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J. Frenkel

Publications and source records attributed to J. Frenkel.

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

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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.

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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.

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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

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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.

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arXiv2017

Fermion propagator in an external potential and generalized Airy functions

We study the behavior of the fermion propagator in an external time dependent potential in 0+1 dimension. We show that, when the potential has upto quadratic terms in time, the propagator can be expressed in terms of generalized Airy functions (or standard Airy functions depending on the exact time dependence). We study various properties of these new generalized functions which reduce to the standard Airy functions in a particular limit.

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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.

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arXiv2016

Generalized Kadanoff-Baym relation in nonequilibrium quenched models

In the context of a broad class of quenched models, we derive a generalized differential form of the Kadanoff-Baym (KB) ansatz which relates the out of equilibrium correlated and spectral Green's functions. This relation holds at any time both before the quench (when it coincides with the fluctuation-dissipation theorem) as well as after it. We also examine, in the context of exactly soluble quenched models, the validity of some of the earlier alternative extensions of the KB ansatz.

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arXiv2016

Effective Action for Hard Thermal Loops in Gravitational Fields

We examine, through a Boltzmann equation approach, the generating action of hard thermal loops in the background of gravitational fields. Using the gauge and Weyl invariance of the theory at high temperature, we derive an explicit closed-form expression for the effective action.

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arXiv2014

Large time behavior in an exactly soluble out of equilibrium model

We study the behavior of out of equilibrium retarded, advanced and correlated Green's functions within the context of an exactly soluble (quenched) model. We show, to the lowest order, that even though the pinch singularities cancel, there is a residual linear dependence on the time interval (after the quench) in the correlated Green's function which may invalidate perturbation theory. We sum the perturbation series to all orders in this simple model and show explicitly that the complete Green's functions are well behaved even for large time intervals. The exact form of the correlated Green's function allows us to extract a manifestly positive distribution function, for large times after the quench, which has a memory of the frequency of the initial system before the quench.

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arXiv2014

QED plasma in a background of static gravitational fields

We obtain the effective Lagrangian of static gravitational fields interacting with a QED plasma at high temperature. Using the equivalence between the static hard thermal loops and those with zero external energy-momentum, we compute the effective Lagrangian up to two-loop order. We also obtain a non-perturbative contribution which arises from the sum of all infrared divergent ring-diagrams. From the gauge and Weyl symmetries of the theory, we deduce to all orders that this effective Lagrangian is equivalent to the pressure of a QED plasma in Minkowski space-time, with the global temperature replaced by the Tolman local temperature.

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arXiv2013

Hard thermal loops in static background fields

We discuss the high temperature behavior of retarded thermal loops in static external fields. We employ an analytic continuation of the imaginary time formalism and use a spectral representation of the thermal amplitudes. We show that, to all orders, the leading contributions of static hard thermal loops can be directly obtained by evaluating them at zero external energies and momenta.

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arXiv2013

The pole of the fermion propagator in a general class of gauges

We study the behavior of the pole of the fermion propagator, in QED in $n$-dimensions, in a general class of gauges which interpolate between the covariant, the axial and the Coulomb gauges. We use Nielsen identities, following from the BRST invariance of the theory, to determine the gauge variation of the fermion two point function in this general class of gauges. This allows us to show directly and in a simple manner, to all orders in perturbation theory, that in the absence of infrared divergences and mass shell singularities, the fermion pole mass is gauge independent.

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arXiv2013

On the gauge independence of the fermion pole mass

We study the question of complete gauge independence of the fermion pole mass by choosing a general class of gauge fixing which interpolates between the covariant, the axial and the Coulomb gauges for different values of the gauge fixing parameters. We derive the Nielsen identity describing the gauge parameter variation of the fermion two point function in this general class of gauges. Furthermore, we relate the denominator of the fermion propagator to the two point function. This then allows us to study directly the gauge parameter dependence of the denominator of the propa- gator using the Nielsen identity for the two point function. This leads to a simple proof that, when infrared divergences and mass shell singularities are not present at the pole, the fermion pole mass is gauge independent, in the complete sense, to all orders in perturbation theory. Namely, the pole is not only independent of the gauge fixing parameters, but has also the same value in both covariant and non-covariant gauges.

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arXiv2013

Infrared divergences, mass shell singularities and gauge dependence of the dynamical fermion mass

We study the behavior of the dynamical fermion mass when infrared divergences and mass shell singularities are present in a gauge theory. In particular, in the massive Schwinger model in covariant gauges we find that the pole of the fermion propagator is divergent and gauge dependent at one loop, but the leading singularities cancel in the quenched rainbow approximation. On the other hand, in physical gauges, we find that the dynamical fermion mass is finite and gauge independent at least up to one loop.

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