D. McKeon - Academia.edu (original) (raw)

Papers by D. McKeon

Canadian Journal of Physics, 2011

Although special relativity limits the actual velocity of a particle to the velocity of light, c,... more Although special relativity limits the actual velocity of a particle to the velocity of light, c, the observed velocity need not be the same as the actual velocity, as the observer is only aware of the position of a particle at the time in the past when it emitted the detected signal. We consider the apparent speed and acceleration of a particle in two cases, one when the particle is moving with a constant speed and the other when it is moving with a constant acceleration. One curious feature of our results is that in both cases, if the actual velocity of the particle approaches c, then the apparent velocity approaches infinity when it is moving toward the observer and c/2 when it is moving away from the observer.

International Journal of Modern Physics E, 2007

Two approaches to renormalization-group improvement are examined: the substitution of the solutio... more Two approaches to renormalization-group improvement are examined: the substitution of the solutions of running couplings, masses and fields into perturbatively computed quantities is compared with the systematic sum of all the leading log (LL), next-to-leading log (NLL) etc. contributions to radiatively corrected processes, with n-loop expressions for the running quantities being responsible for summing Nn-1LL contributions. A detailed comparison of these procedures is made in the context of the effective potential V in the 4-dimensional O(4) massless λϕ4 model, showing the distinction between these procedures at two-loop order when considering the NLL contributions to the effective potential V.

Canadian Journal of Physics, 2016

We consider the canonical structure of the Green–Schwarz superstring in 9 + 1 dimensions using th... more 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 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 ...

Progress of Theoretical and Experimental Physics, 2014

A system in which the free part of the action possesses a gauge symmetry that is not respected by... more 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.

Physical Review D, 1987

We develop a formalism for computing one-particle-irreducible Green's functions in theories with ... more We develop a formalism for computing one-particle-irreducible Green's functions in theories with superfields. To lowest order, this reduces to a perturbative expansion of the [ function. All symmetries of the original theory are preserved as the initial Lagrangian is not altered for the purpose of introducing a regulating parameter. Moreover, no divergent integrals are encountered. We illustrate the formalism by reference to the Wess-Zumino model with one pair of chiral and antichiral superfields. As an example, we show that the result for the massless propagator usually obtained using the Feynman diagrammatic technique is recovered without having to perform any explicit renormalization.

Physical Review D, 1985

Each of three procedures, dimensional regularization, regularization by dimensional reduction (RD... more Each of three procedures, dimensional regularization, regularization by dimensional reduction (RDR), and preregularization, are used to compute the chiral anomaly by considering the full structure of the &#x27;&#x27;un-momentum-contracted&#x27;&#x27;VVA-triangle graph. ...

Physical Review D, 1986

The anomaly in the supercurrent amplitude Smunu is analyzed to one-loop order for N=1 supersymmet... more The anomaly in the supercurrent amplitude Smunu is analyzed to one-loop order for N=1 supersymmetry in the Wess-Zumino gauge within the framework of preregularization, in which loop-momentum-routing ambiguities percolate into shift-of-integration-variable surface terms peculiar to exactly four space-time dimensions. We find the supercurrent anomaly to be a consequence of the inability of such ambiguities (within a demonstrably finite set of quantum corrections) to absorb violations of gauge invariance (qnuSmunu!=0) and supersymmetry (∂muSmunu≡∂.S!=0) simultaneously, a feature quite similar to the inability of VVA-triangle ambiguities to absorb violations of gauge invariance and the axial-vector-current Ward identity simultaneously. We also find that if gauge invariance is preserved, the contribution to the supercurrent anomaly obtained from O(g2) quantum corrections to the supercurrent involves no infrared or ultraviolet infinities and resides in ∂.S rather than gamma.S. This last result is a consequence of maintaining exactly four space-time dimensions, as is necessary for momentum-routing ambiguities to appear at all in the quantum corrections. The connection between our results and similar results obtained from an Adler-Rosenberg symmetry argument is examined in detail.

Physical Review D, 1990

We present in this paper the evaluation of multiloop Green's functions in the context of a recent... more We present in this paper the evaluation of multiloop Green's functions in the context of a recently proposed regulating scheme called operator regularization. We show that, in contrast with other schemes, imposing the requirement of unitarity (rather than finiteness) is crucial in obtaining the (perturbative) renormalized effective action and Green's functions of a given theory. We demonstrate how an evaluation of these quantities may be carried out using this regulating technique in a manner which preserves the unitarity of the S matrix. This method is then applied to a two-loop calculation in the (44)4 theory, yielding agreement with results obtained in other schemes. Specifically, we calculate the B function, y , function, and the anomalous dimension of the field without having to look at the relationship between bare and renormalized quantities. Indeed, they directly come from the finite sector of the Green's functions.

