pith. sign in

arxiv: 2604.26941 · v2 · pith:WQNHMZXMnew · submitted 2026-04-29 · ✦ hep-th · quant-ph

Schwinger-Keldysh Path Integral for Gauge theories

Greg Kaplanek , Maria Mylova , Andrew J. Tolley This is my paper

Pith reviewed 2026-05-25 06:25 UTC · model grok-4.3

classification ✦ hep-th quant-ph
keywords Schwinger-Keldysh formalismBRST symmetrynon-Abelian gauge theoriespath integralWard identitiesOpen EFTinfluence functionalfinite-time initial states
0
0 comments X

The pith

The Schwinger-Keldysh path integral for non-Abelian gauge theories is manifestly invariant under a diagonal retarded BRST symmetry for arbitrary pure or mixed initial states at finite times.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper constructs the Schwinger-Keldysh path-integral formalism for open non-Abelian gauge theories that have been gauge-fixed using the BRST procedure in covariant gauges. It treats generic initial states, both pure and mixed, that are specified at finite times and therefore suitable for non-equilibrium processes. Special care is taken with the indefinite-metric structure of the gauge-fixed Hilbert space, the construction of BRST-invariant Schrödinger-picture wavefunctionals and density matrices, and the Hata-Kugo prescription together with a convenient representation of the Nakanishi-Lautrup field. The resulting path integral is shown to be invariant under a diagonal retarded BRST symmetry, from which perturbative Ward-Takahashi-Slavnov-Taylor identities follow. The same construction yields a BRST-invariant influence functional after charged matter or hard modes are integrated out, and it produces an exact contracted BRST symmetry in the second-order Open EFT expansion.

Core claim

The resulting Schwinger-Keldysh path integral is manifestly invariant under a diagonal (retarded) BRST symmetry for arbitrary physical initial states, whether pure or mixed. From this invariance the corresponding Ward-Takahashi-Slavnov-Taylor identities are obtained and remain valid perturbatively. The naive advanced BRST symmetry is explicitly broken by the in-in boundary conditions, while the Feynman-Vernon influence functional obtained by integrating out charged matter and hard gluon modes stays perturbatively BRST invariant. When the Open EFT action is expanded to second order in advanced fields it exhibits an exact symmetry under a contraction of the original BRST symmetry that is built

What carries the argument

The diagonal (retarded) BRST symmetry of the Schwinger-Keldysh path integral, realized through the Hata-Kugo prescription and the Nakanishi-Lautrup field representation that preserves BRST invariance of the initial-state wavefunctionals and density matrices.

If this is right

  • Perturbative Ward-Takahashi-Slavnov-Taylor identities follow directly from the retarded BRST invariance.
  • The Feynman-Vernon influence functional remains BRST invariant after integration over charged matter or hard gluon modes.
  • Expansion of the Open EFT action to second order in advanced fields yields an exact symmetry under a contracted BRST transformation.
  • The Keldysh BRST symmetry governs the structure of the leading terms in any Open EFT derived from the formalism.
  • In a Higgs phase where all gauge symmetries are spontaneously broken, a general form of the Open EFT can be written down.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same construction may supply a consistent starting point for non-equilibrium transport calculations in hot non-Abelian plasmas.
  • Non-perturbative modifications arising from the Gribov ambiguity are expected to alter or break the BRST symmetry, suggesting a route to study confinement effects inside the in-in formalism.
  • The retarded-BRST structure could be tested by deriving the corresponding Slavnov-Taylor identities for a simple Abelian theory and comparing them with known equilibrium results.
  • The formalism offers a natural language in which to embed gauge-invariant open-system dynamics into holographic or effective-field-theory models of heavy-ion collisions.

Load-bearing premise

The Hata-Kugo prescription together with the chosen Nakanishi-Lautrup field representation permits construction of BRST-invariant Schrödinger-picture wavefunctionals and density matrices for generic initial states without violating the indefinite-metric structure of the gauge-fixed Hilbert space.

