Abstract
Loop corrections to finite-time correlation functions in quantum field theories away from equilibrium can be calculated using the in-in path integral approach. In this paper, we calculate the unequal-time two-point correlator for different massless self-interacting scalar quantum field theories on a Minkowski background, starting the field evolution at an arbitrary initial time. We find the counterterms that need to be added to UV-renormalize the result, including usual in-out counterterms in the dynamics and additional initial state counterterms that are required to cancel all UV divergences. We find that the late-time limit of the renormalized correlation function exhibits a linear or logarithmic growth in time, depending on whether the interaction strength is dimension-one or dimensionless, respectively. The late-time correlations match those obtained in our companion paper and, as shown there, the divergences do not indicate a real IR issue, consistent with what one would expect in Minkowski.
Article PDF
Similar content being viewed by others
References
J.S. Schwinger, Brownian motion of a quantum oscillator, J. Math. Phys. 2 (1961) 407 [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. Part 1, J. Math. Phys. 4 (1963) 1 [INSPIRE].
L.P. Kadanoff and G. Baym, Quantum Statistical Mechanics, W.A. Benjamin, Inc., New York, NY, U.S.A. (1962).
P.M. Bakshi and K.T. Mahanthappa, Expectation value formalism in quantum field theory. Part 2, J. Math. Phys. 4 (1963) 12 [INSPIRE].
L.V. Keldysh, Diagram technique for nonequilibrium processes, Zh. Eksp. Teor. Fiz. 47 (1964) 1515 [INSPIRE].
R.D. Jordan, Effective Field Equations for Expectation Values, Phys. Rev. D 33 (1986) 444 [INSPIRE].
E. Calzetta and B.-L. Hu, Closed Time Path Functional Formalism in Curved Space-Time: Application to Cosmological Back Reaction Problems, Phys. Rev. D 35 (1987) 495 [INSPIRE].
E.A. Calzetta and B.-L. Hu, Nonequilibrium Quantum Field Theory, in Cambridge Monographs on Mathematical Physics, Cambridge University Press (2022) [https://doi.org/10.1017/9781009290036] [INSPIRE].
J. Baacke, K. Heitmann and C. Patzold, On the choice of initial states in nonequilibrium dynamics, Phys. Rev. D 57 (1998) 6398 [hep-th/9711144] [INSPIRE].
J. Baacke, D. Boyanovsky and H.J. de Vega, Initial time singularities in nonequilibrium evolution of condensates and their resolution in the linearized approximation, Phys. Rev. D 63 (2001) 045023 [hep-ph/9907337] [INSPIRE].
H. Collins and R. Holman, Renormalization of initial conditions and the trans-Planckian problem of inflation, Phys. Rev. D 71 (2005) 085009 [hep-th/0501158] [INSPIRE].
H. Collins, R. Holman and T. Vardanyan, Renormalizing an initial state, JHEP 10 (2014) 124 [arXiv:1408.4801] [INSPIRE].
S. Chaykov, N. Agarwal, S. Bahrami and R. Holman, Loop corrections in Minkowski spacetime away from equilibrium. Part I. Late-time resummations, JHEP 02 (2023) 093 [arXiv:2206.11288] [INSPIRE].
J. Berges, Introduction to nonequilibrium quantum field theory, AIP Conf. Proc. 739 (2004) 3 [hep-ph/0409233] [INSPIRE].
A. Kamenev, Field Theory of Non-Equilibrium Systems, Cambridge University Press (2011) [https://doi.org/10.1017/cbo9781139003667].
S. Weinberg, Quantum contributions to cosmological correlations, Phys. Rev. D 72 (2005) 043514 [hep-th/0506236] [INSPIRE].
N. Agarwal and Y.-Z. Chu, Initial value formulation of a quantum damped harmonic oscillator, in preparation.
N. Agarwal, R. Holman, A.J. Tolley and J. Lin, Effective field theory and non-Gaussianity from general inflationary states, JHEP 05 (2013) 085 [arXiv:1212.1172] [INSPIRE].
X. Chen, Y. Wang and Z.-Z. Xianyu, Loop Corrections to Standard Model Fields in Inflation, JHEP 08 (2016) 051 [arXiv:1604.07841] [INSPIRE].
V. Balasubramanian, M.B. McDermott and M. Van Raamsdonk, Momentum-space entanglement and renormalization in quantum field theory, Phys. Rev. D 86 (2012) 045014 [arXiv:1108.3568] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2206.11289
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Chaykov, S., Agarwal, N., Bahrami, S. et al. Loop corrections in Minkowski spacetime away from equilibrium. Part II. Finite-time results. J. High Energ. Phys. 2023, 94 (2023). https://doi.org/10.1007/JHEP02(2023)094
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2023)094