Skip to main content
SpringerLink
Log in
Book cover

Cosmological Applications of Algebraic Quantum Field Theory in Curved Spacetimes pp 1–11Cite as

Introduction

  • Chapter
  • First Online:

Part of the book series: SpringerBriefs in Mathematical Physics ((BRIEFSMAPHY,volume 6))

Abstract

In this chapter we give a pedagogical introduction to algebraic quantum field theory and explain the concepts and the relevance of this framework in quantum field theory on curved spacetimes. This introduction should serve as a guide for the next chapter, where many concepts of and constructions in algebraic quantum field theory on curved spacetimes are reviewed in detail. Afterwards, we give a non-technical overview of the cosmological applications discussed in the final chapter of this monograph.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   49.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Brunetti, R., Duetsch, M., Fredenhagen, K.: Perturbative algebraic quantum field theory and the renormalization groups. Adv. Theor. Math. Phys. 13, 1255–1599 (2009)

    Article  MathSciNet  Google Scholar 

  2. Brunetti, R., Fredenhagen, K., Köhler, M.: The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes. Commun. Math. Phys. 180, 633 (1996)

    Article  MATH  ADS  Google Scholar 

  3. Brunetti, R., Fredenhagen, K.: Microlocal analysis and interacting quantum field theories: renormalization on physical backgrounds. Commun. Math. Phys. 208, 623 (2000)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  4. Brunetti, R., Fredenhagen, K., Rejzner, K.: Quantum gravity from the point of view of locally covariant quantum field theory. arXiv:1306.1058 [math-ph]

  5. Chilian, B., Fredenhagen, K.: The time slice axiom in perturbative quantum field theory on globally hyperbolic spacetimes. Commun. Math. Phys. 287, 513 (2009)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  6. Degner, A.: Properties of states of low energy on cosmological spacetimes. Ph.D. Thesis, University of Hamburg 2013, DESY-THESIS-2013-002

    Google Scholar 

  7. Dimock, J.: Quantized electromagnetic field on a manifold. Rev. Math. Phys. 4, 223–233 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  8. Ellis, G.F.R., Maartens, R., MacCallum, M.A.H.: Relativistic Cosmology. Cambridge University Press, Cambridge (2012)

    Book  MATH  Google Scholar 

  9. Eltzner, B.: Quantization of Perturbations in Inflation. arXiv:1302.5358 [gr-qc]

  10. Fewster, C.J., Hunt, D.S.: Quantization of linearized gravity in cosmological vacuum spacetimes. Rev. Math. Phys. 25, 1330003 (2013)

    Article  MathSciNet  Google Scholar 

  11. Fredenhagen, K., Rejzner, K.: Batalin-Vilkovisky formalism in perturbative algebraic quantum field theory. Commun. Math. Phys. 317, 697 (2013)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  12. Haag, R.: Local Quantum Physics: Fields, Particles, Algebras, 356 pp. Springer, Berlin (1992) (Texts and monographs in physics)

    Google Scholar 

  13. Hack, T.-P.: The Lambda CDM-model in quantum field theory on curved spacetime and Dark Radiation. arXiv:1306.3074 [gr-qc]

  14. Hack, T.-P.: Quantization of the linearised Einstein-Klein-Gordon system on arbitrary backgrounds and the special case of perturbations in Inflation. Class. Quantum Gravity 31(21), 215004 (2014)

    Google Scholar 

  15. Hack, T.-P., Schenkel, A.: Linear bosonic and fermionic quantum gauge theories on curved spacetimes. Gen. Relativ. Gravit. 45, 877 (2013)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  16. Hollands, S.: Renormalized quantum Yang-Mills fields in curved spacetime. Rev. Math. Phys. 20, 1033 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  17. Hollands, S., Ruan, W.: The state space of perturbative quantum field theory in curved space-times. Annales Henri Poincare 3, 635 (2002)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  18. Hollands, S., Wald, R.M.: Local Wick polynomials and time ordered products of quantum fields in curved spacetime. Commun. Math. Phys. 223, 289 (2001)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  19. Hollands, S., Wald, R.M.: Existence of local covariant time ordered products of quantum fields in curved spacetime. Commun. Math. Phys. 231, 309 (2002)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  20. Hollands, S., Wald, R.M.: On the renormalization group in curved space-time. Commun. Math. Phys. 237, 123 (2003)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  21. Hollands, S., Wald, R.M.: Conservation of the stress tensor in interacting quantum field theory in curved spacetimes. Rev. Math. Phys. 17, 227 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  22. Kolb, E.W., Turner, M.S.: The early universe. Front. Phys. 69, 1 (1990)

    MathSciNet  ADS  Google Scholar 

  23. Makino, N., Sasaki, M.: The density perturbation in the chaotic inflation with nonminimal coupling. Prog. Theor. Phys. 86, 103 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  24. Mukhanov, V.: Physical Foundations of Cosmology. Cambridge University Press, Cambridge (2005)

    Book  MATH  Google Scholar 

  25. Olbermann, H.: States of low energy on Robertson-Walker spacetimes. Class. Quantum Gravity 24, 5011 (2007)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  26. Pinamonti, N., Siemssen, D.: Scale-invariant curvature fluctuations from an extended semiclassical gravity. J. Math. Phys. 56, 022303 (2015)

    Article  ADS  Google Scholar 

  27. Straumann, N.: From primordial quantum fluctuations to the anisotropies of the cosmic microwave background radiation. Annalen Phys. 15, 701 (2006)

    Article  MATH  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Theoretical Physics, University of Leipzig, Leipzig, Germany

    Thomas-Paul Hack

Authors
  1. Thomas-Paul Hack
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thomas-Paul Hack .

Rights and permissions

Reprints and permissions

Copyright information

© 2016 The Author(s)

About this chapter

Cite this chapter

Hack, TP. (2016). Introduction. In: Cosmological Applications of Algebraic Quantum Field Theory in Curved Spacetimes. SpringerBriefs in Mathematical Physics, vol 6. Springer, Cham. https://doi.org/10.1007/978-3-319-21894-6_1

Download citation

Publish with us

Policies and ethics

Search

Navigation