analysis of Scalar Fields in Two Dimensional Curved Space

Scalar fields on a two dimensional curved surface are considered and the canonical structure of this theory analyzed. Both the first and second order forms of the Einstein-Hilbert (EH) action for the metric are used (these being inequivalent in two dimensions). The Dirac constraint formalism is used to find the generator of the gauge transformation, using the formalisms of Henneaux, Teitelboim and Zanelli (HTZ) and of Castellani (C). The HTZ formalism is slightly modified in the case of the first order EH action to accommodate the gauge transformation of the metric; this gauge transformation is unusual as it mixes the affine connection with the scalar field.

hep-th↗

arXiv2011

Electrodynamics in a Background Chiral Field

We consider the one loop effective action in four dimensional Euclidean space for a background chiral field coupled to a spinor field. It proves possible to find an exact expression for this action if the mass $m$ of the spinor vanishes. If $m$ does not vanish, one can make a perturbative expansion in powers of the axial field that contributes to the chiral field, while treating the contribution of the vector field exactly when it is a constant. The analogous problem in two dimensions is also discussed.

hep-th↗

arXiv2011

The Double Slit Experiment With Polarizers

The double slit experiment provides a standard way of demonstrating how quantum mechanics works. We consider modifying the standard arrangement so that a photon beam incident upon the double slit encounters a polarizer in front of either one or both of the slits.

quant-ph↗

arXiv2011

Non-Quadratic Gauge Fixing and Ghosts for Gauge Theories on the Hypersphere

It has been suggested that using a gauge fixing Lagrangian that is not quadratic in a gauge fixing condition is most appropriate for gauge theories formulated on a hypersphere. We reexamine the appropriate ghost action that is to be associated with gauge fixing, applying a technique that has been used for ensuring that the propagator for a massless spin-two field is transverse and traceless. It is shown that this non-quadratic gauge fixing Lagrangian leads to two pair of complex Fermionic ghosts and two Bosonic real ghosts.

hep-th↗

arXiv2011

Can the Renormalization Group Improved Effective Potential be used to estimate the Higgs Mass in the Conformal Limit of the Standard Model?

We consider the effective potential $V$ in the standard model with a single Higgs doublet in the limit that the only mass scale $μ$ present is radiatively generated. Using a technique that has been shown to determine $V$ completely in terms of the renormalization group (RG) functions when using the Coleman-Weinberg (CW) renormalization scheme, we first sum leading-log (LL) contributions to $V$ using the one loop RG functions, associated with five couplings (the top quark Yukawa coupling $x$, the quartic coupling of the Higgs field $y$, the SU(3) gauge coupling $z$, and the $SU(2) \times U(1)$ couplings $r$ and $s$). We then employ the two loop RG functions with the three couplings $x$, $y$, $z$ to sum the next-to-leading-log (NLL) contributions to $V$ and then the three to five loop RG functions with one coupling $y$ to sum all the $N^2LL...N^4LL$ contributions to $V$. In order to compute these sums, it is necessary to convert those RG functions that have been originally computed explicitly in the minimal subtraction (MS) scheme to their form in the CW scheme. The Higgs mass can then be determined from the effective potential: the $LL$ result is $m_{H}=219\;GeV/c^2$ decreases to $m_{H}=188\;GeV/c^2$ at $N^{2}LL$ order and $m_{H}=163\;GeV/c^2$ at $N^{4}LL$ order. No reasonable estimate of $m_H$ can be made at orders $V_{NLL}$ or $V_{N^3LL}$. This is taken to be an indication that this mechanism for spontaneous symmetry breaking is in fact viable, though one in which there is slow convergence towards the actual value of $m_H$. The mass $163\;GeV/c^2$ is argued to be an upper bound on $m_H$.

hep-ph↗

arXiv2011

The Renormalization Group and the Effective Action

The renormalization group is used to sum the leading-log (LL) contributions to the effective action for a large constant external gauge field in terms of the one-loop renormalization group (RG) function beta, the next-to-leading-log (NLL) contributions in terms of the two-loop RG function etc. The log independent pieces are not determined by the RG equation, but can be fixed by the anomaly in the trace of the energy-momentum tensor. Similar considerations can be applied to the effective potential V for a scalar field phi; here the log independent pieces are fixed by the condition V'(phi=v)=0.

hep-th↗

arXiv2010

Euler-Heisenberg lagrangians and asymptotic analysis in 1+1 QED, part 1: Two-loop

