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Manifest Causality in QFT with Sources and Detectors

Manifest Causality in QFT with Sources and Detectors. Peter Millington Consortium for Fundamental Physics, University of Manchester Institute for Particle Physics Phenomenology, Durham University IoP Joint HEPP and APP Group Meeting 7 th -9 th April, 2014.

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Manifest Causality in QFT with Sources and Detectors

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  1. Manifest Causality in QFT with Sources and Detectors Peter Millington Consortium for Fundamental Physics, University of Manchester Institute for Particle Physics Phenomenology, Durham University IoP Joint HEPP and APP Group Meeting 7th-9th April, 2014

  2. OutlineBased on R. Dickinson, J. Forshaw, PM and B. Cox, arXiv: 1312.3871. • Motivation • Observations from Thermal Field Theory • A Simple Example • Comparison with the S-matrix • Conclusions Peter Millington (UoM & IPPP) IoP HEPP and APP, Royal Holloway, 7-9th April 2014 2/12

  3. Motivation Question 1: • How are we to calculate transition amplitudes over finite space-time domains in QFT? S-matrix theory is no good. Peter Millington (UoM & IPPP) IoP HEPP and APP, Royal Holloway, 7-9th April 2014 3/12

  4. Motivation Question 2: • QFT is built to be causal, so where is the micro-causality condition in the path integral? Peter Millington (UoM & IPPP) IoP HEPP and APP, Royal Holloway, 7-9th April 2014 4/12

  5. Observations • It only makes sense to talk of transition amplitudes over finite space-time domains in the presence of an observer. • Statistically, the production and scattering processes form an open subsystem held in contact with some reservoir of observers: a detector. • The relevant object is the partition function of the detector • The solution: thermal quantum field theory. Peter Millington (UoM & IPPP) IoP HEPP and APP, Royal Holloway, 7-9th April 2014 5/12

  6. Encouragement • a posteriori, physical reaction rates are obtained from the absorptive parts of retarded functions.[R. Kobes, Phys. Rev. D43, 1269 (1991); M. A. van Eijck and C. G. van Weert, Phys. Lett. B278, 305 (1992)] • Three ‘anecdotal’ reasons: • This gives the correct statistical factors. • Analytic continuation of imaginary-time self-energies gives the retarded self-energy. • The Breit-Wigner width of resummed equilibrium thermal propagators is obtained from the imaginary part of the retarded self-energy. Peter Millington (UoM & IPPP) IoP HEPP and APP, Royal Holloway, 7-9th April 2014 6/12

  7. [J. Schwinger, J. Math. Phys. 2, 407 (1961); L. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1515 (1964); E. Calzetta and B. L. Hu, Phys. Rev. D 35, 495 (1987), Phys. Rev. D 37, 2878 (1988)] CTP Formalism Peter Millington (UoM & IPPP) IoP HEPP and APP, Royal Holloway, 7-9th April 2014 7/12

  8. “Physical” Basis • By an orthogonal transformation, we can move to the so-called Keldysh or “physical” basis:[M. A. van Eijck, R. Kobesand C. G. van Weert, Phys. Rev. D50, 4097 (1994)] • Note that J couples only to the retarded propagator. Peter Millington (UoM & IPPP) IoP HEPP and APP, Royal Holloway, 7-9th April 2014 8/12

  9. 2 to 2 Scattering Entanglement of Final States Peter Millington (UoM & IPPP) IoP HEPP and APP, Royal Holloway, 7-9th April 2014 9/12

  10. S-matrix Limit • To compare with the S-matrix, we must project out plane waves by promoting J and K to operators in Fock space: • We can then sandwich the amplitude between in and out states to project out given initial and final states. Peter Millington (UoM & IPPP) IoP HEPP and APP, Royal Holloway, 7-9th April 2014 10/12

  11. NJ to NK Peter Millington (UoM & IPPP) IoP HEPP and APP, Royal Holloway, 7-9th April 2014 11/12

  12. Conclusions • Working within the paradigm of thermal field theory, one can write down a generating functional in which causality remains manifest. • Results are consistent with S-matrix amplitudes in the relevant limits, specifically if we restrict to positive energy flow forwards in time. • Analytic differences arise at the level of loops. • Potential relevance: • Resummation in the presence of finite-time and volume effects, interplay of positive and negative energy contributions. • Role of CTP Effective Action • QFT on non-stationary spacetimes, where Wick rotation does not always lead to a Riemannian metric. • … Peter Millington (UoM & IPPP) IoP HEPP and APP, Royal Holloway, 7-9th April 2014 12/12

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