arXiv subjects

Agustin Nieto

Publications and source records attributed to Agustin Nieto.

14 recordsLinked to original sources

arXiv1999

Effective field theory approach to N=4 supersymmetric Yang-Mills at finite temperature

We study the perturbation expansion of the free energy of N=4 supersymmetric SU(N) Yang-Mills at finite temperature in powers of 't Hooft's coupling g^2 N in the large N limit. Infrared divergences are controlled by constructing a hierarchy of two 3 dimensional effective field theories. This procedure is applied to the calculation of the free energy to order (g^2 N)^(3/2), but it can be extended to higher order corrections.

hep-th↗

arXiv1998

Quantum Corrections to the Energy Density of a Homogeneous Bose Gas

Quantum corrections to the properties of a homogeneous interacting Bose gas at zero temperature can be calculated as a low-density expansion in powers of $\sqrt{ρa^3}$, where $ρ$ is the number density and $a$ is the S-wave scattering length. We calculate the ground state energy density to second order in $\sqrt{ρa^3}$. The coefficient of the $ρa^3$ correction has a logarithmic term that was calculated in 1959. We present the first calculation of the constant under the logarithm. The constant depends not only on $a$, but also on an extra parameter that describes the low energy $3\to 3$ scattering of the bosons. In the case of alkali atoms, we argue that the second order quantum correction is dominated by the logarithmic term, where the argument of the logarithm is $ρa \ell_V^2$, and $\ell_V$ is the length scale set by the van der Waals potential.

cond-mat.stat-mech↗

arXiv1997

Quantum Corrections to the Ground State of a Trapped Bose-Einstein Condensate

In the mean-field approximation, the number density ρ(r) for the ground state of a Bose-Einstein condensate trapped by an external potential V(r) satisfies a classical field equation called the Gross-Pitaevskii equation. We show that quantum corrections to ρare dominated by quantum fluctuations with wavelengths of order 1/\sqrt{ρa}, where a is the S-wave scattering length. By expanding the equations for the Hartree-Fock approximation to second order in the gradient expansion, we derive local correction terms to the Gross-Pitaevskii equation that take into account the dominant effects of quantum fluctuations. We also show that the gradient expansion for the density breaks down at fourth order.

cond-mat.stat-mech↗

arXiv1997

On Perturbative QCD at High Temperature

Effective field theory methods provide a convenient approach to study static observables in field theory at finite temperature. In this talk, I will outline the construction of the effective field theory that describes effective observables in QCD at high temperature. An analysis of the convergence of the perturbative series for the free energy of QCD will also be presented.

hep-ph↗

arXiv1997

Perturbative QCD at High Temperature

Recent developments of perturbation theory at finite temperature based on effective field theory methods are reviewed. These methods allow the contributions from the different scales to be separated and the perturbative series to be reorganized. The construction of the effective field theory is shown in detail for phi^4 theory and QCD. It is applied to the evaluation of the free energy of QCD at order g^5 and the calculation of the g^6 term is outlined. Implications for the application of perturbative QCD to the quark-gluon plasma are also discussed.

hep-ph↗

arXiv1996

Renormalization Effects in a Dilute Bose Gas

The low-density expansion for a homogeneous interacting Bose gas at zero temperature can be formulated as an expansion in powers of $\sqrt{ρa^3}$, where $ρ$ is the number density and $a$ is the S-wave scattering length. Logarithms of $ρa^3$ appear in the coefficients of the expansion. We show that these logarithms are determined by the renormalization properties of the effective field theory that describes the scattering of atoms at zero density. The leading logarithm is determined by the renormalization of the pointlike $3 \to 3$ scattering amplitude.

hep-th↗

arXiv1996

Thermodynamics of QCD at high temperature

A hierarchy of effective field theories is used to separate the contributions from different momentum scales and to calculate the free energy of QCD at high temperature in powers of the coupling constant up to order $g^5$. The behavior of the perturbative series will also be discussed.

hep-ph↗

arXiv1996

High-Temperature Thermodynamics of QCD

Effective-field-theory methods are used to study the high T limit of QCD. These methods unravel the contributions to the free energy of QCD at high temperature from the scales T, gT, and g^2 T. The free energy is explicitly computed to order g^5. Implications for the application of perturbative QCD to the quark-gluon plasma are also discussed.

