arXiv subjects

M. E. Carrington

Publications and source records attributed to M. E. Carrington.

At least 37 records · Page 2Linked to original sources

arXiv2013

Results from the 4PI Effective Action in 2- and 3-dimensions

We consider a symmetric scalar theory with quartic coupling and solve the equations of motion from the 4PI effective action in 2- and 3-dimensions using an iterative numerical lattice method. For coupling less than 10 (in dimensionless units) good convergence is obtained in less than 10 iterations. We use lattice size up to 16 in 2-dimensions and 10 in 3-dimensions and demonstrate the convergence of the results with increasing lattice size. The self-consistent solutions for the 2-point and 4-point functions agree well with the perturbative ones when the coupling is small and deviate when the coupling is large.

hep-ph↗

arXiv2013

Thermal field theory at next-to-leading order in the hard thermal loop expansion

In this paper we study the hard-thermal-loop effective theory at next-to-leading order. Standard power-counting predicts that a large number of diagrams, including 2-loop diagrams, may need to be calculated. In all of the calculations that have been done however, with the exception of the photon self-energy, the full next-to-leading order contribution can be obtained by calculating only soft 1-loop diagrams with effective lines and vertices. It is of interest to know if the photon self-energy is the only exception to this rule, or if there are others, and which ones. In this paper we perform a refined power-counting analysis using real-time finite temperature field theory which is particularly well suited to the task. We show that the standard power-counting rules obtained from the imaginary time formalism usually over-estimate the size of the 2-loop diagrams. We argue that the only exceptions to the rule that the 1-loop soft diagrams give the next-to-leading order contribution are $2n$-photon vertices.

hep-ph↗

arXiv2012

Renormalization group flow equations connected to the $n$PI effective action

In this paper we derive a hierarchy of integral equations from the 4PI effective action which have the form of Bethe-Salpeter equations. We show that the vertex functions defined by these equations can be used to truncate the exact renormalization group flow equations. This truncation has the property that the flow is a total derivative with respect to the flow parameter. We also show that the truncation is equivalent to solving the $n$PI equations of motion. This result establishes a direct connection between two non-perturbative methods.

hep-ph↗

arXiv2012

A new method to calculate the n-Particle Irreducible Effective Action

In this paper, we present a new method to calculate the n-Loop n-particle irreducible effective action. The key is an organizational trick that involves the introduction of a set of fictitious bare vertices that are set to zero at the end of the calculation. Using these fictitious vertices, we prove that the Schwinger-Dyson equations are the same as the equations of motion obtained from the n-particle irreducible effective action, up to the level at which they respect the symmetries of the original theory. This result allows us to obtain the effective action directly from the Schwinger-Dyson equations, which are comparatively easy to calculate. As a check of our method, we reproduce the known results for the n-Loop n-particle irreducible effective action with n = 4 and n = 5. We also use the technique to calculate the 6-Loop 6-particle irreducible effective action.

hep-ph↗

arXiv2012

Parton Energy Loss in Two-Stream Plasma System

The energy loss of a fast parton scattering elastically in a weakly coupled quark-gluon plasma is formulated as an initial value problem. The approach is designed to study an unstable plasma, but it also reproduces the well known result of energy loss in an equilibrium plasma. A two-stream system, which is unstable due to longitudinal chromoelectric modes, is discussed here some detail. In particular, a strong time and directional dependence of the energy loss is demonstrated.

nucl-th↗

arXiv2011

Perturbative and Nonperturbative Kolmogorov Turbulence in a Gluon Plasma

In numerical simulations of nonabelian plasma instabilities in the hard-loop approximation, a turbulent spectrum has been observed that is characterized by a phase-space density of particles $n(p)\sim p^{-ν}$ with exponent $ν\simeq 2$, which is larger than expected from relativistic $2\leftrightarrow 2$ scatterings. Using the approach of Zakharov, L'vov and Falkovich, we analyse possible Kolmogorov coefficients for relativistic $(m \ge 4)$-particle processes, which give at most $ν=5/3$ perturbatively for an energy cascade. We discuss nonperturbative scenarios which lead to larger values. As an extreme limit we find the result $ν=5$ generically in an inherently nonperturbative effective field theory situation, which coincides with results obtained by Berges et al.\ in large-$N$ scalar field theory. If we instead assume that scaling behavior is determined by Schwinger-Dyson resummations such that the different scaling of bare and dressed vertices matters, we find that intermediate values are possible. We present one simple scenario which would single out $ν=2$.

