scholarly journals On Quantum Fields at High Temperature

Universe ◽  
2019 ◽  
Vol 5 (1) ◽  
pp. 26
Author(s):  
Ingolf Bischer ◽  
Thierry Grandou ◽  
Ralf Hofmann
Keyword(s):  
Perturbation Theory ◽  
High Temperature ◽  
Zero Temperature ◽  
Quantum Fields ◽  
Thermal Perturbation ◽  
Loop Order ◽  
Momentum Scale ◽  
Damping Rate ◽  
Rate Calculation

Revisiting the fast fermion damping rate calculation in a thermalized momentum scale eT (QED) and/or momentum scale gT (QCD) plasma at 4-loop order, focus is put on a peculiar perturbative structure which has no equivalent at zero-temperature. Not surprisingly, and in agreement with previous C ★ -algebraic analyses, this structure renders the use of thermal perturbation theory quite questionable.

scholarly journals Perturbative Peculiarities of Quantum Field Theories at High Temperatures

Universe ◽  
2019 ◽  
Vol 5 (3) ◽  
pp. 81
Author(s):  
Ingolf Bischer ◽  
Thierry Grandou ◽  
Ralf Hofmann
Keyword(s):  
Perturbation Theory ◽  
Thermal Equilibrium ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Zero Temperature ◽  
Thermal Perturbation ◽  
Loop Order ◽  
Damping Rate ◽  
Rate Calculation

Revisiting the fast fermion damping rate calculation in a thermalized QED and/or QCD plasma in thermal equilibrium at four-loop order, focus is put on a peculiar perturbative structure which has no equivalent at zero-temperature. Not surprisingly, and in agreement with previous C ☆ -algebraic analyses, this structure renders the use of thermal perturbation theory more than questionable.

GAUGE INDEPENDENCE OF THE FERMION DAMPING RATE IN A HOT PLASMA - LANDAU GAUGE VS COULOMB GAUGE

1993 ◽  
Vol 08 (08) ◽  
pp. 739-748
Author(s):  
H. NAKKAGAWA ◽  
A. NIÉGAWA ◽  
B. PIRE
Keyword(s):  
Perturbation Theory ◽  
Gluon Propagator ◽  
Landau Gauge ◽  
Coulomb Gauge ◽  
Leading Order ◽  
Loop Order ◽  
Hard Thermal Loop ◽  
Hot Plasma ◽  
Damping Rate

The damping rate of a heavy muon/quark in a hot QED/QCD plasma is calculated in the Landau gauge to the effective one-loop order in the resummed perturbation theory of Braaten and Pisarski. For both a muon/quark at rest and in an energetic case we obtain to leading order the same result as in the Coulomb gauge. Resummation of hard-thermal loop corrections to the photon/gluon propagator is of key importance for this gauge independence.

scholarly journals On the perturbative expansion at high temperature and implications for cosmological phase transitions

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Oliver Gould ◽  
Tuomas V. I. Tenkanen
Keyword(s):  
Phase Transitions ◽  
High Temperature ◽  
Effective Potential ◽  
Bubble Nucleation ◽  
Perturbative Expansion ◽  
Zero Temperature ◽  
Loop Order ◽  
First Order ◽  
First Order Phase ◽  
Renormalisation Scale

Abstract We revisit the perturbative expansion at high temperature and investigate its convergence by inspecting the renormalisation scale dependence of the effective potential. Although at zero temperature the renormalisation group improved effective potential is scale independent at one-loop, we show how this breaks down at high temperature, due to the misalignment of loop and coupling expansions. Following this, we show how one can recover renormalisation scale independence at high temperature, and that it requires computations at two-loop order. We demonstrate how this resolves some of the huge theoretical uncertainties in the gravitational wave signal of first-order phase transitions, though uncertainties remain stemming from the computation of the bubble nucleation rate.

scholarly journals A NOTE ON THE CASIMIR ENERGY OF A MASSIVE SCALAR FIELD IN POSITIVE CURVATURE SPACE

2004 ◽  
Vol 19 (02) ◽  
pp. 111-116 ◽  
Author(s):  
E. ELIZALDE ◽  
A. C. TORT
Keyword(s):  
High Temperature ◽  
Scalar Field ◽  
Zeta Function ◽  
Vacuum Energy ◽  
Positive Curvature ◽  
Zero Point ◽  
Casimir Energy ◽  
Massive Scalar ◽  
Zero Temperature ◽  
Massive Scalar Field

We re-evaluate the zero point Casimir energy for the case of a massive scalar field in R1×S3 space, allowing also for deviations from the standard conformal value ξ=1/6, by means of zero temperature zeta function techniques. We show that for the problem at hand this approach is equivalent to the high temperature regularization of the vacuum energy, as conjectured in a previous publication. The analytic continuation can be performed in two ways, which are seen to be equivalent.

