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D. G. C. McKeon

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

At least 37 records · Page 2Linked to original sources
arXiv2021

Thermal gauge theories with Lagrange multiplier fields

We study the Yang-Mills theory and quantum gravity at finite temperature, in the presence of Lagrange multiplier fields. These restrict the path integrals to field configurations which obey the classical equations of motion. This has the effect of doubling the usual one--loop thermal contributions and of suppressing all radiative corrections at higher loop order. Such theories are renormalizable at all temperatures. Some consequences of this result in quantum gravity are briefly examined.

hep-th↗
arXiv2021

Restricting loop expansions in gauge theories coupled to matter

Quantizing any model in which a Lagrange multiplier (LM) field is used to restrict field configurations to those that satisfy the classical equations of motion, leads to at most one-loop radiative corrections. This approach can be used with both the Yang-Mills (YM) and Einstein-Hilbert (EH) action; the resulting theory is both renormalizable and unitary, has a positive energy spectrum and has no negative norm states contributing to physical processes. Although this approach cannot be consistently used with scalar fields alone, scalar fields can be coupled to gauge fields so that loop effects in the gauge sector are restricted to one-loop order in a way that satisfies the usual criterion for a consistent quantum field theory. The tree-level diagrams are those of the classical theory in which the metric couples to the energy-momentum tensor.

hep-th↗
arXiv2021

On Restricting First Order Form of Gauge Theories to One-Loop Order

The first order form of the Yang-Mills and Einstein-Hilbert actions are quantized, and it is shown how Green's functions computed using the first and the second order form of these theories are related. Next we show how by use of Lagrange multiplier fields (LM), radiative effects beyond one-loop order can be eliminated. This allows one to compute Green's functions exactly without loss of unitarity. The consequences of this restriction on radiative effects are examined for the Yang-Mills and Einstein-Hilbert actions. In these two gauge theories, we find that the quantized theory is both renormalizable and unitary once the LM field is used to eliminate effects beyond one-loop order.

hep-th↗
arXiv2021

Classical Mechanics

These notes provide an introduction to a number of those topics in Classical Mechanics that are useful for field theory.

physics.class-ph↗
arXiv2021

Renormalization Mass Scale and Scheme Dependence in the Perturbative Contribution to Inclusive Semileptonic $b$ Decays

We examine the perturbative calculation of the inclusive semi-leptonic decay rate $Γ$ for the $b$-quark, using mass-independent renormalization. To finite order of perturbation theory the series for $Γ$ will depend on the unphysical renormalization scale parameter $μ$ and on the particular choice of mass-independent renormalization scheme; these dependencies will only be removed after summing the series to all orders. In this paper we show that all explicit $μ$-dependence of $Γ$, through powers of ln$(μ)$, can be summed by using the renormalization group equation. We then find that this explicit $μ$-dependence can be combined together with the implicit $μ$-dependence of $Γ$ (through powers of both the running coupling $a(μ)$ and the running $b$-quark mass $m(μ)$) to yield a $μ$-independent perturbative expansion for $Γ$ in terms of $a(μ)$ and $m(μ)$ both evaluated at a renormalization scheme independent mass scale $I\!\!M$ which is fixed in terms of either the "$\overline{MS}$ mass" $\overline{m}_b$ of the $b$ quark or its pole mass $m_{pole}$. At finite order the resulting perturbative expansion retains a degree of arbitrariness associated with the particular choice of mass-independent renormalization scheme. We use the coefficients $c_i$ and $g_i$ of the perturbative expansions of the renormalization group functions $β(a)$ and $γ(a)$, associated with $a(μ)$ and $m(μ)$ respectively, to characterize the remaining renormalization scheme arbitrariness of $Γ$. We further show that all terms in the expansion of $Γ$ can be written in terms of the $c_i$ and $g_i$ coefficients and a set of renormalization scheme independent parameters $τ_i$.

hep-ph↗
arXiv2020

Renormalization Scheme and Mass Scale Independence

We demonstrate that in the mass independent renormalization scheme. the renormalization group equations associated with the unphysical parameters that characterize the renormalization scheme and the mass scale leads to summation that results in a cancellation between the implicit and explicit dependence on these parameters. The resulting perturbative expansion is consequently independent of these arbitrary parameters. We illustrate this by considering R, the cross section for e+e- -> hadrons.

hep-ph↗
arXiv2020

Structural identities in the first order formulation of quantum gravity

We study the self-consistency of the first order formulation of quantum gravity, which may be attained by introducing, apart from the graviton field, another auxiliary quantum field. By comparing the forms of the generating functional $Z$ before and after integrating out the additional field, we derive a set of structural identities which must be satisfied by the Green's functions at all orders. These are distinct from the usual Ward identities, being necessary for the self-consistency of the first order formalism. They relate the Green's functions involving the additional quantum field to those containing a certain composite graviton field, which corresponds to its classical value. Thereby, the structural identities lead to a simple interpretation of the auxiliary field.

hep-th↗
arXiv2020

A Gauge Theory that mixes Bosonic and Fermionic Gauge Fields

Using a gauge symmetry derived by applying the Dirac constraint formalism to supergravity with cosmological term in 2+1 dimensions, we construct a gauge theory with many characteristics of Yang-Mills theory. The gauge transformation mixes two Bosonic fields and one Fermionic field.

hep-th↗
arXiv2020

Derivation of Gauge Symmetries in Supergravity with a Cosmological Constant in 2 + 1 Dimensions

