Conformal Field Research Articles

Algebraically Decaying Modes in Many Dimensions: Application of Fubini’s Identity to Guided-Wave Optics

We show analytically that application of an identity in conformal invariant field theories to multidimensional guided-wave optics predicts a generic family of modes with algebraic (power-law) tails in the evanescent field.

Generalized Cauchy determinant formula and its applications to Coulomb gas problems

Using only elementary methods, we generalize the classical Cauchy determinant formula and indicate applications to two-dimensional systems including the neutral asymmetric Coulomb gas and conformal quantum field theory.

Factors influencing incidence of acute grade 2 morbidity in conformal and standard radiation treatment of prostate cancer

Purpose : The fundament hypothesis of conformal radiation therapy is that tumor control can be increased by using conformal treatment techniques that allow a higher tumor dose while maintaining an acceptable level of complications. To test this hypothesis, it is necessary first to estimate the incidence of morbidity for both standard and conformal fields. In this study, we examine factors that influence the incidence of acute grade 2 morbidity in patients treated with conformal and standard radiation treatment for prostate cancer. Methods and Materials : Two hundred and forty-seven consecutive patients treated with conformal technique are combined with and compared to 162 consecutive patients treated with standard techniques. The conformal technique includes special immobilization by a cast, careful identification of the target volume in three dimensions, localization of the inferior border of the prostate using the retrograde urethrogram, and individually shaped portals that conform to the Planning Target Volume (PTV). Univariate analysis compares differences in thte incidence of RTOG-EORTC grade two acute morbidity by technique, T stage, age, irradiated volume, and dose. Multivariate logistic regression includes these same variables. Results : In nearly all categories, the conformal treatment group experienced significantly fewer acutet grade 2 complications than the standard treatment group. Only volume (prostate ± whole pelvis) and technique (conformal vs. standard) were significantly related to incidence of morbidity on multivariate analysis. When dose is treated as a continuous variable (rather than being dichotomized into two levels), a trend is observed on multivariate analysis, but it does not reach significant levels. The incidence of acute grade 2 morbidity in patients 65 years or older is significantly reduced by use of the conformal technique. Conclusion : The conformal technique is associated with fewer grade 2 acute toxicities for all patients. This conclusion is valid irrespective of selection criteria except ina few cases. Older age is associated with increased toxicity only with the standard technique and not then at a statistically significant level. Elderly patients should not be excluded from external beam radiation because of increased morbidity especially if conformal treatment is available. Volume is not significantly related to morbidity in patients with standard treatment, but it is for conformal treatment. Furthermore, it remains significant in a multivariate analysis that also shows the advantage of conformal treatment. Grade 2 acute toxicities are more volume dependent than those dependent.

The energy localization problem and the renormalized vacuum energy in static Robertson-Walker universes

We calculate the renormalized quantum vacuum energy inside a spherical boundary for the massless conformal scalar field in curved background Robertson-Walker geometry. We use the mode sum method with an exponential cutoff. In our calculations we do not make assumptions about the exterior geometry or the global topology of the universe.

Winding-angle distribution for Brownian and self-avoiding walks.

We study some generic aspects of the winding-angle distribution around a point in two dimensions for Brownian and self-avoiding walks using corner transfer matrix and conformal field theory.Received 6 December 1993DOI:https://doi.org/10.1103/PhysRevE.50.1123©1994 American Physical Society

CURIOSITIES AT c-EFFECTIVE = 1

The moduli space of all rational conformal quantum field theories with effective central charge c eff = 1 is considered. Whereas the space pf unitary theories essentially forms a manifold, the nonunitary ones form a fractal which lies dense in the parameter plane. Moreover, the points of this set are shown to be in one-to-one correspondence with the elements of the modular group for which an action on this set is defined.

Stability of the inflation in R2 cosmology with massless conformal quantum fields

A semiclassical higher-derivative theory of gravity is investigated for conformally invariant free quantum fields in homogeneous and isotropic spacetime with no cosmological constant nor classical source. In the spatially flat case the stability of the de Sitter solution is studied. Moreover, the Minkowski solution is found to be unstable.

Quantum wormhole with conformal scalar field

In this paper I use the Hartle-Hawking method to discuss quantum wormhole with conformal scalar field. I derive the corresponding Wheeler-De Witt equation, calculate the wormhole wave function, which is found to be the product of two harmonic solutions. Analysis of the wave function reveals that the probability density of the wormhole appearing at a = 0 is zero, that the most probable radius of the wormhole base state is the Planck length and that the wormhole is mostly likely to be in a state of small Φ value.

Casimir energy in a curved background with a spherical boundary: An exactly solvable case.

We reconsider the Casimir effect for the massless conformal scalar field in a ``half Einstein universe.'' This case is interesting in that it could be solved analytically by several different methods. Thus, it allows us to compare and understand effects of different approaches. We first calculate the renormalized vacuum energy by using the mode sum method and study the effects of different cutoff functions. Next, we calculate the renormalized vacuum energy-momentum tensor by using the covariant point-splitting method. We construct the Green's functions by using the eigenfunctions, which are obtained by solving the wave equation with the appropriate boundary conditions (Dirichlet and Neumann). We discuss further properties of this case as well as its relation to previous calculations.

