Skip to main content

Quantum Field Theory: Where We Are

  • Chapter

Part of the book series: Lecture Notes in Physics ((LNP,volume 721))

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D. Buchholz and R. Haag: The quest for understanding in relativistic quantum physics, J. Math. Phys. 41 (2000) 3674–3697.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  2. K. Osterwalder and R. Schrader: Axioms for Euclidean Green’s functions, Commun. Math. Phys. 31 (1973) 83; Commun. Math. Phys. 42 (1975) 281.

    Google Scholar 

  3. H. Bostelmann: Phase space properties and the short distance structure in quantum field theory, J. Math. Phys. 46 (2005) 052301.

    Article  MathSciNet  ADS  Google Scholar 

  4. S. Doplicher and J.E. Roberts: Why there is a field algebra with a compact gauge group describing the superselection structure in particle physics, Commun. Math. Phys. 131 (1990) 51–107.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  5. D. Buchholz: The physical state space of quantum electrodynamics, Commun. Math. Phys. 85 (1982) 49.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. D. Buchholz, M. Porrmann and U. Stein: Dirac versus Wigner: Towards a universal particle concept in local quantum field theory, Phys. Lett. B 267 (1991) 377–381.

    ADS  MathSciNet  Google Scholar 

  7. O. Steinmann: Perturbative Quantum Electrodynamics and Axiomatic Field theory, Springer-Verlag, Berlin etc. 2000.

    MATH  Google Scholar 

  8. Y. Kawahigashi and R. Longo: Classification of two-dimensional local conformal nets with c < 1 and 2-cohomology vanishing for tensor categories, Commun. Math. Phys. 244 (2004) 63–97.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  9. R. Longo and K.-H. Rehren: Nets of subfactors, Rev. Math. Phys. 7 (1995) 567–598.

    Article  MATH  MathSciNet  Google Scholar 

  10. H.-J. Borchers: On revolutionizing quantum field theory with Tomita’s modular theory, J. Math. Phys. 41 (2000) 3604–3673.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  11. B. Schroer and H.-W. Wiesbrock: Modular constructions of quantum field theories with interactions, Rev. Math. Phys. 12 (2000) 301. H.-J. Borchers, D. Buchholz and B. Schroer: Polarization-free generators and the S-matrix, Commun. Math. Phys. 219 (2001) 125–140.

    Google Scholar 

  12. G. Lechner: An existence proof for interacting quantum field theories with a factorizing S-matrix, [arXiv:math-ph/0601022].

    Google Scholar 

  13. S. Weinberg: The Quantum Theory of Fields, Cambridge University Press, Cambridge, 1996.

    Google Scholar 

  14. R. Brunetti, K. Fredenhagen and R. Verch: The generally covariant locality principle: A new paradigm for local quantum physics, Commun. Math. Phys. 237 (2003) 31–68.

    MATH  ADS  MathSciNet  Google Scholar 

  15. R. Stora: Local gauge groups in quantum field theory: Perturbative gauge theories, talk given at ESI workshop “Local Quantum Physics”, Vienna (1997). D.R. Grigore: On the uniqueness of the non-Abelian gauge theories in Epstein-Glaser approach to renormalisation theory, Rom. J. Phys. 44 (1999) 853–913 [arXiv:hep-th/9806244]. \\ M. Duetsch and B. Schroer: Massive vector mesons and gauge theory, J.\ Phys.\ A 33 (2000) 4317.

    Google Scholar 

  16. H. Epstein and V. Glaser: The role of locality in perturbation theory, Ann. Inst. H. Poincaré A 19 (1973) 211.

    MathSciNet  Google Scholar 

  17. J. Glimm and A. Jaffe: Quantum Physics, a Functional Integral Point of View, Springer-Verlag, Berlin etc. 1987.

    Google Scholar 

  18. E. Seiler: Gauge Theories as a Problem of Constructive Quantum Field Theory and Statistical Mechanics, Springer-Verlag, Berlin etc. 1982. M. Creutz: Quarks, Gluons and Lattices, Cambridge University Press, Cambridge 1983. H. J. Rothe: Lattice Gauge Theories: An Introduction, World Scientific, Singapore 1992; I. Montvay and G. Münster: Quantum Fields on a Lattice, Cambridge University Press, Cambridge 1994. J. Smit: Introduction to Quantum Fields on a Lattice – A robust mate, Cambridge University Press, Cambridge 2002.

    Google Scholar 

  19. T. Balaban: The large field renormalization operation for classical $N$-vector models, Commun. Math. Phys. 198 (1998) 493, and references therein.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  20. A. M. Jaffe and E. Witten: Quantum Yang-Mills theory, The Millenium Problems, Official Problem Description, Clay Mathematics Institute 2000.