What would settle it

An explicit computation of the path-integral measure or boundary terms for a mixed initial state that produces a non-vanishing variation under the diagonal retarded BRST transformation would falsify the invariance claim.

read the original abstract

We develop the Schwinger-Keldysh path-integral formalism for open non-Abelian gauge theories that are gauge-fixed via the BRST method in covariant gauges. We focus on generic initial states, pure and mixed, specified at finite times suitable for non-equilibrium processes. We pay particular attention to the handling of the indefinite Hilbert space, the construction of BRST-invariant Schrodinger picture wavefunctionals, density matrices and inner product, the implementation of the Hata-Kugo prescription, and the role of boundary terms at both the initial and final times. We highlight the advantages of the Nakanishi-Lautrup field representation in dealing with initial/final conditions. The resulting Schwinger-Keldysh path integral is manifestly invariant under a diagonal (retarded) BRST symmetry for arbitrary physical initial states, whether pure or mixed. From this, we obtain the corresponding Ward-Takahashi-Slavnov-Taylor identities, valid perturbatively. Non-perturbatively the Gribov ambiguity is expected to break or modify the BRST symmetry. The naive advanced BRST symmetry is shown to be explicitly violated by the in-in boundary conditions. We show that the Feynman-Vernon influence functional derived by integrating out charged matter and/or hard gluon modes remains (perturbatively) BRST invariant. When the Open EFT action is expanded to second order in advanced fields it exhibits an exact symmetry under a contraction of the original BRST symmetry. This Keldysh BRST symmetry is equivalent to the BRST associated with the retarded gauge transformations together with a linearly realized BRST transformation of the advanced fields. These govern the structure of the leading terms in an Open EFT. We illustrate this with the explicit example of Hard Thermal Loop Effective Theory, and construct the general form of the Open EFT in a Higgs phase when all gauge symmetries are spontaneously broken.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The paper develops the Schwinger-Keldysh path-integral formalism for open non-Abelian gauge theories gauge-fixed via the BRST method in covariant gauges. It treats generic initial states (pure or mixed) at finite times, addresses the indefinite-metric Hilbert space via the Hata-Kugo prescription and Nakanishi-Lautrup field representation, constructs BRST-invariant Schrödinger-picture wavefunctionals and density matrices, and shows that the resulting in-in path integral is manifestly invariant under a diagonal (retarded) BRST symmetry. From this invariance the authors derive the corresponding Ward-Takahashi-Slavnov-Taylor identities (perturbatively), demonstrate explicit violation of the naive advanced BRST symmetry by the boundary conditions, establish perturbative BRST invariance of the Feynman-Vernon influence functional after integrating out matter or hard modes, and obtain a contracted Keldysh BRST symmetry for the second-order Open EFT expansion, illustrated with the Hard Thermal Loop effective theory and the general form in a Higgs phase.

Significance. If the central construction is correct, the work supplies a technically consistent BRST-symmetric starting point for non-equilibrium gauge-theory calculations that preserves the symmetry for arbitrary physical initial states. This removes a long-standing obstacle to applying the Schwinger-Keldysh formalism to gauge theories while retaining the full power of BRST cohomology, and it directly yields the symmetry constraints that govern the structure of Open EFTs. The explicit treatment of boundary terms, the Hata-Kugo prescription, and the distinction between retarded and advanced BRST symmetries are concrete advances that can be used in perturbative computations and in the construction of effective actions for systems such as the quark-gluon plasma or early-universe gauge dynamics.

minor comments (3)
  1. [§3] §3 (or the section introducing the Hata-Kugo prescription): the precise definition of the inner product on the indefinite-metric space after the Nakanishi-Lautrup shift should be written explicitly, including the sign conventions for the ghost and antighost sectors, to make the BRST invariance of the initial-state density matrix fully transparent.
  2. [advanced BRST section] The discussion of the advanced BRST violation (near Eq. (boundary term) or the paragraph following the diagonal symmetry claim) would benefit from an explicit one-line calculation showing how the in-in boundary conditions produce a non-vanishing surface term under the advanced transformation.
  3. [Open EFT section] In the Open EFT expansion to second order in advanced fields, the statement that the contracted symmetry is 'equivalent to the BRST associated with retarded gauge transformations together with a linearly realized BRST transformation of the advanced fields' should be accompanied by the explicit transformation rules for the advanced fields.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the detailed and positive summary of our work, the assessment of its significance, and the recommendation of minor revision. No specific major comments were provided in the report, so we have no points to address point-by-point. We will incorporate any minor editorial suggestions in the revised manuscript.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper constructs the Schwinger-Keldysh path integral for gauge theories via standard BRST quantization in covariant gauges, applying the Hata-Kugo prescription to build BRST-invariant Schrödinger wavefunctionals and density matrices for generic initial states at finite times. The manifest diagonal retarded BRST invariance for arbitrary pure or mixed physical states follows directly from this construction together with the Nakanishi-Lautrup representation and explicit boundary-term handling; the resulting Ward-Takahashi-Slavnov-Taylor identities are then derived from that invariance. No step reduces by definition to its own inputs, no fitted parameters are relabeled as predictions, and no load-bearing premise rests on a self-citation chain. The non-perturbative Gribov issue and advanced-BRST violation are flagged separately as expected limitations rather than hidden assumptions. The central claim therefore retains independent content from the listed standard ingredients.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 0 invented entities

