Convenient versus unique effective action formalism in 2d dilaton-Maxwell quantum gravity

The structure of one-loop divergences of two-dimensional dilaton-Maxwell quantum gravity is investigated in two formalisms: one using a convenient effective action and the other a unique effective action. The one-loop divergences (including surface divergences) of the convenient effetive action are calculated in three different covariant gauges: (i) De Witt, (ii) Ω-degenerate De Witt, and (iii) simplest covariant. The on-shell effective action is given by surface divergences only (finiteness of theS-matrix), which yet depend upon the gauge condition choice. Off-shell renormalizability is discussed and classes of renormalizable dilaton and Maxwell potentials are found which coincide in the cases of convenient and unique effective actions. A detailed comparison of both situations, i.e. convenient vs. unique effective action, is given. As an extension of the procedure, the one-loop effective action in two-dimensional dilaton-Yang-Mills gravity is calculated.     

IR renormalization of general effective actions and Hawking flux in 2D gravity theories

The infrared problem of the effective action in 2D is discussed in the framework of the covariant perturbation theory. The divergences are regularized by a mass and the leading term is evaluated up to the third order of perturbation theory. A summation scheme is proposed which isolates the divergences from the finite part of the series and results in a single term. The latter turns out to be equivalent to the coupling to a certain classical external field. This suggests renormalization by factorization. PACS 4.60.-m; 4.60.Kz; 4.70.Dy     

Generalized causality condition in quantum field theory with torsion

The Schwinger-De Witt method of local expansion of the effective action is applied to a model vector field theory which satisfies a generalized causality condition. One loop divergences are computed. It is shown that the theory is non-renormalizable. The effective potential of the theory has a local minimum with a nonzero average value of the vector field, stable with respect to small slowly varying perturbations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 74–78, May, 1989.     

Matrix Theory in Curved Space

We study curved-space versions of matrix stringtheory taking as a definition of the theory a gaugedmatrix sigma model. By computing the contribution to theone-loop divergent terms in the effective action coming from the diagonal matrix elements weshow that these versions of matrix theory in curvedspace reproduce the string equations of motion and theR⁴ correction to the Hilbert-Einstein action.It is then demonstrated that the divergences due tothe nondiagonal elements induce terms in the effectiveaction that cannot be removed by appropriatecounterterms. This implies that the model can only beconsistent for Ricci flat manifolds with vanishingsix-dimensional Euler density.     

Stochastic quantization of the nonlinear sigma model and the background field method

The background field method is a useful scheme for calculation of the effective action in conventional quantum field theory. In stochastic quantization this approach is introduced by using auxiliary fields, as suggested by Okano. In this work, we implement the background field method, using the normal coordinate expansion, for the nonlinear sigma model on a general Riemannian manifold in the context of stochastic quantization. We also calculate, making use of this novel formulation, the action necessary for investigation of the divergences, at least at the one-loop level.     

Holographic renormalization in teleparallel gravity

We consider the problem of IR divergences of the action in the covariant formulation of teleparallel gravity in asymptotically Minkowski spacetimes. We show that divergences are caused by inertial effects and can be removed by adding an appropriate surface term, leading to the renormalized action. This process can be viewed as a teleparallel analog of holographic renormalization. Moreover, we explore the variational problem in teleparallel gravity and explain how the variation with respect to the spin connection should be performed.     

The Maxwell–Einstein system,Ward identities and the Vilkovisky construction

The gauge fixing dependence of the one-loop effective action of quantum gravity in the proper-time representation is investigated for a space of arbitrary curvature, and the investigation is extended to Maxwell–Einstein theory. The construction of Vilkovisky and DeWitt for removal of this dependence is then considered in general gauges, and it is shown that nontrivial criteria arising from a Ward identity of the theory must be obeyed by the regularization scheme, if the construction is to remove the gauge dependence of quadratic and quartic divergences. The results apply also to non-Abelian gauge theories; they are used to address the question of gauge dependence of asymptotic freedom arising through internal graviton lines at one-loop order as suggested by Robinson and Wilczek.     

Strongly interacting particles with strongly singular potentials

A statistical system of particles is considered for which interaction potentials are strongly singular so that the standard perturbation theory cannot be used. A regular procedure for constructing a mass operator is suggested, having no ultraviolet divergences and giving the possibility of finding corrections for any approximation chosen. In this procedure, the divergences connected with the potential singularity are eliminated with the help of a smoothing function, for which a simple equation is given and whose properties are analyzed both analytically and numerically. Two effective regularization methods are formulated, eliminating divergences occurring while iterating propagator equations. A continuous iterative procedure is invented for calculating observable quantities and the fast convergence conditions for this procedure are shown to be equivalent to the fixed-point conditions.     

A Process Algebra Approach to Quantum Electrodynamics

The process algebra program is directed towards developing a realist model of quantum mechanics free of paradoxes, divergences and conceptual confusions. From this perspective, fundamental phenomena are viewed as emerging from primitive informational elements generated by processes. The process algebra has been shown to successfully reproduce scalar non-relativistic quantum mechanics (NRQM) without the usual paradoxes and dualities. NRQM appears as an effective theory which emerges under specific asymptotic limits. Space-time, scalar particle wave functions and the Born rule are all emergent in this framework. In this paper, the process algebra model is reviewed, extended to the relativistic setting, and then applied to the problem of electrodynamics. A semiclassical version is presented in which a Minkowski-like space-time emerges as well as a vector potential that is discrete and photon-like at small scales and near-continuous and wave-like at large scales. QED is viewed as an effective theory at small scales while Maxwell theory becomes an effective theory at large scales. The process algebra version of quantum electrodynamics is intuitive and realist, free from divergences and eliminates the distinction between particle, field and wave. Computations are carried out using the configuration space process covering map, although the connection to second quantization has not been fully explored.     

