A new algorithm counts degrees of freedom in open EFTs from equations of motion using dual advanced equations for non-Lagrangian systems with constraints and gauges.
Canonical reference
EFT Beyond the Horizon: Stochastic Inflation and How Primordial Quantum Fluctuations Go Classical
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abstract
We identify the effective theory describing inflationary super-Hubble scales and show it to be a special case of effective field theories appropriate to open systems. Open systems allow information to be exchanged between the degrees of freedom of interest and those that are integrated out, such as for particles moving through a fluid. Strictly speaking they cannot in general be described by an effective lagrangian; rather the appropriate `low-energy' limit is instead a Lindblad equation describing the evolution of the density matrix of the slow degrees of freedom. We derive the equation relevant to super-Hubble modes of quantum fields in near-de Sitter spacetimes and derive two implications. We show the evolution of the diagonal density-matrix elements quickly approaches the Fokker-Planck equation of Starobinsky's stochastic inflationary picture. This provides an alternative first-principles derivation of this picture's stochastic noise and drift, as well as its leading corrections. (An application computes the noise for systems with a sub-luminal sound speed.) We argue that the presence of interactions drives the off-diagonal density-matrix elements to zero in the field basis. This shows why the field basis is the `pointer basis' for the decoherence of primordial quantum fluctuations while they are outside the horizon, thus allowing them to re-enter as classical fluctuations, as assumed when analyzing CMB data. The decoherence process is efficient, occurring after several Hubble times even for interactions as weak as gravitational-strength. Crucially, the details of the interactions largely control only the decoherence time and not the nature of the final late-time stochastic state, much as interactions can control the equilibration time for thermal systems but are largely irrelevant to the properties of the resulting equilibrium state.
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Constructs a manifestly diagonal-BRST-invariant Schwinger-Keldysh path integral for open non-Abelian gauge theories with arbitrary physical initial states, yielding Ward-Takahashi-Slavnov-Taylor identities and a Keldysh BRST symmetry for the Open EFT.
The conventional truncation in stochastic inflation is inconsistent because quadratic-noise contributions are the same perturbative order as the deterministic non-Markovian corrections.
Develops open EFT for stochastic inflation with a distinct stochastic RG channel, derives nonlocal master equations including Fokker-Planck and Klein-Kramers forms, and demonstrates stochastic renormalization with an analytic regulator.
Derives gauge-invariant influence functionals for photons and Stueckelberg fields in open U(1) gauge EFTs via BRST on the in-in contour after integrating out matter.
Derives stochastic equations from Schwinger-Keldysh formalism that include quantum diffusion and classical metric perturbations for non-perturbative ultra-slow-roll inflation, validated on Starobinsky and critical Higgs models.
citing papers explorer
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Counting Degrees of Freedom in Open Effective Theories
A new algorithm counts degrees of freedom in open EFTs from equations of motion using dual advanced equations for non-Lagrangian systems with constraints and gauges.
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Schwinger-Keldysh Path Integral for Gauge theories
Constructs a manifestly diagonal-BRST-invariant Schwinger-Keldysh path integral for open non-Abelian gauge theories with arbitrary physical initial states, yielding Ward-Takahashi-Slavnov-Taylor identities and a Keldysh BRST symmetry for the Open EFT.
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A consistent formulation of stochastic inflation I: Non-Markovian effects and issues beyond linear perturbations
The conventional truncation in stochastic inflation is inconsistent because quadratic-noise contributions are the same perturbative order as the deterministic non-Markovian corrections.
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Stochastic inflation as an open quantum system II: open effective field theory and stochastic matching
Develops open EFT for stochastic inflation with a distinct stochastic RG channel, derives nonlocal master equations including Fokker-Planck and Klein-Kramers forms, and demonstrates stochastic renormalization with an analytic regulator.
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Gauging Open EFTs from the top down
Derives gauge-invariant influence functionals for photons and Stueckelberg fields in open U(1) gauge EFTs via BRST on the in-in contour after integrating out matter.
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Nonperturbative stochastic inflation in perturbative dynamical background
Derives stochastic equations from Schwinger-Keldysh formalism that include quantum diffusion and classical metric perturbations for non-perturbative ultra-slow-roll inflation, validated on Starobinsky and critical Higgs models.