The construction relies on standard BRST quantization and the Hata-Kugo prescription for physical states; no new free parameters or invented entities are introduced in the abstract.

axioms (3)
  • domain assumption BRST symmetry exists and can be preserved in covariant gauges for non-Abelian theories
    Invoked throughout the construction of the path integral and Ward identities.
  • domain assumption Hata-Kugo prescription correctly identifies physical states in the indefinite-metric Hilbert space
    Used to construct BRST-invariant wavefunctionals and density matrices.
  • domain assumption Boundary terms at initial and final times can be arranged to preserve the diagonal BRST symmetry
    Central to the claim of manifest invariance for arbitrary initial states.

pith-pipeline@v0.9.0 · 5866 in / 1495 out tokens · 57979 ms · 2026-05-25T06:25:35.270966+00:00 · methodology

Review history (2 revisions) →

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Counting Degrees of Freedom in Open Effective Theories

    hep-th 2026-05 unverdicted novelty 7.0

    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.

  2. Bottom-up open EFT for non-Abelian gauge theory with dynamical color environment

    hep-th 2026-05 unverdicted novelty 7.0

    Develops a local open EFT for non-Abelian gauge theories using dynamical color-frame variables and color-current sectors in Schwinger-Keldysh formalism, yielding nonlocal dissipative kernels and naturally incorporatin...

  3. Stochastic inflation as an open quantum system II: open effective field theory and stochastic matching

    hep-th 2026-05 unverdicted novelty 6.0

    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 ...

Reference graph

Works this paper leans on

259 extracted references · 259 canonical work pages · cited by 3 Pith papers · 101 internal anchors

  1. [1]

    J. S. Schwinger,Field theory methods in non-field theory contexts, in(transcribed by A.C. Manoharan), 3rd Brandeis University Summer Institute in Theoretical Physics, pp. 223–374, 1960

    work page 1960

  2. [2]

    J. S. Schwinger,Brownian motion of a quantum oscillator,J. Math. Phys.2(1961) 407–432

    work page 1961

  3. [3]

    Korenman,Nonequilibrium quantum statistics; application to the laser,Annals of Physics39(1966) 72–126

    V. Korenman,Nonequilibrium quantum statistics; application to the laser,Annals of Physics39(1966) 72–126

    work page 1966

  4. [4]

    P. M. Bakshi and K. T. Mahanthappa,Expectation value formalism in quantum field theory. 1.,J. Math. Phys.4(1963) 1–11

    work page 1963

  5. [5]

    P. M. Bakshi and K. T. Mahanthappa,Expectation value formalism in quantum field theory. 2.,J. Math. Phys.4(1963) 12–16

    work page 1963

  6. [6]

    K. T. Mahanthappa,Multiple production of photons in quantum electrodynamics,Phys. Rev.126 (1962) 329–340

    work page 1962

  7. [7]

    Korenman,Dynamical computation of photon correlations and counting statistics,Phys

    V. Korenman,Dynamical computation of photon correlations and counting statistics,Phys. Rev.154 (Feb, 1967) 1233–1240

    work page 1967

  8. [8]

    R. P. Feynman and F. L. Vernon, Jr.,The Theory of a general quantum system interacting with a linear dissipative system,Annals Phys.24(1963) 118–173

    work page 1963

  9. [9]

