Search

We examine the Einstein-Cartan (EC) theory in first-order form, which has a diffeomorphism as well as a local Lorentz invariance. We study the renormalizability of this theory in the framework of the Batalin-Vilkovisky formalism, which allows for a gauge invariant renormalization. Using the background field method, we discuss the gauge invariance of the background effective action and analyze the Ward identities which reflect the symmetries of the EC theory. As an application, we compute, in a general background gauge, the self-energy of the tetrad field at one-loop order., Comment: 23 pages, 6 figures. To appear in Annals of Physics

We consider the Einstein-Cartan theory with the tetrad $e_{\mu}^{a}$ and spin connection $\omega_{\mu ab}$ taken as being independent fields. Diffeomorphism invariance and local Lorentz invariance result in there being two distinct gauge transformations in this approach, and consequently two ghost fields arise when employing the usual Faddeev-Popov quantization procedure. Our choice of gauge fixing retains the gauge invariances of the background field. We show that the gauge algebra is closed even in the presence of torsion, and the resulting BRST invariance can be found for the effective action. We also derive the Slavnov-Taylor identities, which reflect the BRST symmetries of this theory., Comment: 18 pages. To be published in Annals of Physics

We calculate in a general background gauge, to one-loop order, the leading logarithmic contribution from the graviton self-energy at finite temperature $T$, extending a previous analysis done at $T=0$. The result, which has a transverse structure, is applied to evaluate the leading quantum correction of the gravitational vacuum polarization to the Newtonian potential. An analytic expression valid at all temperatures is obtained, which generalizes the result obtained earlier at $T=0$. One finds that the magnitude of this quantum correction decreases as the temperature rises., Comment: Added references

We examine some features of the non-renormalizability induced through the use of low-energy effective Lagrangians in loop diagrams, in the context of a scalar model which is ultraviolet finite and partially soluble. In this framework, one can directly demonstrate the mechanism leading to the non-renormalizability of the effective theory. This behavior is generated by approximations that are applicable at low energies but are generally inappropriate for evaluating loop diagrams that contain virtual high-energy particles. However, it is explicitly shown that one can match the results obtained in the renormalized effective theory with those found in the full theory at low energy. We argue that the infrared sectors of these theories are inherently similar, independently of the matching procedure. A closed-form expression is obtained, to leading order in the energy expansion, for the complete effective Lagrangian at all orders in perturbation theory. The model may be useful to clarify certain aspects of realistic, but more complex, effective field theories., Comment: 8 pages, 4 figures

We deduce, in a general background gauge, the counter-term Lagrangian for pure quantum gravity to one-loop order. As an application, we evaluate the leading quantum correction to the classical gravitational potential, generated by the vacuum polarization. We find that, in specific background gauges, this yields the complete result for the one-loop quantum corrections to the Newtonian potential. This approach is also applied to calculate the $\ln(T)$ contributions in quantum gravity at high-temperature., Comment: Corrected typos; added references. Accepted for publication in the Physical Review D

It is shown that the usual expression for a Feynman diagram in terms of the Feynman propagator $\Delta_F(x-y)$ can be replaced by an equivalent expression involving the positive-energy on-shell propagator $\Delta^+(x-y)$, supplemented by appropriate functions associated with time-ordering. When this alternate way of expressing a Feynman diagram is Fourier transformed into momentum space, the momentum associated with each function $\Delta^+(x-y)$ is on-shell, and is only conserved at each vertex if an energy is attributed to the contributions of the time-ordering functions. The resulting expression is analogous to what Kadyshevsky had obtained by deriving an alternate expansion for the $S$--matrix. A detailed explanation of how this alternate expansion is derived is given, and it is shown how it provides a straightforward way of determining the imaginary part of a Feynman diagram, which makes it useful when using unitarity methods for computing a Feynman diagram. By considering a number of specific Feynman diagrams in self-interacting scalar models and in QED, we show how this alternate approach can be related to the old perturbation theory and can simplify direct calculations of Feynman diagrams., Comment: 13 pages, 11 figures, accepted for publication in the Physical Review D