We continue an effort to obtain information on the QED perturbation series at high loop orders, and particularly on the issue of large cancellations inside gauge invariant classes of graphs, using the example of the l - loop N - photon amplitudes in the limit of large photons numbers and low photon energies. As was previously shown, high-order information on these amplitudes can be obtained from a nonperturbative formula, due to Affleck et al., for the imaginary part of the QED effective lagrangian in a constant field. The procedure uses Borel analysis and leads, under some plausible assumptions, to a number of nontrivial predictions already at the three-loop level. Their direct verification would require a calculation of this `Euler-Heisenberg lagrangian' at three-loops, which seems presently out of reach. Motivated by previous work by Dunne and Krasnansky on Euler-Heisenberg lagrangians in various dimensions, in the present work we initiate a new line of attack on this problem by deriving and proving the analogous predictions in the simpler setting of 1+1 dimensional QED. In the first part of this series, we obtain a generalization of the formula of Affleck et al. to this case, and show that, for both Scalar and Spinor QED, it correctly predicts the leading asymptotic behaviour of the weak field expansion coefficients of the two loop Euler-Heisenberg lagrangians.

hep-th↗

arXiv2010

Summing Radiative Corrections to the Effective Potential

When one uses the Coleman-Weinberg renormalization condition, the effective potential $V$ in the massless $ϕ_4^4$ theory with O(N) symmetry is completely determined by the renormalization group functions. It has been shown how the $(p+1)$ order renormalization group function determine the sum of all the N$^{\mbox{\scriptsize p}}$LL order contribution to $V$ to all orders in the loop expansion. We discuss here how, in addition to fixing the N$^{\mbox{\scriptsize p}}$LL contribution to $V$, the $(p+1)$ order renormalization group functions also can be used to determine portions of the N$^{\mbox{\scriptsize p+n}}$LL contributions to $V$. When these contributions are summed to all orders, the singularity structure of \mcv is altered. An alternate rearrangement of the contributions to $V$ in powers of $\ln ϕ$, when the extremum condition $V^\prime (ϕ= v) = 0$ is combined with the renormalization group equation, show that either $v = 0$ or $V$ is independent of $ϕ$. This conclusion is supported by showing the LL, $\cdots$, N$^4$LL contributions to $V$ become progressively less dependent on $ϕ$.

hep-th↗

arXiv2010

The Canonical Structure of the First Order Einstein-Hilbert Action

The Dirac constraint formalism is used to analyze the first order form of the Einstein-Hilbert action in d > 2 dimensions. Unlike previous treatments, this is done without eliminating fields at the outset by solving equations of motion that are independent of time derivatives when they correspond to first class constraints. As anticipated by the way in which the affine connection transforms under a diffeomorphism, not only primary and secondary but also tertiary first class constraints arise. These leave d(d - 3) degrees of freedom in phase space. The gauge invariance of the action is discussed, with special attention being paid to the gauge generators of Henneaux, Teitelboim and Zanelli and of Castellani.

gr-qc↗

arXiv2009

Three-loop Euler-Heisenberg Lagrangian and asymptotic analysis in 1+1 QED

In recent years, the Euler-Heisenberg Lagrangian has been shown to be a useful tool for the analysis of the asymptotic growth of the N-photon amplitudes at large N. Moreover, certain results and conjectures on its imaginary part allow one, using Borel analysis, to make predictions for those amplitudes at large loop orders. Extending work by G.V. Dunne and one of the authors to the three-loop level, but in the simpler context of 1+1 dimensional QED, we calculate the corresponding Euler-Heisenberg Lagrangian, analyse its weak field expansion, and study the congruence with predictions obtained from worldline instantons. We discuss the relevance of these issues for Cvitanovic's conjecture.

hep-th↗

arXiv2009

Radiative Corrections in Vector-Tensor Models

We consider a two-form antisymmetric tensor field ϕminimally coupled to a non-abelian vector field with a field strength F. Canonical analysis suggests that a pseudoscalar mass term \frac{μ^2}{2} \tr (ϕ\wedge ϕ) for the tensor field eliminates degrees of freedom associated with this field. Explicit one loop calculations show that an additional coupling m\tr(ϕ\wedge F) (which can be eliminated classically by a tensor field shift) reintroduces tensor field degrees of freedom. We attribute this to the lack of the renormalizability in our vector-tensor model. We also explore a vector-tensor model with a tensor field scalar mass term \frac {μ^2}{2} \tr (ϕ\wedge\star ϕ) and coupling m\tr(ϕ\wedge \star F). We comment on the Stueckelberg mechanism for mass generation in the Abelian version of the latter model.

hep-th↗

arXiv2009

Resummation of infrared divergences in the free-energy of spin-two fields

We derive a closed form expression for the sum of all the infrared divergent contributions to the free-energy of a gas of gravitons. An important ingredient of our calculation is the use of a gauge fixing procedure such that the graviton propagator becomes both traceless and transverse. This has been shown to be possible, in a previous work, using a general gauge fixing procedure, in the context of the lowest order expansion of the Einstein-Hilbert action, describing non-interacting spin two fields. In order to encompass the problems involving thermal loops, such as the resummation of the free-energy, in the present work, we have extended this procedure to the situations when the interactions are taken into account.