hep-ph↗

arXiv2011

Transport Coefficients and nPI Methods

Transport coefficients can be obtained from 2-point correlators using the Kubo formulae. It has been shown that the full leading order result for electrical conductivity and (QCD) shear viscosity is contained in the re-summed 2-point function that is obtained from the 3-loop 3PI effective action. The theory produces all leading order contributions without the necessity for power counting, and in this sense it provides a natural framework for the calculation and suggests that one can calculate the next-to-leading contribution to transport coefficients from the 4-loop 4PI effective action. The integral equations have been derived for shear viscosity for a scalar theory with cubic and quartic interactions, with a non-vanishing field expectation value. We review these results, and explain how the calculation could be done at higher orders.

hep-ph↗

arXiv2011

Geometrical entanglement of highly symmetric multipartite states and the Schmidt decomposition

In a previous paper we examined a geometric measure of entanglement based on the minimum distance between the entangled target state of interest and the space of unnormalized product states. Here we present a detailed study of this entanglement measure for target states with a large degree of symmetry. We obtain analytic solutions for the extrema of the distance function and solve for the Hessian to show that, up to the action of trivial symmetries, the solutions correspond to local minima of the distance function. In addition, we show that the conditions that determine the extremal solutions for general target states can be obtained directly by parametrizing the product states via their Schmidt decomposition.

quant-ph↗

arXiv2011

Techniques for n-Particle Irreducible Effective Theories

In this paper we show that the skeleton diagrams in the m-Loop nPI effective action correspond to an infinite resummation of perturbative diagrams which is void of double counting at the m-Loop level. We also show that the variational equations of motion produced by the n-Loop nPI effective theory are equivalent to the Schwinger-Dyson equations, up to the order at which they are consistent with the underlying symmetries of the original theory. We use a diagrammatic technique to obtain the 5-Loop 5PI effective action for a scalar theory with cubic and quartic interactions, and verify that the result satisfies these two statements.

hep-ph↗

arXiv2010

Geometric measures of entanglement and the Schmidt decomposition

In the standard geometric approach, the entanglement of a pure state is $\sin^2θ$, where $θ$ is the angle between the entangled state and the closest separable state of products of normalised qubit states. We consider here a generalisation of this notion by considering separable states that consist of products of unnormalised states of different dimension. The distance between the target entangled state and the closest unnormalised product state can be interpreted as a measure of the entanglement of the target state. The components of the closest product state and its norm have an interpretation in terms of, respectively, the eigenvectors and eigenvalues of the reduced density matrices arising in the Schmidt decomposition of the state vector. For several cases where the target state has a large degree of symmetry, we solve the system of equations analytically, and look specifically at the limit where the number of qubits is large.

quant-ph↗

arXiv2010

Next-to-Leading Order Transport Coefficients from the Four-Particle Irreducible Effective Action

Transport coefficients can be obtained from 2-point correlators using the Kubo formulae. It has been shown that the full leading order result for electrical conductivity and (QCD) shear viscosity is contained in the re-summed 2-point function that is obtained from the 3-loop 3PI re-summed effective action. The theory produces all leading order contributions without the necessity for power counting, and in this sense it provides a natural framework for the calculation. In this article we study the 4-loop 4PI effective action for a scalar theory with cubic and quartic interactions in the presence of spontaneous symmetry breaking. We obtain a set of integral equations that determine the re-summed 2-point vertex function. A next-to-leading order contribution to the viscosity could be obtained from this set of coupled equations.

hep-ph↗

arXiv2009

On the imaginary part of the next-to-leading-order static gluon self-energy in an anisotropic plasma