We examine, in the `t Hooft renormalization scheme, the analytic running coupling $\bar\alpha_t(Q^2)$ in QCD, using the two-loop $\beta$-function with positive expansion parameters $\beta_0$ and $\beta_1$. An exact integral representation is derived for this causal coupling, which is fully expressed in terms of the imaginary part of the Lambert function $W$. This integral form manifestly accounts for the universal value of the infrared limit $\bar\alpha_t(Q^2=0)= 4 \pi /\beta_0$., Comment: 9 pages, one figure; accepted for publication in Modern Physics Letters A

We study, in the imaginary time formalism, the relation between loops and on-shell forward scattering tree amplitudes in thermal field theories. This allows for an efficient evaluation, at all temperatures, of Green's functions with causal retarded boundary conditions. We present an application of this relation in quantum gravity coupled to scalar matter fields. We show that at one or two loops, involving planar diagrams, the 1PI retarded thermal Green's functions may respectively be expressed in terms of connected forward scattering tree amplitudes of one or two on-shell particles., Comment: 15 pages, four figures. Published in Physical Review D (typos corrected)

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., Comment: 8 pages, 4 figures. To appear in the Canadian Journal of Physics (typos corrected)

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., Comment: 28 pages, 8 figures. To appear in the Annals of Physics (the references have been sorted)

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., Comment: 24 pages, 12 figures. Added more details and a new reference; typos corrected. To be published in Annals of Physics

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., Comment: 19 pages, 4 figures. Added references

We examine the self-consistency of the first-order formulation of the Yang-Mills theory. By comparing the generating functional $Z$ before and after integrating out the additional field $F^a_{\mu\nu}$, we derive a set of structural identities that must be satisfied by the Green's functions at all orders. These identities, which hold in any dimension, are distinct from the usual Ward identities and are necessary for the internal consistency of the first-order formalism. They relate the Green's functions involving the fields $F^a_{\mu\nu}$, to Green's functions in the second-order formulation which contain the gluon strength tensor $f^a_{\mu\nu}$. In particular, such identities may provide a simple physical interpretation of the additional field $F^a_{\mu\nu}$., Comment: 15 pages, 6 figures

The problem of eliminating divergences arising in quantum gravity is generally addressed by modifying the classical Einstein-Hilbert action. These modifications might involve the introduction of local supersymmetry, the addition of terms that are higher-order in the curvature to the action, or invoking compactification of superstring theory from ten to four dimensions. An alternative to these approaches is to introduce a Lagrange multiplier field that restricts the path integral to field configurations that satisfy the classical equations of motion; this has the effect of doubling the usual one-loop contributions and of eliminating all effects beyond one loop. We show how this reduction of loop contributions occurs and find the gauge invariances present when such a Lagrange multiplier is introduced into the Yang-Mills and Einstein-Hilbert actions. Moreover, we quantize using the path integral, discuss the renormalization, and then show how Becchi-Rouet-Stora-Tyutin (BRST) invariance can be used to both demonstrate that unitarity is retained and to find BRST relations between Greens functions. In the Appendices, we show how the background field quantization can be implemented, consider the use of a Lagrange multiplier field to restrict higher-order contributions in supersymmetric theories, and derive the BRST equations satisfied by the generating functional., Comment: Eighteen pages, one figure. Published in Physical Review D (typos corrected)

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., Comment: 16 pages, 3 figures; Revisions and additions in section III; Reference added; Accepted for publication in Physical Review D

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, Comment: 8 pages. This version contains more background material

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., Comment: Corrected typos; 14 pages, two figures. A new appendix has been added. Published in Annals of Physics

We study the BRST renormalization of an alternative formulation of the Yang-Mills theory, where the matrix-propagator of the gluon and the complementary fields is diagonal. This procedure involves scalings as well as non-linear mixings of the fields and sources. We show, in the Landau gauge, that the BRST identities implement a recursive proof of renormalizability to all orders., Comment: 13 pages; added references

We show that the BRST identities can be used to control the renormalization of the background gauge in QCD, in spite of the fact that one-particle reducible graphs have to be omitted. We obtain the all orders renormalized affective action for the background field theory.