hep-ph↗

arXiv1995

Free Energy of QCD at High Temperature

Effective-field-theory methods are used to separate the free energy for a nonabelian gauge theory at high temperature $T$ into the contributions from the momentum scales $T$, $gT$, and $g^2T$, where $g$ is the coupling constant at the scale $2 πT$. The effects of the scale $T$ enter through the coefficients in the effective lagrangian for the 3-dimensional effective theory obtained by dimensional reduction. These coefficients can be calculated as power series in $g^2$. The contribution to the free energy from the scale $gT$ can be calculated using perturbative methods in the effective theory. It can be expressed as an expansion in $g$ starting at order $g^3$. The contribution from the scale $g^2T$ must be calculated using nonperturbative methods, but nevertheless it can be expanded in powers of $g$ beginning at order $g^6$. We calculate the free energy explicitly to order $g^5$. We also outline the calculations necessary to obtain the free energy to order $g^6$.

hep-ph↗

arXiv1995

On the Convergence of Perturbative QCD at High Temperature

The free energy for QCD at high temperature $T$ is calculated to order $g^5$ using effective-field-theory methods to separate the contributions from the momentum scales $T$ and $gT$. The effects of the scale $T$ enter through the coefficients in the effective lagrangian for the 3-dimensional effective theory obtained by dimensional reduction. The perturbation series for these coefficients seem to be well-behaved if the running coupling constant is sufficiently small: $α_s(2 πT) \ll 1$. For the contribution to the free energy from the scale $gT$, the perturbation series is well-behaved only if $α_s(2 πT)$ is an order of magnitude smaller. The implication for applications of perturbative QCD to the quark-gluon plasma are briefly discussed.

hep-ph↗

arXiv1995

Effective Field Theory Approach to High-Temperature Thermodynamics

An effective field theory approach is developed for calculating the thermodynamic properties of a field theory at high temperature $T$ and weak coupling $g$. The effective theory is the 3-dimensional field theory obtained by dimensional reduction to the bosonic zero-frequency modes. The parameters of the effective theory can be calculated as perturbation series in the running coupling constant $g^2(T)$. The free energy is separated into the contributions from the momentum scales $T$ and $gT$, respectively. The first term can be written as a perturbation series in $g^2(T)$. If all forces are screened at the scale $gT$, the second term can be calculated as a perturbation series in $g(T)$ beginning at order $g^3$. The parameters of the effective theory satisfy renormalization group equations that can be used to sum up leading logarithms of $T/(gT)$. We apply this method to a massless scalar field with a $Φ^4$ interaction, calculating the free energy to order $g^6 \log g$ and the screening mass to order $g^5 \log g$.

hep-ph↗

arXiv1994

Asymptotic Behavior of the Correlator for Polyakov Loops

The asymptotic behavior of the correlator for Polyakov loop operators separated by a large distance $R$ is determined for high temperature QCD. It is dominated by nonperturbative effects related to the exchange of magnetostatic gluons. To analyze the asymptotic behavior, the problem is formulated in terms of the effective field theory of QCD in 3 space dimensions. The Polyakov loop operator is expanded in terms of local gauge-invariant operators constructed out of the magnetostatic gauge field, with coefficients that can be calculated using resummed perturbation theory. The asymptotic behavior of the correlator is $\exp(-MR)/R$, where $M$ is the mass of the lowest-lying glueball in $(2+1)$-dimensional QCD. This result implies that existing lattice calculations of the Polyakov loop correlator at the highest temperatures available do not probe the true asymptotic region in $R$.

hep-ph↗

arXiv1994

Next-to-leading Order Debye Mass for the Quark-gluon Plasma

The Debye screening mass for a quark-gluon plasma at high temperature is calculated to next-to-leading order in the QCD coupling constant from the correlator of two Polyakov loops. The result agrees with the screening mass defined by the location of the pole in the gluon propagator as calculated by Rebhan. It is logarithmically sensitive to nonperturbative effects associated with the screening of static chromomagnetic fields.

hep-ph↗

arXiv1993

Evaluating Sums over the Matsubara Frequencies

Perturbative calculations in field theory at finite temperature involve sums over the Matsubara frequencies. Besides the usual difficulties that appear in perturbative computations, these sums give rise to some new obstacles that are carefully analized here. I present a fast and realible recipe to work out sums over the Matsubara frequencies. As this algorithm leads to deal with very cumbersome algebraic expressions, it has been written for computers by using the symbolic manipulation program Mathematica. It is also shown this algorithm to be self-consistent when it is applied to more than one loop computations.

hep-ph↗