Classical kinetic theory of Landau damping for self-interacting scalar fields in the broken phase

Patkós, A.; Szép, Zsolt

doi:10.1016/s0370-2693(98)01571-8

Cited by 2 publications

(5 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For very small values of k 0 a simplified form can be derived which coincides with the result of the conventional kinetic treatment of the Higgs-modes [6]. One arrives at this approximate expression of J 1 (k) if one performs an appropriate three-momentum shift p → p ∓ k/2 on the p variable in Eq.…”

Section: Nonlinear Dynamicsmentioning

confidence: 67%

“…In this sense one has to go beyond the usual hard thermal loop approximation, since the effect of loops with momentum p ≃ M < T should be taken into account. The classical statistical mechanical system proposed in [6] reproduces the linear sourceamplitude response computed in quantum theory [7].…”

Section: Introductionmentioning

confidence: 85%

“…Recently we have shown that a similar interpretation is possible for fluctuations of the onecomponent self-interacting scalar field in the broken symmetry phase [6]. The evolution of the modes with wave number |k| was considered under the assumption M < T ; that is the mass scale set by the spontanous symmetry breakdown is smaller than the temperature.…”

Section: Introductionmentioning

confidence: 94%

See 2 more Smart Citations

Effective theory for the soft fluctuation modes in the spontaneously broken phase of theN-component scalar field theory

et al. 1999

Self Cite

View full text Add to dashboard Cite

The effective dynamics of the low-frequency modes is derived for the O(N) symmetric scalar field theory in the broken symmetry phase. The effect of the high-frequency fluctuations is taken into account at one-loop level exactly. A new length scale is shown to govern the long-time asymptotics of the linear response function of the Goldstone modes. The large time asymptotic decay of an arbitrary fluctuation is determined in the linear regime. We propose a set of local equations for the numerical solution of the effective nonlinear dynamics. The applicability of the usual gradient expansion is carefully assessed.

show abstract

Section: Nonlinear Dynamicsmentioning

confidence: 67%

Section: Introductionmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 94%

See 1 more Smart Citation

Effective theory for the soft fluctuation modes in the spontaneously broken phase of theN-component scalar field theory

et al. 1999

Self Cite

View full text Add to dashboard Cite

show abstract

“…1b, and in general there are of course also corrections from higher loop diagrams. Let us now briefly compare the above world line formulation with the classical kinetic theory, as studied in [50,51]. Within the kinetic theory we would write the current as j kin (y) = 12λφ(y) dP f (y, p) ,…”

Section: A the Effective Action In The Imaginary Time World Line Formmentioning

confidence: 99%

“…1b with four soft fields), in the limit of zero external four-momentum. Collecting the same powers of λ, by usingṗ µ ∼ λ∂ µ φ 2 s (which also follows from the world line action), the Boltzmann equation gives the solution for f 1 (y, p) as [50,51,52], dP f 1 (y, p) ∼ φ 2 (y) dP 1 p 0 df 0 dp 0 ∼ φ 2 (y) T Λ ,…”

Section: A the Effective Action In The Imaginary Time World Line Formmentioning

confidence: 99%

Minding one’s P’s and Q’s: From the one loop effective action in quantum field theory to classical transport theory

et al. 2000

View full text Add to dashboard Cite

The one loop effective action in quantum field theory can be expressed as a quantum mechanical path integral over world lines, with internal symmetries represented by Grassmanian variables. In this paper, we develop a real time, many body, world line formalism for the one loop effective action. In particular, we study hot QCD and obtain the classical transport equations which, as Litim and Manuel have shown, reduce in the appropriate limit to the non-Abelian Boltzmann-Langevin equation first obtained by Bödeker. In the Vlasov limit, the classical kinetic equations are those that correspond to the hard thermal loop effective action. We also discuss the imaginary time world line formalism for a hot φ 4 theory, and elucidate its relation to classical transport theory. IntroductionIn classical kinetic theory, a covariant formalism can be obtained in terms of phase space averages over the trajectories of particle world lines [1]. In quantum field theory, there are many instances at finite temperature and density where classical ideas are relevant, and where a classical kinetic picture would be useful. However, it is not immediately apparent how one recovers the classical world line picture directly from quantum field theory. This is especially problematic in theories with internal symmetries.Fortunately, in the last decade, there has been a considerable body of work relating the one loop effective action in quantum field theory to quantum mechanical path integrals over point particle Lagrangians 1 . For a survey of recent developments, see the review by Schubert [4]. These recent developments follow from the key insight by Berezin and Marinov [5] that internal symmetries such as color and spin had classical analogues in terms of Grassmanian variables. These obeyed classical commutation relations which, when quantized, gave the usual commutation relations for spin and color.Brink, DiVecchia, and Howe used these Grassmanian variables to construct a classical Lagrangian for spinning world lines in an Abelian background field [6]. Subsequently, Balachandran et al. [7] and Barducci et al. [8] wrote down the following Lagrangian for a classical colored particle in a non-Abelian background field 2 :Here the λ a (τ ) with a = 1, · · · , N are Grassmanian dynamical variables, and D ab λ b =λ a + igẋ µ A α µ T α ab λ b . The variables T α ab 's are N × N matrices in an irreducible representation of the Lie algebra of the group. The EulerLagrange equations of motion are deduced in the usual way from the above Lagrangian. It was shown by Balachandran et al. and by Barducci et al. that these equations are precisely the equations written down nearly thirty years ago by S.K. Wong [9].The connection of the work on point particle Lagrangians to quantum field theory was first made by Strassler [10]. He showed that the one loop effective action in quantum field theory could be expressed in terms of a quantum mechanical path integral over a point particle Lagrangian. For an Abelian gauge theory, Strassler showed that this Lag...

show abstract

Classical kinetic theory of Landau damping for self-interacting scalar fields in the broken phase

Cited by 2 publications

References 19 publications

Effective theory for the soft fluctuation modes in the spontaneously broken phase of theN-component scalar field theory

Effective theory for the soft fluctuation modes in the spontaneously broken phase of theN-component scalar field theory

Minding one’s P’s and Q’s: From the one loop effective action in quantum field theory to classical transport theory

Contact Info

Product

Resources

About