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., Comment: 9 pages, 3 figures

We examine the renormalization of the first order formulation of Yang-Mills theory, by using the BRST idenities. These preserve the gauge invariance of the theory and enable a recursive proof of renormalizability to higher orders in perturbation theory. The renormalization involves non-linear mixings as well as re-scalings of the fields and sources, which lead to a renormalized action at all orders.

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., Comment: Four pages. Accepted for publication in Modern Physics Letters A

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., Comment: 9 pages

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., Comment: 4 pages, 2 figures

In the context of an exactly soluble out of equilibrium (quenched) model, we study an extension of the fluctuation-dissipation relation. This involves a modified differential form of this relation, with an effective temperature which may have an explicit dependence on time scales., Comment: 5 pages

Using the closed time path formalism in thermal field theory, we give a derivation of the fluctuation-dissipation theorem which is based on the unitarity of the $S$-matrix., Comment: 4 pages, 2 figures

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., Comment: 5 pages

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., Comment: Revised version to be published in Phys. Rev. D (9 pages, 4 figures)

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., Comment: 5 pages, to be published in The European Physical Journal C

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., Comment: 13 pages, 1 figure

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., Comment: 4 pages, published version

We study, in the long wave-length and static limits, the structure of the n-point graviton functions at high temperature. Using the gauge and Weyl invariance of the theory, we derive a simple expression for the hard thermal amplitudes in these two limits., Comment: 3 pages, 1 figure

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., Comment: 5pages, 3 figures, some minor clarifications included, to appear in Physics Letters B

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., Comment: Published in Phys. Rev. D

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., Comment: 3 pages, one figure. To be published in the Brazilian Journal of Physics

We show, in the imaginary time formalism, that the temperature dependent parts of all the retarded (advanced) amplitudes vanish in the Schwinger model. We trace this behavior to the CPT invariance of the theory and give a physical interpretation of this result in terms of forward scattering amplitudes of on-shell thermal particles., Comment: 4 pages with 5 figures, two minor typos corrected, to appear in Physical Review D

From microscopic models, a Langevin equation can in general be derived only as an approximation. Two possible conditions to validate this approximation are studied. One is, for a linear Langevin equation, that the frequency of the Fourier transform should be close to the natural frequency of the system. The other is by the assumption of `slow' variables. We test this method by comparison with an exactly soluble model, and point out its limitations. We base our discussion on two approaches. The first is a direct, elementary treatment of Senitzky. The second is via a generalized Langevn equation as an intermediate step.

In the Schwinger model at finite temperature, we derive a closed form result for the chiral anomaly which arises from the long distance behavior of the electric field \cite{frenkel}. We discuss the general properties associated with this thermal anomaly as well as its relation with the "index" of the Dirac operator. We further show that the thermal anomaly, like the zero temperature anomaly which arises from the ultraviolet behavior of the theory, does not receive any contribution from higher loops. Finally, we determine the complete effective action as well as the anomaly functional on both the thermal branches in the closed time path formalism., Comment: RevTex 5 pages

The validity of the Langevin equation (both classical and quantum) is studied in cases when not all the equations of motion are linear. In particular, a model is studied in which the interaction is bilinear in the environment variables. We conclude that the equation is valid only for frequencies close to the frequency of the system alone. If the equation of motion of the system alone is nonlinear, we are unable to find a condition for the validity of the Langevin equation., Comment: Revised version is available

We study the Schwinger model at finite temperature and show that a temperature dependent chiral anomaly may arise from the long distance behavior of the electric field. At high temperature this anomaly depends linearly on the temperature $T$ and is present not only in the two point function, but also in all even point amplitudes., Comment: revtex, 5pages