hep-th↗

arXiv2009

Non-Quadratic Gauge Fixing and Global Gauge Invariance in the Effective Action

The possibility of having a gauge fixing term in the effective Lagrangian that is not a quadratic expression has been explored in spin-two theories so as to have a propagator that is both traceless and transverse. We first show how this same approach can be used in spontaneously broken gauge theories as an alternate to the 't Hooft gauge fixing which avoids terms quadratic in the scalar fields. This "non-quadratic" gauge fixing in the effective action results in there being two complex Fermionic and one real Bosonic ghost fields. A global gauge invariance involving a Fermionic gauge parameter, analogous to the usual BRST invariance, is present in this effective action.

hep-th↗

arXiv2009

The Relationship between Bare and Renormalized Couplings in Scalar Electrodynamics

When using dimensional regularization, the bare couplings are expressed as a power series in (2 - n/2)^{-1} where n is the number of dimensions. It is shown how the renormalization group can be used to sum the leading pole, next to leading pole etc. contributions to these sums in scalar electrodynamics (or any theory with multiple couplings.)

hep-th↗

arXiv2008

A Reexamination of the Canonical Structure of the Einstein-Hilbert Action in First-Order Form

A canonical analysis of the Einstein-Hilbert action S_d (d>2) is considered, using the first order form with the metric and affine connection as independent fields. We adopt a conservative approach to using the Dirac constraint formalism; we do not use equations of motion which are independent of time derivatives and correspond to first class constraints to eliminate fields. Applying the Dirac procedure, we find that the primary constraints lead to secondary constraints which are equations of motion not involving time derivatives, and that those secondary constraints which are first class imply novel tertiary constraints which are also first class. Once the constraints and their associated gauge conditions are used to eliminate the non-dynamical degrees of freedom in S_d, there are d(d-3) degrees of freedom left in phase space. We also consider the simpler limiting case of the non-interacting graviton in the first order formalism as well as the effect of adding the action for a massless scalar field to the Einstein-Hilbert action.

gr-qc↗

arXiv2008

Exact One Loop Running Couplings in the Standard Model

Taking the dominant couplings in the standard model to be the quartic scalar coupling, the Yukawa coupling of the top quark, and the SU(3) gauge coupling, we consider their associated running couplings to one loop order. Despite the non-linear nature of the differential equations governing these functions, we show that they can be solved exactly. The nature of these solutions is discussed and their singularity structure is examined. It is shown that for a sufficiently small Higgs mass, the quartic scalar coupling decreases with increasing energy scale and becomes negative, indicative of vacuum instability. This behavior changes for a Higgs mass greater than 168 GeV, beyond which this couplant increases with increasing energy scales and becomes singular prior to the ultraviolet (UV) pole of the Yukawa coupling. Upper and lower bounds on the Higgs mass corresponding to new physics at the TeV scale are obtained and compare favourably with the numerical results of the one-loop and two-loop analyses with inclusion of electroweak couplings.

hep-ph↗

arXiv2008

Using the Renormalization Group Functions to Uniquely Determine the Effective Potential in Massless Scalar Electrodynamics

It has been demonstrated that the effective potential V(ϕ) in a massless O(N) λϕ^4_4 model is determined completely by the renormalization group functions provided the renormalization condition \frac{d^4V}{d ϕ^4}|_{ϕ=μ}=λis used. This is shown to also hold in massless scalar electrodynamics. By employing a variant of the method of characteristics, the sums contributing to the leading-log, next-to-leading-log etc. contributions to V(ϕ) can be evaluated.

hep-th↗

arXiv2008

A Unique Determination of the Effective Potential in Terms of Renormalization Group Functions

The perturbative effective potential V in the massless $λϕ^4$ model with a global O(N) symmetry is uniquely determined to all orders by the renormalization group functions alone when the Coleman-Weinberg renormalization condition $\frac{d^4V}{dϕ^4}|_{ϕ= μ} = λ$ is used, where $μ$ represents the renormalization scale. Systematic methods are developed to express the n-loop effective potential in the Coleman-Weinberg scheme in terms of the known n-loop minimal subtraction (MS) renormalization-group functions. Moreover, it also proves possible to sum the leading- and subsequent-to-leading-logarithm contributions to V. An essential element of this analysis is a conversion of the renormalization group functions in the Coleman-Weinberg scheme to the renormalization group functions in the MS scheme. As an example, the explicit five-loop effective potential is obtained from the known five-loop MS renormalization group functions and we explicitly sum the leading logarithm (LL), next-to-leading (NLL), and further subleading-logarithm contributions to V. Extensions of these results to massless scalar QED are also presented. Because massless scalar QED has two couplings, conversion of the RG functions from the MS scheme to the CW scheme requires the use of multi-scale renormalization group methods.

hep-ph↗