    L. V. Keldysh,Diagram technique for nonequilibrium processes,Zh. Eksp. Teor. Fiz.47(1964) 1515–1527. – 61 –

    work page 1964

  10. [10]

    Baym and L

    G. Baym and L. P. Kadanoff,Conservation Laws and Correlation Functions,Phys. Rev.124(1961) 287–299

    work page 1961

  11. [11]

    L. P. Kadanoff and G. Baym,Quantum Statistical Mechanics: Green’s Function Methods in Equilibrium and Nonequilibrium Problems. W. A. Benjamin, 1962

    work page 1962

  12. [12]

    Fujita,Partial self-energy parts of kadanoff-baym,Physica30(1964) 848–856

    S. Fujita,Partial self-energy parts of kadanoff-baym,Physica30(1964) 848–856

    work page 1964

  13. [13]

    Danielewicz,Quantum Theory of Nonequilibrium Processes

    P. Danielewicz,Quantum Theory of Nonequilibrium Processes. 1.,Annals Phys.152(1984) 239–304

    work page 1984

  14. [14]

    A. O. Caldeira and A. J. Leggett,Path integral approach to quantum Brownian motion,Physica A: Statistical Mechanics and its Applications121(1983) 587–616

    work page 1983

  15. [15]

    A. O. Caldeira and A. J. Leggett,Influence of dissipation on quantum tunneling in macroscopic systems,Phys. Rev. Lett.46(1981) 211

    work page 1981

  16. [16]

    B. S. DeWitt,The global approach to quantum field theory. Vol. 1, 2, vol. 114. 2003

    work page 2003

  17. [17]

    Gauging Open EFTs from the top down

    G. Kaplanek, M. Mylova and A. J. Tolley,Gauging Open EFTs from the top down,2512.17089

    work page internal anchor Pith review Pith/arXiv arXiv

  18. [18]

    Hamiltonian approach to QCD in Coulomb gauge - a survey of recent results

    H. Reinhardt, G. Burgio, D. Campagnari, E. Ebadati, J. Heffner, M. Quandt et al.,Hamiltonian approach to QCD in Coulomb gauge - a survey of recent results,Adv. High Energy Phys.2018(2018) 2312498, [1706.02702]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  19. [19]

    V. N. Gribov,Quantization of Nonabelian Gauge Theories,Nucl. Phys. B139(1978) 1

    work page 1978

  20. [20]

    Becchi, A

    C. Becchi, A. Rouet and R. Stora,Renormalization of Gauge Theories,Annals Phys.98(1976) 287–321

    work page 1976

  21. [21]

    I. V. Tyutin,Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism, 0812.0580

    work page internal anchor Pith review Pith/arXiv arXiv

  22. [22]

    Henneaux and C

    M. Henneaux and C. Teitelboim,Quantization of gauge systems. 1992

    work page 1992

  23. [23]

    Ojima,Gauge Fields at Finite Temperatures: Thermo Field Dynamics, KMS Condition and their Extension to Gauge Theories,Annals Phys.137(1981) 1

    I. Ojima,Gauge Fields at Finite Temperatures: Thermo Field Dynamics, KMS Condition and their Extension to Gauge Theories,Annals Phys.137(1981) 1

    work page 1981

  24. [24]

    Matsumoto, Y

    H. Matsumoto, Y. Nakano and H. Umezawa,Equivalence Theorem and Gauge Theory at Finite Temperature,Phys. Rev. D28(1983) 1931

    work page 1983

  25. [25]

    N. P. Landsman and C. G. van Weert,Real and Imaginary Time Field Theory at Finite Temperature and Density,Phys. Rept.145(1987) 141

    work page 1987

  26. [26]

    E. A. Calzetta and B.-L. B. Hu,Nonequilibrium Quantum Field Theory. Oxford University Press, 2009, 10.1017/9781009290036

    work page doi:10.1017/9781009290036 2009

  27. [27]

    Gauge-Invariant Renormalization Group at Finite Temperature

    M. D’Attanasio and M. Pietroni,Gauge invariant renormalization group at finite temperature,Nucl. Phys. B498(1997) 443–466, [hep-th/9611038]

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  28. [28]

