Search results for "equation"
showing 10 items of 4219 documents
Gluon mass generation in the PT-BFM scheme
2006
In this article we study the general structure and special properties of the Schwinger-Dyson equation for the gluon propagator constructed with the pinch technique, together with the question of how to obtain infrared finite solutions, associated with the generation of an effective gluon mass. Exploiting the known all-order correspondence between the pinch technique and the background field method, we demonstrate that, contrary to the standard formulation, the non-perturbative gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions. We next present a comprehensive review of several subtle issues relevant to the search …
Limits on the parameters of the equation of state for interacting dark energy
2010
Under the assumption that cold dark matter and dark energy interact with each other through a small coupling term, $Q$, we constrain the parameter space of the equation of state $w$ of those dark energy fields whose variation of the field since last scattering do not exceed Planck's mass. We use three parameterizations of $w$ and two different expressions for $Q$. Our work extends previous ones.
Cosmological Horizon Modes and Linear Response in de Sitter Spacetime
2009
Linearized fluctuations of quantized matter fields and the spacetime geometry around de Sitter space are considered in the case that the matter fields are conformally invariant. Taking the unperturbed state of the matter to be the de Sitter invariant Bunch-Davies state, the linear variation of the stress tensor about its self-consistent mean value serves as a source for fluctuations in the geometry through the semiclassical Einstein equations. This linear response framework is used to investigate both the importance of quantum backreaction and the validity of the semiclassical approximation in cosmology. The full variation of the stress tensor delta bi contains two kinds of terms: (1) those…
Noncommutative space and the low-energy physics of quasicrystals
2008
We prove that the effective low-energy, nonlinear Schroedinger equation for a particle in the presence of a quasiperiodic potential is the potential-free, nonlinear Schroedinger equation on noncommutative space. Thus quasiperiodicity of the potential can be traded for space noncommutativity when describing the envelope wave of the initial quasiperiodic wave.
Free field realization of cylindrically symmetric Einstein gravity
1998
Cylindrically reduced Einstein gravity can be regarded as an $SL(2,R)/SO(2)$ sigma model coupled to 2D dilaton gravity. By using the corresponding 2D diffeomorphism algebra of constraints and the asymptotic behaviour of the Ernst equation we show that the theory can be mapped by a canonical transformation into a set of free fields with a Minkowskian target space. We briefly discuss the quantization in terms of these free-field variables, which is considerably simpler than in the other approaches.
Lorentz harmonics and superfield action. D=10, N=1 superstring
2000
We propose a new version of the superfield action for a closed D=10, N=1 superstring where the Lorentz harmonics are used as auxiliary superfields. The incorporation of Lorentz harmonics into the superfield action makes possible to obtain superfield constraints of the induced worldsheet supergravity as equations of motion. Moreover, it becomes evident that a so-called 'Wess-Zumino part' of the superfield action is basically a Lagrangian form of the generalized action principle. We propose to use the second Noether theorem to handle the essential terms in the transformation lows of hidden gauge symmetries, which remove dynamical degrees of freedom from the Lagrange multiplier superfield.
General invertible transformation and physical degrees of freedom
2017
An invertible field transformation is such that the old field variables correspond one-to-one to the new variables. As such, one may think that two systems that are related by an invertible transformation are physically equivalent. However, if the transformation depends on field derivatives, the equivalence between the two systems is nontrivial due to the appearance of higher derivative terms in the equations of motion. To address this problem, we prove the following theorem on the relation between an invertible transformation and Euler-Lagrange equations: If the field transformation is invertible, then any solution of the original set of Euler-Lagrange equations is mapped to a solution of …
The Bethe ansatz and the Tzitzéica–Bullough–Dodd equation
2012
The theory of classically integrable nonlinear wave equations, and the Bethe Ansatz systems describing massive quantum field theories defined on an infinite cylinder, are related by an important mathematical correspondence that still lacks a satisfactory physical interpretation. In this paper we shall describe this link for the case of the classical and quantum versions of the (Tzitz\'eica-)Bullough-Dodd model.
Gluon mass scale through nonlinearities and vertex interplay
2019
We present a novel analysis of the gluon gap equation, where its full nonlinear structure is duly taken into account. In particular, while in previous treatments the linearization of this homogeneous integral equation introduced an indeterminacy in the scale of the corresponding mass, the current approach determines it uniquely, once the value of the gauge coupling at a given renormalization point is used as input. A crucial ingredient for this construction is the "kinetic term" of the gluon propagator, whose form is not obtained from the complicated equation governing its evolution, but is rather approximated by suitable initial {\it Ans\"atze}, which are subsequently improved by means of …
Generalized Slow Roll in the Unified Effective Field Theory of Inflation
2017
We provide a compact and unified treatment of power spectrum observables for the effective field theory (EFT) of inflation with the complete set of operators that lead to second-order equations of motion in metric perturbations in both space and time derivatives, including Horndeski and GLPV theories. We relate the EFT operators in ADM form to the four additional free functions of time in the scalar and tensor equations. Using the generalized slow roll formalism, we show that each power spectrum can be described by an integral over a single source that is a function of its respective sound horizon. With this correspondence, existing model independent constraints on the source function can b…