Physical Review D, 1993

(Some reference links may require a separate subscription.) ... DGC McKeon, Can. J. Phys. 70, 652... more (Some reference links may require a separate subscription.) ... DGC McKeon, Can. J. Phys. 70, 652 (1992) [INSPEC][ADS][SPIRES]; Ann. Phys. (NY) 224, 139 (1993) [SPIN][INSPEC][ADS ]. ... DGC McKeon and TN Sherry, Phys. Rev. D 35, 3854 (1987) [SPIN];[INSPEC];[CAS];[ ...

Journal of Cosmology and Astroparticle Physics, 2005

The Wilkinson Microwave Anisotropy Probe microwave background data suggest that the primordial sp... more The Wilkinson Microwave Anisotropy Probe microwave background data suggest that the primordial spectrum of scalar curvature fluctuations is suppressed at small wavenumbers. We propose a UV/IR mixing effect in small-field inflationary models that can explain the observable deviation in WMAP data from the concordance model. Specifically, in inflationary models where the inflaton couples to an asymptotically free gauge theory, the radiative corrections to the effective inflaton potential can be anomalously large. This occurs for small values of the inflaton field which are of the order of the gauge theory strong coupling scale. Radiative corrections cause the inflaton potential to blow up at small values of the inflaton field. As a result, these corrections can violate the slow-roll condition at the initial stage of the inflation and suppress the production of scalar density perturbations.

International Journal of Modern Physics A, 2008

The tensor self-energy is computed at one-loop order in a model in which a vector and tensor inte... more The tensor self-energy is computed at one-loop order in a model in which a vector and tensor interact in a way that eliminates all tensor degrees of freedom. Divergencies arise which cannot be eliminated without introducing a kinetic term for the tensor field which does not appear in the classical action. A field redefinition serves to eliminate these divergences.

International Journal of Modern Physics A, 2010

We consider a two-form antisymmetric tensor field ϕ minimally coupled to a non-Abelian vector fie... more We consider a two-form antisymmetric tensor field ϕ minimally coupled to a non-Abelian vector field with a field strength F. Canonical analysis suggests that a pseudoscalar mass term [Formula: see text] for the tensor field eliminates degrees of freedom associated with this field. Explicit one-loop calculations show that an additional coupling m Tr (ϕ ∧ 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 [Formula: see text] and coupling m Tr (ϕ ∧ ⋆F). We comment on the Stueckelberg mechanism for mass generation in the Abelian version of the latter model.

Canadian Journal of Physics, 2013

The introduction of a Lagrange multiplier field to ensure that the classical equations of motion ... more 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 only one loop. The consequences of this for a massive non-abelian vector model are considered.

Canadian Journal of Physics, 1992

It is shown how one can do perturbative calculations about a flat background in two-dimensional m... more It is shown how one can do perturbative calculations about a flat background in two-dimensional models of quantum gravity. The Jackiw–Teitelboim model and the induced gravitational action of Polyakov are considered. A suitable choice of gauge allows one to employ operator regularization, a symmetry-preserving procedure that is particularly convenient as it does not alter the dimensionality of these models, allowing one to exploit some properties peculiar to two dimensions. A specific example is provided by the graviton two-point function.

Physics Letters B, 2006

In a recently proposed model in which a vector non-Abelian gauge field interacts with an antisymm... more In a recently proposed model in which a vector non-Abelian gauge field interacts with an antisymmetric tensor field, it has been shown that the tensor field possesses no physical degrees of freedom. This formal demonstration is tested by computing the one-loop contributions of the tensor field to the self-energy of the vector field. It is shown that despite the large number of Feynman diagrams in which the tensor field contributes, the sum of these diagrams vanishes, confirming that it is not physical. Furthermore, if the tensor field were to couple with a spinor field, it is shown at oneloop order that the spinor self-energy is not renormalizable, and hence this coupling must be excluded. In principle though, this tensor field does couple to the gravitational field.

International Journal of Modern Physics A, 2017

By using the renormalization group (RG) equation it has proved possible to sum logarithmic correc... more 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 [Formula: see text] 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 a Yukawa model 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 [Formula: see text] where [Formula: see text] is the vacuum expectation value of the ...

Quantum Field Theory Under the Influence of External Conditions (QFEXT09), 2010

In recent years, the Euler-Heisenberg Lagrangian has been shown to be a useful tool for the analy... more 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.