    Kubo,Statistical mechanical theory of irreversible processes

    R. Kubo,Statistical mechanical theory of irreversible processes. 1. General theory and simple applications in magnetic and conduction problems,J. Phys. Soc. Jap.12(1957) 570–586

    work page 1957

  29. [29]

    P. C. Martin and J. S. Schwinger,Theory of many particle systems. 1.,Phys. Rev.115(1959) 1342–1373

    work page 1959

  30. [30]

    C. W. Bernard,Feynman Rules for Gauge Theories at Finite Temperature,Phys. Rev. D9(1974) 3312

    work page 1974

  31. [31]

    Hata and T

    H. Hata and T. Kugo,An Operator Formalism of Statistical Mechanics of Gauge Theory in Covariant Gauges,Phys. Rev. D21(1980) 3333

    work page 1980

  32. [32]

    P. V. Landshoff and A. Rebhan,Covariant gauges at finite temperature,Nucl. Phys. B383(1992) 607–621, [hep-ph/9205235]. – 62 –

    work page internal anchor Pith review Pith/arXiv arXiv 1992

  33. [33]

    Mills,Propagators for many-particle systems: an elementary treatment

    R. Mills,Propagators for many-particle systems: an elementary treatment. CRC Press, 1969

    work page 1969

  34. [34]

    Craig,Perturbation expansion for real-time green’s functions,Journal of Mathematical Physics9 (1968) 605–611

    R. Craig,Perturbation expansion for real-time green’s functions,Journal of Mathematical Physics9 (1968) 605–611

    work page 1968

  35. [35]

    A. J. Niemi and G. W. Semenoff,Finite Temperature Quantum Field Theory in Minkowski Space, Annals Phys.152(1984) 105

    work page 1984

  36. [36]

    Matsumoto, H

    H. Matsumoto, H. Umezawa and J. P. Whitehead,Vacuum diagrams in perturbative thermo field dynamics,Prog. Theor. Phys.76(1986) 260–282

    work page 1986

  37. [37]

    T. S. Evans and A. C. Pearson,A Reexamination of the path ordered approach to real time thermal field theory,Phys. Rev. D52(1995) 4652–4659, [hep-ph/9412217]

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  38. [38]

    H. A. Weldon,Covariant Calculations at Finite Temperature: The Relativistic Plasma,Phys. Rev. D 26(1982) 1394

    work page 1982

  39. [39]

    On the screening of static electromagnetic fields in hot QED plasmas

    J.-P. Blaizot, E. Iancu and R. R. Parwani,On the screening of static electromagnetic fields in hot QED plasmas,Phys. Rev. D52(1995) 2543–2562, [hep-ph/9504408]

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  40. [40]

    Sakagami,Evolution From Pure States Into Mixed States in De Sitter Space,Prog

    M.-a. Sakagami,Evolution From Pure States Into Mixed States in De Sitter Space,Prog. Theor. Phys. 79(1988) 442

    work page 1988

  41. [41]

    Morikawa,Dissipation and fluctuation of quantum fields in expanding universes,Physical Review D 42(1990) 1027

    M. Morikawa,Dissipation and fluctuation of quantum fields in expanding universes,Physical Review D 42(1990) 1027

    work page 1990

  42. [42]

    Quantum Fluctuations, Decoherence of the Mean Field, and Structure Formation in the Early Universe

    E. Calzetta and B. L. Hu,Quantum fluctuations, decoherence of the mean field, and structure formation in the early universe,Phys. Rev. D52(1995) 6770–6788, [gr-qc/9505046]

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  43. [43]

    Coarse graining and decoherence in quantum field theory

    F. Lombardo and F. D. Mazzitelli,Coarse graining and decoherence in quantum field theory,Phys. Rev. D53(1996) 2001–2011, [hep-th/9508052]

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  44. [44]

    Entanglement entropy in free quantum field theory

    H. Casini and M. Huerta,Entanglement entropy in free quantum field theory,J. Phys. A42(2009) 504007, [0905.2562]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  45. [45]

    Decoherence in the cosmic background radiation

    M. Franco and E. Calzetta,Decoherence in the cosmic background radiation,Class. Quant. Grav.28 (2011) 145024, [1103.0188]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  46. [46]