    Google Scholar 

  21. S. Elitzur: Impossibility of spontaneously breaking local symmteries, Phys. Rev. D 12 (1975) 3978.

    ADS  Google Scholar 

  22. K. Osterwalder and E. Seiler: Gauge field theories on a lattice, Ann. Physics 110 (1978) 440.

    Article  ADS  MathSciNet  Google Scholar 

  23. E. Fradkin and S.H. Shenker: Phase diagrams of lattice gauge theories with Higgs fields, Phys. Rev. D19 (1979) 3682.

    ADS  Google Scholar 

  24. G. ’t Hooft: Why do we need local gauge invariance in theories with vector particles? An introduction, in: G. ’t Hooft et al. (eds.), Recent Developments in Gauge Theories, Proceedings NATO Advanced Study Institute, Cargése 1979, Plenum, New York 1980.

    Google Scholar 

  25. J. Fröhlich, G. Morchio and F. Strocchi: Higgs phenomenon without symmtery breaking order parameter, Nucl. Phys. B 190[FS3] (1981) 553.

    Article  ADS  Google Scholar 

  26. T. Kennedy and C. King: Spontaneous symmetry breakdown in the Abelian Higgs model, Commun. Math. Phys. 104 (1986) 327.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  27. K. Gawedzki and A. Kupiainen: Renormalizing the nonrenormalizable, Phys. Rev. Lett. 54 (1985) 2191; Renormalization of a nonrenormalizable quantum field theory, Nucl. Phys. B 262 (1985) 33; Gross-Neveu model through convergent perturbation expansions, Commun. Math. Phys. 102 (1985) 1.

    Google Scholar 

  28. J. Gasser and H. Leutwyler: Chiral perturbation theory: expansions in the mass of the strange quark, Nucl. Phys. B 250 (1985) 465; Low-energy expansion of meson form factors, Nucl. Phys. B 250 (1985) 517; η\to3π to one loop, Nucl. Phys. B 250 (1985) 539.

    Google Scholar 

  29. E. Eichten and B. Hill: An effective field theory for the calculation of matrix elements involving heavy quarks, Phys. Lett. B 234 (1990) 511; Static effective field theory: 1/m corrections, Phys. Lett. B 243 (1990) 427.

    Google Scholar 

  30. W.E. Caswell and G.P. Lepage: Effective Lagrangians for bound state problems in QED, QCD, and other field theories, Phys. Lett. B 167 (1986) 437.

    ADS  Google Scholar 

  31. G.T. Bodwin, E. Braaten and G.P. Lepage: Rigorous QCD analysis of inclusive annihilation and production of heavy quarkonium, Phys. Rev. D 51 (1995) 1125; erratum Phys. Rev. D 55 (1997) 5853.

    Google Scholar 

  32. A. Pich: Effective field theory (Les Houches lectures 1997), in: Probing the Standard Model of Particle Interactions, R. Gupta, A. Morel, E. de Rafael and F. David (eds.), Vol. 2, pp. 949–1049, North Holland, Amsterdam 1999 [arXiv:hep-ph/9806303].

    Google Scholar 

  33. S. Hollands and R.M. Wald: On the renormalization group in curved spacetime, Commun. Math. Phys. 237 (2003) 123–160.

    MATH  ADS  MathSciNet  Google Scholar 

  34. D. Bahns, S. Doplicher, K. Fredenhagen and G. Piacitelli: On the unitarity problem in space/time noncommutative theories, Phys. Lett. B 533 (2002) 178–181.

    ADS  MathSciNet  Google Scholar 

  35. A. Ashtekar: Gravity and the quantum, New J. Phys. 7 (2005) 198.

    Article  ADS  MathSciNet  Google Scholar 

  36. L. Smolin: How far are we from the quantum theory of gravity? [arXiv:hep-th/0303185].

    Google Scholar 

  37. G. T. Horowitz: Spacetime in string theory, New J. Phys. 7 (2005) 201.

    Article  ADS  MathSciNet  Google Scholar 

  38. J. Dimock: Locality in free string field theory, J. Math. Phys. 41 (2000) 40; Ann. H. Poinc. 3 (2002) 613.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Fredenhagen, K., Rehren, KH., Seiler, E. (2007). Quantum Field Theory: Where We Are. In: Stamatescu, IO., Seiler, E. (eds) Approaches to Fundamental Physics. Lecture Notes in Physics, vol 721. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71117-9_4

Download citation

Publish with us

Policies and ethics