scholarly journals Effective high-temperature estimates for intermittent maps

2017 ◽  
Vol 39 (8) ◽  
pp. 2159-2175
Author(s):  
BENOÎT R. KLOECKNER
Keyword(s):  
Perturbation Theory ◽  
High Temperature ◽  
Limit Theorem ◽  
Spectral Gap ◽  
Lipschitz Constant ◽  
Transfer Operator ◽  
Linear Operators ◽  
Suitable Assumption ◽  
Unimodal Map ◽  
Definition Of

Using quantitative perturbation theory for linear operators, we prove a spectral gap for transfer operators of various families of intermittent maps with almost constant potentials (‘high-temperature’ regime). Hölder and bounded $p$-variation potentials are treated, in each case under a suitable assumption on the map, but the method should apply more generally. It is notably proved that for any Pommeau–Manneville map, any potential with Lipschitz constant less than 0.0014 has a transfer operator acting on $\operatorname{Lip}([0,1])$ with a spectral gap; and that for any two-to-one unimodal map, any potential with total variation less than 0.0069 has a transfer operator acting on $\operatorname{BV}([0,1])$ with a spectral gap. We also prove under quite general hypotheses that the classical definition of spectral gap coincides with the formally stronger one used in Giulietti et al [The calculus of thermodynamical formalism. J. Eur. Math. Soc., to appear. Preprint, 2015, arXiv:1508.01297], allowing all results there to be applied under the high-temperature bounds proved here: analyticity of pressure and equilibrium states, central limit theorem, etc.

THE CALCULATION OF VARIOUS QUANTITIES WITHIN PERTURBATION THEORY AT THE 3- AND 4-LOOP ORDER

1995 ◽  
Vol 06 (04) ◽  
pp. 513-518 ◽  
Author(s):  
T. VAN RITBERGEN ◽  
J.A.M. VERMASEREN ◽  
S.A. LARIN ◽  
P. NOGUEIRA
Keyword(s):  
Perturbation Theory ◽  
Quark Mass ◽  
Decay Rates ◽  
High Order ◽  
Loop Order ◽  
Perturbative Calculations ◽  
Methods And Techniques ◽  
Mass Expansion

We discuss methods and techniques that were recently used in the following high order perturbative calculations: the large quark mass expansion of the decay rates Z0→ hadrons and τ→ν+ hadrons and the calculation of various quantities for deep inelastic lepton hadron scattering. Progress on the automatization of some general procedures is discussed.

scholarly journals Two-flavor chiral perturbation theory at nonzero isospin: pion condensation at zero temperature

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
Prabal Adhikari ◽  
Jens O. Andersen ◽  
Patrick Kneschke
Keyword(s):  
Perturbation Theory ◽  
Equation Of State ◽  
Condensed Phase ◽  
Chiral Perturbation Theory ◽  
Chemical Potential ◽  
Tree Level ◽  
Zero Temperature ◽  
Leading Order ◽  
Chiral Perturbation ◽  
Pion Condensation

Abstract In this paper, we calculate the equation of state of two-flavor finite isospin chiral perturbation theory at next-to-leading order in the pion-condensed phase at zero temperature. We show that the transition from the vacuum phase to a Bose-condensed phase is of second order. While the tree-level result has been known for some time, surprisingly quantum effects have not yet been incorporated into the equation of state.  We find that the corrections to the quantities we compute, namely the isospin density, pressure, and equation of state, increase with increasing isospin chemical potential. We compare our results to recent lattice simulations of 2 + 1 flavor QCD with physical quark masses. The agreement with the lattice results is generally good and improves somewhat as we go from leading order to next-to-leading order in $$\chi $$χPT.

scholarly journals Quark and pion condensates at finite isospin density in chiral perturbation theory

2020 ◽  
Vol 80 (11) ◽  
Author(s):  
Prabal Adhikari ◽  
Jens O. Andersen
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Chemical Potential ◽  
Chiral Condensate ◽  
Zero Temperature ◽  
Leading Order ◽  
Chiral Perturbation ◽  
Pion Condensate ◽  
Independent Analysis ◽  
Model Independent

AbstractIn this paper, we consider two-flavor QCD at zero temperature and finite isospin chemical potential $$\mu _I$$ μ I using a model-independent analysis within chiral perturbation theory at next-to-leading order. We calculate the effective potential, the chiral condensate and the pion condensate in the pion-condensed phase at both zero and nonzero pionic source. We compare our finite pionic source results for the chiral condensate and the pion condensate with recent (2+1)-flavor lattice QCD results. Agreement with lattice results generally improves as one goes from leading order to next-to-leading order.

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