Real-time thermal propagators and the QED effective action for an external magnetic field☆

Elmfors, Per; Persson, Daniel; Skagerstam, Bo-Sture

doi:10.1016/0927-6505(94)90008-6

Cited by 59 publications

(86 citation statements)

References 43 publications

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“…Similar logarithmic terms appear in a weak field expansion of the effective potential in Ref. [34] although, as pointed out by the authors of that work, their weak field expansion is not necessarily reliable since it is given in terms of a Borel summable rather than a convergent series. In this work we have not come across such terms but a detailed comparison between the methods used in the above mentioned works with ours to include the effects of the magnetic field is certainly called for.…”

Section: Discussionmentioning

confidence: 93%

Effective potential at finite temperature in a constant hypermagnetic field: Ring diagrams in the standard model

2007

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Section: Discussionmentioning

confidence: 93%

Effective potential at finite temperature in a constant hypermagnetic field: Ring diagrams in the standard model

2007

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“…We refer interested readers to the discussion in Ref. [42]. Now introduce the dummy integrals dQ δ (n) (Q − Q(τ )) = 1 and…”

Section: The Many Body World Line Formalismmentioning

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

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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...

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“…was calculated in Refs. [14,15] using the solutions to the Dirac equation in a uniform magnetic field to construct the fermion thermal propagator. In this paper I calculate using the thermal propagator of Equation (14), which is constructed using the Schwinger proper time method, and use the following identity [14,15] to evaluate the contribution to the effective lagrangian of a charged lepton field whose thermal propagator is S( )…”

Section: Finite Temperature and Density Effective Electromagnetic Lagmentioning

confidence: 99%

“…These pioneering papers lead to a number of important physical insights and applications: lightlight scattering in QED [9], pair production from vacuum in the presence of an electric field [10][11][12] and vacuum birefringence [13], among others. The one-loop QED effective lagrangian at finite temperature and density has been investigated in magnetic field background [14][15][16][17], in electric field background [18,19], in general background fields for the case of 0 + 1 [20,21] and 1 + 1 dimensional massless QED [22,23] and is very relevant and closely related to many physical phenomena such as, for example, the Casimir effect. When evaluating the QED effective lagrangian at finite temperature, the time component of the momentum four vector, over which we integrate, takes on only discrete values for a fixed temperature, while when computing the Casimir energy, an analogous substitution takes place in a space component of the momentum vector for a fixed distance between the plates.…”

Section: Introductionmentioning

confidence: 99%

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Effective electromagnetic lagrangian at finite temperature and density in the electroweak model

Erdas

2011

Open Physics

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Abstract:Using the exact propagators in a constant magnetic field, the effective electromagnetic lagrangian at finite temperature and density is calculated to all orders in the field strength B within the framework of the complete electroweak model, in the weak coupling limit. The partition function and free energy are obtained explicitly and the finite temperature effective coupling is derived in closed form. Some implications of this result, potentially interesting to astrophysics and cosmology, are discussed. PACS

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Real-time thermal propagators and the QED effective action for an external magnetic field☆

Cited by 59 publications

References 43 publications

Effective potential at finite temperature in a constant hypermagnetic field: Ring diagrams in the standard model

Effective potential at finite temperature in a constant hypermagnetic field: Ring diagrams in the standard model

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

Effective electromagnetic lagrangian at finite temperature and density in the electroweak model

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