Effective Action for Noncommutative U(1) Gauge Theory with Higher Dimensional Terms

In this paper we apply the assumption of our recent work in noncommutative scalar models to the noncommutative U(1) gauge theories. This assumption is that the noncommutative effects start to be visible continuously from a scale λ_NC and that below this scale the theory is a commutative one. Based on thisassumption and using background field method and loop calculations, an effective action is derived for noncommutative U(1) gauge theory. It will be shown that the corresponding low energy effective theory is asymptotically free and that under this condition the noncommutative quadratic IR divergences will not appear. The effective theory contains higher dimensional terms, which become more important at high energies. These terms predict an elastic photon-photon scattering due to the noncommutativity of space. Thecoefficients of these higher dimensional terms also satisfy a positivity constraint indicating that in this theory the related diseases of superluminal signal propagating and bad analytic properties of S-matrix do not exist. In the last section, we will apply our method to the noncommutative extra dimension theories.     

Virtual photons in chiral perturbation theory

In the framework of chiral perturbation theory virtual photons are included. We calculate the divergences of the generating functional to one loop and determine the structure of the local action that incorporates the counterterms which cancel the divergences. As an application we discuss the corrections to Dashen's theorem at order e²M_q.     

Real and virtual infrared behaviour in Yang-Mills theory

We have calculated the leading infrared divergences, up to fourth order, from both virtual and from real soft gluon corrections to massive quark scattering in an external colourless potential. In the combined corrections, the infrared divergences cancel, as expected. The form of the correction is very simple, and can be expressed in terms of the effective coupling constant of the pure Yang-Mills theory.     

Effective action,conformal anomaly and the issue of quadratic divergences

For massless ?⁴${?}^4$ theory, we explicitly compute the lowest order non-local contributions to the one-loop effective action required for the determination of the trace anomaly. Imposing exact conformal invariance of the local part of the effective action, we argue that the issue of quadratic divergences does not arise in a theory where exact conformal symmetry is only broken by quantum effects. Conformal symmetry can thus replace low energy supersymmetry as a possible guide towards stabilizing the weak scale and solving the hierarchy problem, if (i) there are no intermediate scales between the weak scale and the Planck scale, and (ii) the running couplings exhibit neither Landau poles nor instabilities over this whole range of energies.     

Universality of the rho meson coupling in effective field theory

It is shown that both the universal coupling of the rho meson and the Kawarabayashi-Suzuki-Riadzuddin-Fayyazuddin expression for the magnitude of its coupling constant follow from the requirement that chiral perturbation theory of pions, nucleons, and rho mesons is a consistent effective field theory. The prerequisite of the derivation is that all ultraviolet divergences can be absorbed in the redefinition of fields and the available parameters of the most general effective Lagrangian.     

Are nonrenormalizable gauge theories renormalizable?

We raise the issue whether gauge theories, that are not renormalizable in the usual powercounting sense, are nevertheless renormalizable in the modern sense that all divergences can be cancelled by renormalization of the infinite number of terms in the bare action. We find that a theory is renormalizable in this sense if the a priori constraints that we impose on the form of the bare action correspond to the cohomology of the BRST-transformations generated by the action. Recent cohomology theorems of Bamich, Brandt, and Henneaux are used to show that conventionally nomenormalizable theories of Yang-Mills fields (such as quantum chromodynamics with heavy quarks integrated out) and/or gravitation are renormalizable in the modern sense.     

Thermodynamic properties of asymptotically Reissner–Nordström black holes

Motivated by possible relation between Born–Infeld type nonlinear electrodynamics and an effective low-energy action of open string theory, asymptotically Reissner–Nordström black holes whose electric field is described by a nonlinear electrodynamics (NLED) are studied. We take into account a four dimensional topological static black hole ansatz and solve the field equations, exactly, in terms of the NLED as a matter field. The main goal of this paper is investigation of thermodynamic properties of the obtained black holes. Moreover, we calculate the heat capacity and find that the nonlinearity affects the minimum size of stable black holes. We also use Legendre-invariant metric proposed by Quevedo to obtain scalar curvature divergences. We find that the singularities of the Ricci scalar in Geometrothermodynamics (GTD) method take place at the Davies points.     

Equation of state of gluon plasma from a fundamental modular region

Despite considerable practical success in dealing with the gluon plasma, finite-temperature perturbation theory suffers at the fundamental level from infrared divergences discovered by Linde. However, if gauge or Gribov copies are properly eliminated from the physical state space, infrared modes are strongly suppressed. We describe the gluon plasma in zeroth order as a gas of free quasiparticles with a temperature-independent dispersion relation of Gribov type, E(k)=k(2)sqrt[+M4 / k(2)], that results from the reduction of the physical state space. The effective mass M2 / k controls infrared divergences and allows finite calculable corrections. The equation of state of this gas is calculated and compared with numerical lattice data.     

Guises and disguises of quadratic divergences

In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale λ$\lambda$. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.