Using hard-loop (HL) effective theory for an anisotropic non-Abelian plasma, which even in the static limit involves nonvanishing HL vertices, we calculate the imaginary part of the static next-to-leading-order gluon self energy in the limit of a small anisotropy and with external momentum parallel to the anisotropy direction. At leading order, the static propagator has space-like poles corresponding to plasma instabilities. On the basis of a calculation using bare vertices, it has been conjectured that, at next-to-leading order, the static gluon self energy acquires an imaginary part which regulates these space-like poles. We find that the one-loop resummed expression taken over naively from the imaginary-time formalism does yield a nonvanishing imaginary part even after including all HL vertices. However, this result is not correct. Starting from the real-time formalism, which is required in a non-equilibrium situation, we construct a resummed retarded HL propagator with correct causality properties and show that the static limit of the retarded one-loop-resummed gluon self-energy is real. This result is also required for the time-ordered propagator to exist at next-to-leading order.

hep-ph↗

arXiv2009

Leading Order QCD Shear Viscosity from the 3PI Effective Action

In this article we calculate the leading order shear viscosity in QCD using the resummed 3PI effective action. We work to 3-loop order in the effective action. We show that the integral equations that resum the pinching and collinear contributions are produced naturally by the formalism. All leading order terms are included, without the need for any kind of power counting arguments.

hep-ph↗

arXiv2008

Next-to-leading order static gluon self-energy for anisotropic plasmas

In this paper the structure of the next-to-leading (NLO) static gluon self energy for an anisotropic plasma is investigated in the limit of a small momentum space anisotropy. Using the Ward identities for the static hard-loop (HL) gluon polarization tensor and the (nontrivial) static HL vertices, we derive a comparatively compact form for the complete NLO correction to the structure function containing the space-like pole associated with magnetic instabilities. On the basis of a calculation without HL vertices, it has been conjectured that the imaginary part of this structure function is nonzero, rendering the space-like poles integrable. We show that there are both positive and negative contributions when HL vertices are included, highlighting the necessity of a complete numerical evaluation, for which the present work provides the basis.

hep-ph↗

arXiv2008

The fermion mass at next-to-leading order in the HTL effective theory

The calculation of the real part of a quasi-particle dispersion relation at next-to-leading order in the hard thermal loop effective theory is a very difficult problem. Even though the hard thermal loop effective theory is almost 20 years old, there is only one next-to-leading order calculation of the real part of a quasi-particle dispersion relation in the literature. In this paper, we calculate the fermion mass in QED and QCD at next-to-leading order. For QED the result is M=eT/sqrt{8} * [1-(1.427 \pm 0.02)e/4pi] and for QCD with N_f=2 and N_c=3 we obtain M=gT/sqrt{6} * [1+(1.867 \pm 0.02)g/4pi].

hep-ph↗

arXiv2007

Energetic di-leptons from the Quark Gluon Plasma

In this paper we study the production of energetic di-leptons. We calculate the rate for 2 $\to$ 2 processes. The log term is obtained analytically and the constant term is calculated numerically. When the photon mass is of the order of the thermal quark mass, the result is insensitive to the photon mass and the soft logarithmic divergence is regulated by the thermal quark mass, exactly as in the case of real photons. We also consider the production of thermal Drell-Yan dileptons (thermal quark and antiquark pairs produced by virtual photons) and calculate the rate systematically in the context of the hard thermal loop effective theory. We obtain analytic and numerical results. We compare our results with those of previous calculations.

hep-ph↗

arXiv2007

Leading Order QED Electrical Conductivity from the 3PI Effective Action

In this article we study the electrical conductivity in QED using the resummed 3PI effective action. We work to 3-loop order in the effective action. We show that the resulting expression for the conductivity is explicitly gauge invariant, and that the integral equations that resum the pinching and colinear contributions are produced naturally by the formalism. All leading order terms are included, without the need for any kind of power counting arguments.

hep-ph↗

arXiv2007

QED Electrical Conductivity using the 2PI Effective Action

In this article we calculate the electrical conductivity in QED using the 2PI effective action. We use a modified version of the usual 2PI effective action which is defined with respect to self-consistent solutions of the 2-point functions. We show that the green functions obtained from this modified effective action satisfy ward identities and that the conductivity obtained from the kubo relation is gauge invariant. We work to 3-loop order in the modified 2PI effective action and show explicitly that the resulting expression for the conductivity contains the square of the amplitude that corresponds to all binary collision and production processes.

hep-ph↗