Abstract
We use the in-in or Schwinger-Keldysh formalism to explore the construction and interpretation of effective field theories for time-dependent systems evolving out of equilibrium. Starting with a simple model consisting of a heavy and a light scalar field taken to be in their free vacuum states at a finite initial time, we study the effects from the heavy field on the dynamics of the light field by analyzing the equation of motion for the expectation value of the light background field. New terms appear which cannot arise from a local action of an effective field theory in terms of the light field, though they disappear in the adiabatic limit. We discuss the origins of these terms as well as their possible implications for time dependent situations such as inflation.
Similar content being viewed by others
References
H. Georgi, Effective field theory, Ann. Rev. Nucl. Part. Sci. 43 (1993) 209 [INSPIRE].
I.Z. Rothstein, TASI lectures on effective field theories, hep-ph/0308266 [INSPIRE].
C. Burgess, Introduction to effective field theory, Ann. Rev. Nucl. Part. Sci. 57 (2007) 329 [hep-th/0701053] [INSPIRE].
T. Appelquist and J. Carazzone, Infrared singularities and massive fields, Phys. Rev. D 11 (1975) 2856 [INSPIRE].
E. Witten, Quantum gravity in de Sitter space, hep-th/0106109 [INSPIRE].
J.S. Schwinger, Brownian motion of a quantum oscillator, J. Math. Phys. 2 (1961) 407 [INSPIRE].
L. Keldysh, Diagram technique for nonequilibrium processes, Zh. Eksp. Teor. Fiz. 47 (1964) 1515 [Sov. Phys. JETP 20 (1965) 1018] [INSPIRE].
K.T. Mahanthappa, Multiple production of photons in quantum electrodynamics, Phys. Rev. 126 (1962) 329 [INSPIRE].
P.M. Bakshi and K.T. Mahanthappa, Expectation value formalism in quantum field theory. 1, J. Math. Phys. 4 (1963) 1 [INSPIRE].
P.M. Bakshi and K.T. Mahanthappa, Expectation value formalism in quantum field theory. 2, J. Math. Phys. 4 (1963) 12 [INSPIRE].
A. Kamenev, Many-body theory of non-equilibrium systems, cond-mat/0412296.
D. Boyanovsky, H. de Vega, R. Holman, D. Lee and A. Singh, Dissipation via particle production in scalar field theories, Phys. Rev. D 51 (1995) 4419 [hep-ph/9408214] [INSPIRE].
S. Weinberg, Perturbative calculations of symmetry breaking, Phys. Rev. D 7 (1973) 2887 [INSPIRE].
D. Boyanovsky and H. de Vega, Dynamical renormalization group approach to relaxation in quantum field theory, Annals Phys. 307 (2003) 335 [hep-ph/0302055] [INSPIRE].
H. Collins, R. Holman and A. Ross, in progress.
R. Feynman and F.L. Vernon Jr., The theory of a general quantum system interacting with a linear dissipative system, Annals Phys. 24 (1963) 118 [Annals Phys. 281 (2000) 547] [INSPIRE].
S. Weinberg, Quantum contributions to cosmological correlations, Phys. Rev. D 72 (2005) 043514 [hep-th/0506236] [INSPIRE].
S. Weinberg, Effective field theory for inflation, Phys. Rev. D 77 (2008) 123541 [arXiv:0804.4291] [INSPIRE].
C. Cheung, P. Creminelli, A.L. Fitzpatrick, J. Kaplan and L. Senatore, The effective field theory of inflation, JHEP 03 (2008) 014 [arXiv:0709.0293] [INSPIRE].
L. Senatore and M. Zaldarriaga, On loops in inflation, JHEP 12 (2010) 008 [arXiv:0912.2734] [INSPIRE].
A. Achucarro, J.-O. Gong, S. Hardeman, G.A. Palma and S.P. Patil, Effective theories of single field inflation when heavy fields matter, JHEP 05 (2012) 066 [arXiv:1201.6342] [INSPIRE].
A. Achucarro, J.-O. Gong, S. Hardeman, G.A. Palma and S.P. Patil, Features of heavy physics in the CMB power spectrum, JCAP 01 (2011) 030 [arXiv:1010.3693] [INSPIRE].
G. Shiu and J. Xu, Effective field theory and decoupling in multi-field inflation: an illustrative case study, Phys. Rev. D 84 (2011) 103509 [arXiv:1108.0981] [INSPIRE].
A. Avgoustidis et al., Decoupling survives inflation: a critical look at effective field theory violations during inflation, JCAP 06 (2012) 025 [arXiv:1203.0016] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1208.3255
Rights and permissions
About this article
Cite this article
Collins, H., Holman, R. & Ross, A. Effective field theory in time-dependent settings. J. High Energ. Phys. 2013, 108 (2013). https://doi.org/10.1007/JHEP02(2013)108
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2013)108