Nonequilibrium quantum fields: Closed-time-path effective action, Wigner function, and Boltzmann equation

Calzetta, Esteban; Hu, B. L.

doi:10.1103/physrevd.37.2878

Cited by 535 publications

(744 citation statements)

References 79 publications

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“…In the quantum theory the initial conditions can be represented by non-local n-point vertex functions that act only at the initial time τ H , as explained for example in [30]. These vertex functions can have any number of dashed and full lines.…”

Section: Early Time Contributionsmentioning

confidence: 99%

“…In the Closed Time Path (CTP) formalism (or in-in formalism) [30] this expectation value can also be calculated using path integrals, from the generating functional…”

Section: Ctp Formalismmentioning

confidence: 99%

“…We consider correlation functions with (external) momenta much smaller than the Hubble scale H in the quantum theory, using the Closed Time Path (CTP) formalism (also known as in-in formalism, see e.g. [29,30]), as is also done by Weinberg in [31,32]. Furthermore we formulate a classical theory with statistical fluctuations, in such a way that correlation functions in this theory can easily be compared with those in the quantum theory.…”

Section: Introductionmentioning

confidence: 99%

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Classical approximation to quantum cosmological correlations

Meulen¹,

Smit²

2007

J. Cosmol. Astropart. Phys.

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Abstract:We investigate up to which order quantum effects can be neglected in calculating cosmological correlation functions after horizon exit. As a toy model, we study φ 3 theory on a de Sitter background for a massless minimally coupled scalar field φ. We find that for tree level and one loop contributions in the quantum theory, a good classical approximation can be constructed, but for higher loop corrections this is in general not expected to be possible. The reason is that loop corrections get non-negligible contributions from loop momenta with magnitude up to the Hubble scale H, at which scale classical physics is not expected to be a good approximation to the quantum theory. An explicit calculation of the one loop correction to the two point function, supports the argument that contributions from loop momenta of scale H are not negligible. Generalization of the arguments for the toy model to derivative interactions and the curvature perturbation leads to the conclusion that the leading orders of non-Gaussian effects generated after horizon exit, can be approximated quite well by classical methods. Furthermore we compare with a theorem by Weinberg. We find that growing loop corrections after horizon exit are not excluded, even in single field inflation.

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Section: Early Time Contributionsmentioning

confidence: 99%

“…In the Closed Time Path (CTP) formalism (or in-in formalism) [30] this expectation value can also be calculated using path integrals, from the generating functional…”

Section: Ctp Formalismmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Classical approximation to quantum cosmological correlations

Meulen¹,

Smit²

2007

J. Cosmol. Astropart. Phys.

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“…Kinetic theory, described by Boltzmann equations, is a useful tool to describe the dynamics of an ensemble of quantum states [28][29][30][31]. For a single species, characterized by the distribution function f (k, x) of states with momentum k µ = (ω k , k) and spacetime coordinate x µ ≡ (t, x), the usual Boltzmann equation is (in flat spacetime)…”

Section: Quantum Boltzmann Equationsmentioning

confidence: 99%

Resonant flavor oscillations in electroweak baryogenesis

2011

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Electroweak baryogenesis (EWBG) in extensions of the Standard Model will be tested quantitatively in upcoming nuclear and particle physics experiments, but only to the extent that theoretical computations are robust. Currently there exist ordersof-magnitude discrepancies between treatments of charge transport dynamics during EWBG performed by different groups, each relying on different sets of approximations. In this work, we introduce a consistent power counting scheme (in ratios of length scales) for treating systematically the dynamics of EWBG: CP-asymmetric flavor oscillations, collisions, and diffusion. Within the context of a simplified model of EWBG, we derive the relevant Boltzmann equations using non-equilibrium field theory, and solve them exactly without ansatz for the functional form of the density matrices. We demonstrate the existence of a resonant enhancement in charge production when the flavor oscillation length is comparable to the wall thickness. We compare our results with the existing treatment of EWBG by Konstandin, Prokopec, Schmidt, and Seco (KPSS) who previously identified the importance of flavor oscillations in EWBG. We conclude: (i) the power counting of KPSS breaks down in the resonant regime, and (ii) this leads to substantial underestimation of the charge generated in the unbroken phase, and potentially of the final baryon asymmetry.

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“…The nonequilibrium time evolution is inherently nonperturbative in the sense that approximations based on a finite order in standard perturbation theory break down at sufficiently late times. Practicable approximations for nonequilibrium dynamics may be based on the two-particle irreducible (2P I) generating functional for Green's functions [1,2]. Recently, the 2P I effective action has been solved for a 1+1 dimensional scalar quantum field theory at next-to-leading order in the 2P I-loop expansion [3] and in the 2P I-1/N expansion [4].…”

mentioning

confidence: 99%

Nonequilibrium quantum fields and the classical field theory limit

Berges¹

2002

Nuclear Physics A

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We calculate the far-from-equilibrium dynamics and thermalization both for the quantum and the classical O(N)-model. The early and late-time behavior can be described from the 2P I-loop expansion for weak couplings or the nonperturbative 2P I-1/N expansion of the effective action beyond leading order. A comparison with exact simulations in 1 + 1 dimensions in the classical limit shows that the 2P I-1/N expansion at next-to-leading order gives quantitatively precise results already for moderate values of N. We derive a criterion for the validity of the classical approximation and verify it by comparing far-fromequilibrium quantum and classical dynamics. At late times one observes the expected deviations due to the difference between classical and quantum thermal equilibrium.In recent years we have witnessed an enormous increase of interest in the dynamics of quantum fields out of equilibrium. Strong motivation comes from a wide range of applications including current and upcoming relativistic heavy-ion collision experiments, phase transitions in the early universe or the dynamics of Bose-Einstein condensation. Directly simulating quantum fields in real time, such as solving the Schrödinger equation for the wave functional is prohibitively difficult and one has to find suitable approximations. The nonequilibrium time evolution is inherently nonperturbative in the sense that approximations based on a finite order in standard perturbation theory break down at sufficiently late times. Practicable approximations for nonequilibrium dynamics may be based on the two-particle irreducible (2P I) generating functional for Green's functions [1,2]. Recently, the 2P I effective action has been solved for a 1+1 dimensional scalar quantum field theory at next-to-leading order in the 2P I-loop expansion [3] and in the 2P I-1/N expansion [4]. Both the far-from-equilibrium early-time behavior and the late-time physics of thermalization were successfully described. For a recent review on the use of the 2P I effective action in nonequilibrium field theory see Ref. [5].A unique possibility to calculate the exact time evolution, which includes all orders in loops or 1/N, is provided by the classical statistical field theory limit. The exact evolution (up to statistical errors) of correlation functions can be constructed by numerical integration and sampling of initial conditions from a given probability distribution function. On the level of correlation functions classical and quantum evolution equations are remarkably similar 1 and the same approximation schemes and initial conditions can be applied. This aspect of classical field theory has been stressed in Refs. [7][8][9][10]. In Ref. [9] this is applied to the next-to-leading order classical φ 4 -model. In Ref.[10] it is shown that 1 Of course, in contrast to the quantum theory the classical limit suffers from Rayleigh-Jeans divergences and has to be regulated. In 1+1 dimensions such divergences are absent in φφ-correlation functions [6].

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Nonequilibrium quantum fields: Closed-time-path effective action, Wigner function, and Boltzmann equation

Cited by 535 publications

References 79 publications

Classical approximation to quantum cosmological correlations

Classical approximation to quantum cosmological correlations

Resonant flavor oscillations in electroweak baryogenesis

Nonequilibrium quantum fields and the classical field theory limit

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