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Journal of High Energy Physics

, 2017:55 | Cite as

Tree-level correlations in the strong field regime

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Regular Article - Theoretical Physics
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Abstract

We consider the correlation function of an arbitrary number of local observables in quantum field theory, in situations where the field amplitude is large. Using a quasi-classical approximation (valid for a highly occupied initial mixed state, or for a coherent initial state if the classical dynamics has instabilities), we show that at tree level these correlations are dominated by fluctuations at the initial time. We obtain a general expression of the correlation functions in terms of the classical solution of the field equation of motion and its derivatives with respect to its initial conditions, that can be arranged graphically as the sum of labeled trees where the nodes are the individual observables, and the links are pairs of derivatives acting on them. For 3-point (and higher) correlation functions, there are additional tree-level terms beyond the quasi-classical approximation, generated by fluctuations in the bulk.

Keywords

Thermal Field Theory Nonperturbative Effects 
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References

  1. [1]
    V.F. Mukhanov, H.A. Feldman and R.H. Brandenberger, Theory of cosmological perturbations. Part 1. Classical perturbations. Part 2. Quantum theory of perturbations. Part 3. Extensions, Phys. Rept. 215 (1992) 203 [INSPIRE].
  2. [2]
    S. Weinberg, Quantum contributions to cosmological correlations, Phys. Rev. D 72 (2005) 043514 [hep-th/0506236] [INSPIRE].ADSMathSciNetGoogle Scholar
  3. [3]
    F. Gelis, E. Iancu, J. Jalilian-Marian and R. Venugopalan, The color glass condensate, Ann. Rev. Nucl. Part. Sci. 60 (2010) 463 [arXiv:1002.0333].ADSCrossRefGoogle Scholar
  4. [4]
    F. Gelis, Color glass condensate and glasma, Int. J. Mod. Phys. A 28 (2013) 1330001 [arXiv:1211.3327] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    J.S. Schwinger, Brownian motion of a quantum oscillator, J. Math. Phys. 2 (1961) 407 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    P.M. Bakshi and K.T. Mahanthappa, Expectation value formalism in quantum field theory. 1., J. Math. Phys. 4 (1963) 1 [INSPIRE].
  7. [7]
    P.M. Bakshi and K.T. Mahanthappa, Expectation value formalism in quantum field theory. 2, J. Math. Phys. 4 (1963) 12 [INSPIRE].
  8. [8]
    L.V. Keldysh, Diagram technique for nonequilibrium processes, Zh. Eksp. Teor. Fiz. 47 (1964) 1515 [INSPIRE].Google Scholar
  9. [9]
    K.-c. Chou, Z.-b. Su, B.-l. Hao and L. Yu, Equilibrium and nonequilibrium formalisms made unified, Phys. Rept. 118 (1985) 1 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  10. [10]
    R.D. Jordan, Effective field equations for expectation values, Phys. Rev. D 33 (1986) 444 [INSPIRE].ADSMathSciNetGoogle Scholar
  11. [11]
    F. Gelis and R. Venugopalan, Particle production in field theories coupled to strong external sources, Nucl. Phys. A 776 (2006) 135 [hep-ph/0601209] [INSPIRE].
  12. [12]
    F. Gelis and R. Venugopalan, Particle production in field theories coupled to strong external sources. II. Generating functions, Nucl. Phys. A 779 (2006) 177 [hep-ph/0605246] [INSPIRE].
  13. [13]
    F. Gelis, T. Lappi and R. Venugopalan, High energy factorization in nucleus-nucleus collisions, Phys. Rev. D 78 (2008) 054019 [arXiv:0804.2630] [INSPIRE].ADSGoogle Scholar
  14. [14]
    F. Gelis, T. Lappi and R. Venugopalan, High energy factorization in nucleus-nucleus collisions. II. Multigluon correlations, Phys. Rev. D 78 (2008) 054020 [arXiv:0807.1306] [INSPIRE].
  15. [15]
    S. Weinberg, A tree theorem for inflation, Phys. Rev. D 78 (2008) 063534 [arXiv:0805.3781] [INSPIRE].ADSMathSciNetGoogle Scholar
  16. [16]
    P. Aurenche, T. Becherrawy and E. Petitgirard, Retarded/advanced correlation functions and soft photon production in the hard loop approximation, hep-ph/9403320 [INSPIRE].
  17. [17]
    M.A. van Eijck, R. Kobes and C.G. van Weert, Transformations of real time finite temperature Feynman rules, Phys. Rev. D 50 (1994) 4097 [hep-ph/9406214] [INSPIRE].
  18. [18]
    X. Chen, M.H. Namjoo and Y. Wang, On the equation-of-motion versus in-in approach in cosmological perturbation theory, JCAP 01 (2016) 022 [arXiv:1505.03955] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    T. Epelbaum, F. Gelis and B. Wu, Nonrenormalizability of the classical statistical approximation, Phys. Rev. D 90 (2014) 065029 [arXiv:1402.0115] [INSPIRE].ADSGoogle Scholar
  20. [20]
    P.B. Greene, L. Kofman, A.D. Linde and A.A. Starobinsky, Structure of resonance in preheating after inflation, Phys. Rev. D 56 (1997) 6175 [hep-ph/9705347] [INSPIRE].
  21. [21]
    K. Dusling, T. Epelbaum, F. Gelis and R. Venugopalan, Role of quantum fluctuations in a system with strong fields: Onset of hydrodynamical flow, Nucl. Phys. A 850 (2011) 69 [arXiv:1009.4363] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    P. Flajolet and R. Sedgewick, Analytic combinatorics, Cambridge University Press, Cambridge U.K. (2009).CrossRefMATHGoogle Scholar

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© The Author(s) 2017

Authors and Affiliations

  1. 1.Institut de Physique Théorique, CEA, CNRS, Université Paris-SaclayGif-sur-YvetteFrance

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