BOSONIC SUPERCONFORMAL AFFINE TODA THEORY: EXCHANGE ALGEBRA AND DRESSING SYMMETRY

We propose and investigate a new conformal invariant integrable field theory called bosonic superconformal affine Toda theory. This theory can be viewed either as the affine generalization of the so-called bosonic superconformal Toda theory studied by the authors sometime earlier, or as the generalization to the case of half-integer conformal weights of the conformal affine Toda theory, and can also be obtained from the Hamiltonian reduction of WZNW theory (with an affine WZNW group). The fundamental Poisson stracture is established in terms of the classical r matrix. Then the exchange algebra for the chiral vectors is obtained as well as the reconstruction formula for the classical solutions. The dressing transformations of the fundamental fields are found explicitly, and the Poisson-Lie structure of the dressing group is also constructed with the aid of classical exchange algebras, which turns out to be the semiclassical limit of the quantum affine group. The conformal breaking orbit of the model is also studied, which is called bosonic super loop Toda theory in the context. In addition, the quantum exchange relation and quantum group symmetry are discussed briefly.

Cancellation of quantum effects (〈T 00〉reg = 0) for a massive conformal scalar field in Robertson-Walker universe

It is shown that the regularized 00 component of the vacuum expectation value of the energy-momentum tensor of the matter field is null, when the following conditions are taken into account: i) Massive conformai scalar field in Robertson-Walker metric. ii) Diagonalization of the Hamiltonian at the observation time. iii) WKB approximation of the matter field. iv) Adiabatic regularization.

Infinite symmetry group in D-dimensional conformal quantum field theory

The diffeomorphism group of the D-dimensional space as the symmetry group for conformal quantum field theory models is proposed. The problem of calculation of critical exponents turns out to be reduced to the study of special diffeomorphism group representations. The general properties of these representations on the space of symmetric traceless tensors are investigated.

Inflation inR 2 cosmology with massless conformal scalar field and adiabatic regularization

A cosmology described by a Robertson-Walker metric with Lagrangian √-g(@#@R+σR2) and a massless conformal scalar field as matter content is considered. It is shown that, when the adiabatic regularization is performed, there is, in the spatially flat case, an inflationary solution which is not stable in the future, at first perturbative order, if the condition σ>t p 2 /2160π (tp Planck time) is fulfilled and stable in the opposite case.

RENORMALISED STRESS-ENERGY TENSOR OF CONFORMAL SCALAR FIELD IN BOULWARE STATE IN REISSNER-NORDSTR?M SPACE-TIME

The renormalised stress-energy tensor of a conformal invariant scalar field in the Boul-ware stale in Reissner-Nordstr?m sapace-time is calculated by using the Page-Zannias method and with the help of a personal computer and REDUCE language. The tensor vanishes inthe asymptotically flat region and is not regular at the event horizon.

Qualitative study of multidimensional cosmological models

A qualitative analysis of cosmological models induced by the multidimensional theories is performed. The Einstein-Maxwell system written in an arbitrary n-dimensional manifold, with n>4 is studied. Firstly, the original system is reduced to four dimensions. The analysis of the resulting equations is made by the dynamical system method. The evolution of the corresponding solutions is represented by curves in the phase diagram. Also a comparison of the results is made with those found previously in the context of the coupling of the Einstein-Hilbert lagrangian with a conformal field in higher dimensions.

CONFORMAL FIELDS: A CLASS OF REPRESENTATIONS OF Vect(N)

Vect (N), the algebra of vector fields in N dimensions, is studied. Some aspects of local differential geometry are formulated as Vect(N) representation theory. There is a new class of modules, conformal fields, whose restrictions to the subalgebra sl(N+1)⊂ Vect (N) are finite-dimensional sl (N+1) representations. In this regard they are simpler than tensor fields. Fock modules are also constructed. Infinities, which are unremovable even by normal ordering, arise unless bosonic and fermionic degrees of freedom match.

WORMHOLE SOLUTIONS IN R1×S1×S2 TOPOLOGICAL SPACE

Wormhole solutions are discussed for two different physical situations in the background of a homogeneous anisotropic space-time. In the first case, the wormholes are solutions of the Euclidean Einstein equations with a cosmological constant and a two-index anti-symmetric tensor for monopole configuration on a space with three-surface of topology S1×S2. In the second step, conformal scalar field is coupled to gravity and wormhole are considered for both λ=0 and λ>0. These results are analogous to the wormhole solutions for FRW metric.

Conformal complex scalar field wormhole at finite temperature

In this paper, we discuss the wormhole model with spontaneous symmetry breakdown coupled to conformal complex scalar field at finite temperature, and find that the temperature has great influence on the Coleman-Lee wormholes. This kind of wormholes can exist in the regions of 0≤T≲MP.

CONFORMAL AFFINE TODA FIELD THEORIES

The conformal affine sl2 Toda field theory is introduced and analyzed both in the continuum and on the lattice.

Projections of Virasoro singular vectors

We use recently derived explicit formulae for the Virasoro algebra's singular vectors to give constructive proofs of three results due to Feigin and Fuchs. The main result, which is needed for a rigorous treatment of fusion, describes the action of the singular vectors on conformal fields.