    Dissipative effects in the Effective Field Theory of Inflation

    D. Lopez Nacir, R. A. Porto, L. Senatore and M. Zaldarriaga,Dissipative effects in the Effective Field Theory of Inflation,JHEP01(2012) 075, [1109.4192]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  47. [47]

    Momentum-space entanglement and renormalization in quantum field theory

    V. Balasubramanian, M. B. McDermott and M. Van Raamsdonk,Momentum-space entanglement and renormalization in quantum field theory,Phys. Rev. D86(2012) 045014, [1108.3568]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  48. [48]

    L. M. Sieberer, M. Buchhold and S. Diehl,Keldysh field theory for driven open quantum systems, Reports on Progress in Physics79(2016) 096001

    work page 2016

  49. [49]

    Marino and S

    J. Marino and S. Diehl,Quantum dynamical field theory for nonequilibrium phase transitions in driven open systems,Physical Review B94(2016) 085150

    work page 2016

  50. [50]

    An effective field theory during inflation: reduced density matrix and its quantum master equation

    D. Boyanovsky,Effective field theory during inflation: Reduced density matrix and its quantum master equation,Phys. Rev. D92(2015) 023527, [1506.07395]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  51. [51]

    An effective field theory during inflation II: stochastic dynamics and power spectrum suppression

    D. Boyanovsky,Effective field theory during inflation. II. Stochastic dynamics and power spectrum suppression,Phys. Rev. D93(2016) 043501, [1511.06649]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  52. [52]

    Renormalization in Open Quantum Field theory I: Scalar field theory

    A. Baidya, C. Jana, R. Loganayagam and A. Rudra,Renormalization in open quantum field theory. Part I. Scalar field theory,JHEP11(2017) 204, [1704.08335]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  53. [53]

    Burrage, C

    C. Burrage, C. K¨ ading, P. Millington and J. Min´ aˇ r,Open quantum dynamics induced by light scalar fields,Phys. Rev. D100(2019) 076003, [1812.08760]. – 63 –

    work page arXiv 2019

  54. [54]

    Effective field theory of time-translational symmetry breaking in nonequilibrium open system

    M. Hongo, S. Kim, T. Noumi and A. Ota,Effective field theory of time-translational symmetry breaking in nonequilibrium open system,JHEP02(2019) 131, [1805.06240]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  55. [55]

    Hongo, S

    M. Hongo, S. Kim, T. Noumi and A. Ota,Effective Lagrangian for Nambu-Goldstone modes in nonequilibrium open systems,Phys. Rev. D103(2021) 056020, [1907.08609]

    work page arXiv 2021

  56. [56]

    Subsystem Trace Distance in Quantum Field Theory

    J. Zhang, P. Ruggiero and P. Calabrese,Subsystem Trace Distance in Quantum Field Theory,Phys. Rev. Lett.122(2019) 141602, [1901.10993]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  57. [57]

    Nagy and J

    S. Nagy and J. Polonyi,Renormalizing Open Quantum Field Theories,Universe8(2022) 127, [2012.13811]

    work page arXiv 2022

  58. [58]

    Pinol, S

    L. Pinol, S. Renaux-Petel and Y. Tada,A manifestly covariant theory of multifield stochastic inflation in phase space: solving the discretisation ambiguity in stochastic inflation,JCAP04(2021) 048, [2008.07497]

    work page arXiv 2021

  59. [59]

    Chaykov, N

    S. Chaykov, N. Agarwal, S. Bahrami and R. Holman,Loop corrections in Minkowski spacetime away from equilibrium. Part II. Finite-time results,JHEP02(2023) 094, [2206.11289]

    work page arXiv 2023

  60. [60]

    Tinwala, A

    A. Tinwala, A. Narang, S. Mohanty and S. Panda,Open EFT treatment of Inflation with Thermal Initial Conditions,2402.18494

    work page arXiv

  61. [61]

    Ota,Fluctuation-dissipation relation in cosmic microwave background,JCAP05(2024) 062, [2402.07623]

    A. Ota,Fluctuation-dissipation relation in cosmic microwave background,JCAP05(2024) 062, [2402.07623]

    work page arXiv 2024

  62. [62]

    S. A. Salcedo, T. Colas and E. Pajer,The open effective field theory of inflation,JHEP10(2024) 248, [2404.15416]

    work page arXiv 2024

  63. [63]