The canonical structure of supergravity with a cosmological constant is analyzed in 2 + 1 dimensions using the Dirac constraint formalism. The first class constraints are used to find two Bosonic and one Fermionic gauge symmetries that satisfy a superalgebra. Provided the cosmological constant is negative, this novel algebra closes, without having to invoke the equations of motion or introducing auxiliary fields.

gr-qc↗
arXiv2019

First order formulation of the Yang-Mills theory in a background field

The background gauge renormalization of the first order formulation of the Yang-Mills theory is studied by using the BRST identities. Together with the background symmetry, these identities allow for an iterative proof of renormalizability to all orders in perturbation theory. However, due to the fact that certain improper diagrams which violate the BRST symmetry should be removed, the renormalizability must be deduced indirectly. The recursive method involves rescalings and mixings of the fields, which lead to a renormalized effective action for the background field theory.

hep-th↗
arXiv2019

On Restricting to One Loop Order the Radiative Effects in Quantum Gravity

The dimensionful nature of the coupling in the Einstein-Hilbert action in four dimensions implies that the theory is non-renormalizable; explicit calculation shows that beginning at two loop order, divergences arise that cannot be removed by renormalization without introducing new terms in the classical action. It has been shown that, by use of a Lagrange multiplier field to ensure that the classical equation of motion is satisfied in the path integral, radiative effects can be restricted to one loop order. We show that by use of such Lagrange multiplier fields, the Einstein-Hilbert action can be quantized without the occurrence of non-renormalizable divergences. We then apply this mechanism to a model in which there is in addition to the Einstein-Hilbert action, a fully covariant action for a self-interacting scalar field coupled to the metric. It proves possible to restrict loop diagrams involving internal lines involving the metric to one-loop order; diagrams in which the scalar field propagates occur at arbitrary high order in the loop expansion. This model also can be shown to be renormalizable. Incorporating spinor and vector fields in the same way as scalar fields is feasible, and so a fully covariant Standard Model with a dynamical metric field can also be shown to be renormalizable

hep-th↗
arXiv2019

A Systematic Expansion of Running Couplings and Masses

As an alternative to directly integrating their defining equations to find the running coupling $a(μ)$ and the running mass $m(μ)$, we expand these quantities in powers of $\ln\left(\fracμ{μ^\prime}\right)$ and their boundary values $a(μ^\prime)$ and $m(μ^\prime)$. Renormalization group summation is used to partially sum these logarithms. We consider this approach using both the $\overline{MS}$ and 't Hooft renormalization schemes. We also show how the couplings and masses in any two mass independent renormalization schemes are related.

hep-th↗
arXiv2019

Renormalization Scheme Ambiguities in the Models with More than One Coupling

The process of renormalization to eliminate divergences arising in quantum field theory is not uniquely defined; one can always perform a finite renormalization, rendering finite perturbative results ambiguous. The consequences of making such finite renormalizations have been examined in the case of there being one or two couplings. In this paper we consider how finite renormalizations can affect more general models in which there are more than two couplings. In particular, we consider the Standard Model in which there are essentially five couplings. We show that in this model (when neglecting all mass parameters) if we use mass independent renormalization, then the renormalization group beta-functions are not unique beyond one loop order, that it is not in general possible to eliminate all terms beyond certain order for all these beta-functions, but that for a physical process all contributions beyond one loop order can be subsumed into the beta-functions.

hep-ph↗
arXiv2018

Renormalization of six-dimensional Yang-Mills theory in a background gauge field

Using the background field method, we study in a general covariant gauge the renormalization of the 6-dimensional Yang-Mills theory. This requires background gauge invariant counterterms, some of which do not vanish on shell. Such counterterms occur, even off-shell, with gauge-independent coefficients. The analysis is done at one loop order and the extension to higher orders is discussed by means of the BRST identities. We examine the behaviour of the beta function, which implies that this theory is not asymptotically free.

hep-th↗
arXiv2018

The Renormalization Group and the Effective Potential in the Wess-Zumino model

We consider the effective potential V in the massless Wess-Zumino model. By using the renormalization group equation, we show that the explicit dependence of V on the renormalization mass scale mu cancels. If V has an extremum at some non-vanishing value of the background field, then it follows that V is "flat", independent of the background field. This is consistent with the general requirement that V be complex. The consequences for supersymmetric gauge theories are briefly considered.

hep-th↗
arXiv2018

Multiple Couplings and Renormalization Scheme Ambiguities

The ambiguities inherent in renormalization are considered when using mass-independent renormalization in massless theories that involve two coupling coupling constants. We review how there is no renormalization scheme in which the beta-functions can be chosen to vanish beyond a certain order in perturbation theory, but that the beta-functions always contain ambiguities beyond first order. We examine how the coupling constants depend on the coefficients of the beta-function beyond one loop order. A way of characterizing renormalization schemes that doesn't use coefficients of the beta-function is considered for models with either one or two couplings. The renormalization scheme ambiguities of physical quantities computed to finite order in perturbation theory are also examined. We demonstrate how summation of the logarithms that have explicit dependence on the renormalization scale parameter mu in a physical quantity R leads to a cancellation with the implicit dependence of R on mu through the running couplings. It is also shown that there exists a renormalization scheme in which all radiative effects beyond lowest order are incorporated into the behaviour of the running couplings.

hep-ph↗
arXiv2018

Supersymmetry and the Rotation Group

A model invariant under a supersymmetric extension of the rotation group O(3) is mapped, using a stereographic projection, from the spherical surface S2 to two dimensional Euclidean space. The resulting model does not have a manifest local structure.

physics.gen-ph↗