Kinetic theory and classical limit for real scalar quantum field in curved space-time

Abstract

Starting from a real scalar quantum field theory with quartic self-interactions and non-minimal coupling to classical gravity, we define four equal-time, spatially covariant phase-space operators through a Wigner transformation of spatially translated canonical operators within a 3+1 decomposition. A subset of these operators can be interpreted as fluctuating particle densities in phase-space whenever the quantum state of the system allows for a classical limit. We come to this conclusion by expressing hydrodynamic variables through the expectation values of these operators and moreover, by deriving the dynamics of the expectation values within a spatial gradient expansion and a 1-loop approximation which subsequently yields the Vlasov equation with a self-mass correction as a limit. We keep an arbitrary classical metric in the 3+1 decomposition which is assumed to be determined semi-classically. Our formalism allows to systematically study the transition from quantum field theory in curved space-time to classical particle physics for this minimal model of self-interacting, gravitating matter. As an application we show how to include relativistic and self-interaction corrections to existing dark matter models in a kinetic description by taking into account the gravitational slip, vector perturbations and tensor perturbations.

arXiv commentThis version matches the one accepted for publication in Physical Review D

References in corpus (48)

• Planck 2015 results. XIII. Cosmological parameters
• Large-Scale Structure of the Universe and Cosmological Perturbation Theory
• Cold and Fuzzy Dark Matter
• Ultralight scalars as cosmological dark matter
• Non-Gaussianity from Inflation: Theory and Observations
• Quintessence: A Review
• Cosmological perturbations
• First constraints on fuzzy dark matter from Lyman-$\alpha$ forest data and hydrodynamical simulations
• Late time Cosmological Phase Transition and Galactic Halo as Bose-liquid
• Fluid Dark Matter
• Repulsive Dark Matter
• Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond
• Constraining the mass of light bosonic dark matter using SDSS Lyman-$\alpha$ forest
• Theory of Dark Matter Superfluidity
• Galactic Halos As Boson Stars
• Quantum fields in curved spacetime
• Finite temperature field theory and phase transitions
• Stochastic Gravity: Theory and Applications
• Conservation of the stress tensor in perturbative interacting quantum field theory in curved spacetimes
• Stochastic Gravity: Theory and Applications
• Transport equations for chiral fermions to order \hbar and electroweak baryogenesis: Part II
• On the Schrodinger-Poisson--Vlasov-Poisson correspondence
• Axion as a Cold Dark Matter candidate
• A Consistent Effective Theory of Long-Wavelength Cosmological Perturbations
• Renormalized Quantum Yang-Mills Fields in Curved Spacetime
• QFT on curved spacetimes: axiomatic framework and examples
• Cosmological particle production and the precision of the WKB approximation
• Schrödinger method as N-body double and UV completion of dust
• Hydrodynamic representation of the Klein-Gordon-Einstein equations in the weak field limit: I. General formalism and perturbations analysis
• Evolution of Cosmological Perturbation in Reheating Phase of the Universe
• Relativistic Corrections to Nonrelativistic Effective Field Theories
• Equal-Time Hierarchies in Quantum Transport Theory
• Equal-Time Hierarchies for Quantum Transport Theory
• The geometry of the tangent bundle and the relativistic kinetic theory of gases
• Non-linear hydrodynamics of axion dark matter: relative velocity effects and "quantum forces"
• Nonequilibrium Quantum Fields: From Cold Atoms to Cosmology
• How Cold is Cold Dark Matter?
• Particle number in kinetic theory
• Far from equilibrium dynamics of Bose-Einstein condensation for Axion Dark Matter
• A New Non-Perturbative Approach to Quantum Theory in Curved Spacetime Using the Wigner Function
• Wigner function and quantum kinetic theory in curved space-time and external fields
• On the Backreaction of Scalar and Spinor Quantum Fields in Curved Spacetimes - From the Basic Foundations to Cosmological Applications
• Gravitational collapse in the Schrödinger-Poisson system
• Scalar field dark matter in hybrid approach
• Classical and Quantum Theory of Perturbations in Inflationary Universe Models
• Decoherence and Dynamical Entropy Generation in Quantum Field Theory
• The renormalized and Renormalization-Group invariant Hartree-Fock approximation
• Decoherence in an Interacting Quantum Field Theory: Thermal Case

Cited by in corpus (9)

• Finding closure: approximating Vlasov-Poisson using finitely generated cumulants
• Real scalar field, non-relativistic limit, and cosmological expansion
• General relativistic non-ideal fluid equations for dark matter from a truncated cumulant expansion
• Field-theoretic approach to large-scale structure formation
• Spatial correlations of dark energy from quantum fluctuations in inflation
• Fluctuating Dark Energy and the Luminosity Distance
• Covariances of density probability distribution functions. Lessons from hierarchical models
• Cosmological Particle Creation Using an Equal-Time Wigner Formalism
• Kinetic equation for Lifshitz scalar