arXiv subjects

F. T. Brandt

Publications and source records attributed to F. T. Brandt.

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↗

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↗

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↗

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↗

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

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 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↗

arXiv2015

Induced magnetic moment for a spinless charged particle in the thin-layer approach

We determine the effective dynamics for a spinless charged particle, in the presence of electromagnetic fields, constrained to a space curve. We employ the thin-layer procedure and a perturbative expansion for the Schrödinger equation is derived. We find that the first-order term in the perturbative expansion couples the dynamics of the normal and tangent degrees of freedom. However, there is always a gauge transformation that allows decouple the dynamics. We find that the effective Schrödinger equation in the curve contains an induced Zeeman coupling, independent of the curvature and torsion, which has not been previously reported. This coupling is characteristic of reducing the dimension by two and allows to identify an induced magnetic moment.

cond-mat.other↗

arXiv2015

Classical Boltzmann equation and high-temperature QED

The equivalence between thermal field theory and the Boltzmann transport equation is investigated at higher orders in the context of quantum electrodynamics. We compare the contributions obtained from the collisionless transport equation with the high temperature limit of the one-loop thermal Green's function. Our approach employs the representation of the thermal Green's functions in terms of forward scattering amplitudes. The general structure of these amplitudes clearly indicates that the physics described by the leading high temperature limit of quantum electrodynamics can be obtained from the Boltzmann transport equation. We also present some explicit examples of this interesting equivalence.

hep-th↗

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.

hep-th↗

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.

hep-th↗

arXiv2012

Nonanalyticity of the free energy in thermal field theory

We study, in a d-dimensional space-time, the nonanalyticity of the thermal free energy in the scalar phi^4 theory as well as in QED. We find that the infrared divergent contributions induce, when d is even, a nonanalyticity in the coupling alpha of the form (alpha)^[(d-1)/2] whereas when d is odd the nonanalyticity is only logarithmic.

hep-th↗

arXiv2012

High temperature limit in static backgrounds

We prove that the hard thermal loop contribution to static thermal amplitudes can be obtained by setting all the external four-momenta to zero before performing the Matsubara sums and loop integrals. At the one-loop order we do an iterative procedure for all the 1PI one-loop diagrams and at the two-loop order we consider the self-energy. Our approach is sufficiently general to the extent that it includes theories with any kind of interaction vertices, such as gravity in the weak field approximation, for $d$ space-time dimensions. This result is valid whenever the external fields are all bosonic.

hep-th↗

arXiv2012

Hard Thermal Loops in the n-Dimensional phi3 Theory

We derive a closed-form result for the leading thermal contributions which appear in the n-dimensional phi3 theory at high temperature. These contributions become local only in the long wavelength and in the static limits, being given by different expressions in these two limits.

hep-th↗