Abstract
The intricate machinery of perturbative quantum field theory has largely been devoted to the ‘dynamical’ side of the theory: simple states are evolved in complicated ways. This article begins to address this lopsided treatment. Although it is rarely possible to solve for the eigenstates of an interacting theory exactly, a general state and its evolution can nonetheless be constructed perturbatively in terms of the propagators and structures defined with respect to the free theory. The detailed form of the initial state in this picture is fixed by imposing suitable ‘renormalization conditions’ on the Green’s functions. This technique is illustrated with an example drawn from inflation, where the presence of nonrenormalizable operators and where an expansion that naturally couples early times with short distances make the ability to start the theory at a finite initial time especially desirable.
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References
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].
H. Collins, Initial state propagators, JHEP 11 (2013) 077 [arXiv:1309.2656] [INSPIRE].
J.M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP 05 (2003) 013 [astro-ph/0210603] [INSPIRE].
H. Collins, Primordial non-gaussianities from inflation, arXiv:1101.1308 [INSPIRE].
J.S. Schwinger, Brownian motion of a quantum oscillator, J. Math. Phys. 2 (1961) 407 [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].
L.V. Keldysh, Diagram technique for nonequilibrium processes, Zh. Eksp. Teor. Fiz. 47 (1964) 1515 [Sov. Phys. JETP 20 (1965) 1018] [INSPIRE].
S. Weinberg, Quantum contributions to cosmological correlations, Phys. Rev. D 72 (2005) 043514 [hep-th/0506236] [INSPIRE].
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ArXiv ePrint: 1408.4801
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Collins, H., Holman, R. & Vardanyan, T. Renormalizing an initial state. J. High Energ. Phys. 2014, 124 (2014). https://doi.org/10.1007/JHEP10(2014)124
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DOI: https://doi.org/10.1007/JHEP10(2014)124