    C. P. Burgess, T. Colas, R. Holman and G. Kaplanek,Does decoherence violate decoupling?, 2411.09000

    work page arXiv

  64. [64]

    Green and G

    D. Green and G. Sun,Effective Field Theory and In-In Correlators,2412.02739

    work page arXiv

  65. [65]

    R. K. Panda, S. Panda and A. Tinwala,Revisiting Lagrangian Formulation of Stochastic inflation, 2510.03171

    work page arXiv

  66. [66]

    C. O. Akyuz and R. Penco,Effective description of ajar systems with a U(1) symmetry,Phys. Rev. D 112(2025) L011901, [2503.22840]

    work page arXiv 2025

  67. [67]

    K¨ ading and M

    C. K¨ ading and M. Pitschmann,Density matrices in quantum field theory: Non-Markovianity, path integrals and master equations,2503.08567

    work page arXiv

  68. [68]

    Wang and Y

    Z. Wang and Y. Gong,Observational constraints on inflationary decoherence with polynomial attractor model,2503.03349

    work page arXiv

  69. [69]

    Cespedes, S

    S. Cespedes, S. de Alwis and F. Quevedo,Cosmology, Decoherence and the Second Law,2509.07077

    work page arXiv

  70. [70]

    Cespedes, Z

    S. Cespedes, Z. Qin and D.-G. Wang,λϕ 4˜as an Effective Theory in de Sitter,2510.25826

    work page arXiv

  71. [71]

    M. H. G. Lee and S. Melville,Propagator positivity bounds for cosmological correlators,2512.20706

    work page arXiv

  72. [72]

    Colas, Z

    T. Colas, Z. Qin and X. Tong,Open Effective Field Theory and the Physics of Cosmological Collider Signals,2512.07941

    work page arXiv

  73. [73]

    Burrage and C

    C. Burrage and C. K¨ ading,Fock state probability changes in open quantum systems,Eur. Phys. J. C 86(2026) 246, [2502.07673]

    work page arXiv 2026

  74. [74]

    Real-time Relaxation and Kinetics in Hot Scalar QED: Landau Damping

    D. Boyanovsky, H. J. de Vega, R. Holman, S. P. Kumar and R. D. Pisarski,Real time relaxation of condensates and kinetics in hot scalar QED: Landau damping,Phys. Rev. D58(1998) 125009, [hep-ph/9802370]. – 64 –

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  75. [75]

    Non-equilibrium quantum plasmas in scalar QED: photon production, magnetic and Debye masses, and conductivity

    D. Boyanovsky, H. J. de Vega and M. Simionato,Nonequilibrium quantum plasmas in scalar QED: Photon production, magnetic and Debye masses and conductivity,Phys. Rev. D61(2000) 085007, [hep-ph/9909259]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  76. [76]

    Heavy quark bound states in a quark-gluon plasma: dissociation and recombination

    J.-P. Blaizot, D. De Boni, P. Faccioli and G. Garberoglio,Heavy quark bound states in a quark–gluon plasma: Dissociation and recombination,Nucl. Phys. A946(2016) 49–88, [1503.03857]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  77. [77]

    N. Bao, A. Chatwin-Davies, J. Pollack and G. N. Remmen,Cosmological Decoherence from Thermal Gravitons,JHEP08(2020) 065, [1911.10207]

    work page arXiv 2020

  78. [78]

    Gravitational Decoherence, Asymptotic Quantization, and Entanglement Measures

    C. DeLisle, J. Wilson-Gerow and P. Stamp,Gravitational Decoherence, Asymptotic Quantization, and Entanglement Measures,1905.05333

    work page internal anchor Pith review Pith/arXiv arXiv 1905

  79. [79]

    T. He, R. Loganayagam, M. Rangamani and J. Virrueta,An effective description of momentum diffusion in a charged plasma from holography,JHEP01(2022) 145, [2108.03244]

    work page arXiv 2022

  80. [80]

    S. A. Salcedo, T. Colas and E. Pajer,An Open Effective Field Theory for light in a medium,JHEP03 (2025) 138, [2412.12299]

    work page arXiv 2025

Showing first 80 references.