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Applications in One Space Dimension

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Spectral Methods in Quantum Field Theory

Part of the book series: Lecture Notes in Physics ((LNP,volume 777))

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In this chapter we will apply the techniques we have developed to compute vacuum polarization energies for various systems.

We start by considering models in d = 1 + 1 dimensions. Systems with one space dimension provide a particularly simple testing ground for our approach. We will also see that they contain subtleties that our approach is well-suited to address. In later chapters we will thoroughly investigate models in three spatial dimensions.

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References

  1. G. Pöschl and E. Teller, Z. Phys. 83 (1933) 143.

    Google Scholar 

  2. R. Rajaraman, Solitons and Instantons. North Holland, 1982.

    Google Scholar 

  3. R. F. Dashen, B. Hasslacher, and A. Neveu, Phys. Rev. D10 (1974) 4114.

    ADS  Google Scholar 

  4. E. B. Bogomolny, Sov. J. Nucl. Phys. 24 (1976) 449.

    Google Scholar 

  5. M. K. Prasad and C. M. Sommerfield, Phys. Rev. Lett. 35 (1975) 760.

    Article  ADS  Google Scholar 

  6. J. F. Schonfeld, Nucl. Phys. B161 (1979) 125.

    Article  ADS  Google Scholar 

  7. H. Nastase, M. A. Stephanov, P. van Nieuwenhuizen, and A. Rebhan, Nucl. Phys. B542 (1999) 471.

    Article  ADS  Google Scholar 

  8. K. Schoutens, Nucl. Phys. B344 (1990) 665.

    Article  ADS  MathSciNet  Google Scholar 

  9. C. Ahn, D. Bernard, and A. LeClair, Nucl. Phys. B346 (1990) 409.

    Article  ADS  MathSciNet  Google Scholar 

  10. C.-r. Ahn, Nucl. Phys. B354 (1991) 57.

    Article  ADS  Google Scholar 

  11. G. V. Dunne, Phys. Lett. B467 (1999) 238.

    ADS  MathSciNet  Google Scholar 

  12. L.-H. Chan, Phys. Rev. D55 (1997) 6223.

    ADS  Google Scholar 

  13. M. Bordag, A. S. Goldhaber, P. van Nieuwenhuizen, and D. Vassilevich, Phys. Rev. D66 (2002) 125014.

    ADS  Google Scholar 

  14. A. S. Goldhaber, A. Litvintsev, and P. van Nieuwenhuizen, Phys. Rev. D64 (2001) 045013.

    ADS  Google Scholar 

  15. D. V. Vassilevich, Phys. Rev. D68 (2003) 045005.

    ADS  MathSciNet  Google Scholar 

  16. A. Rebhan and P. van Nieuwenhuizen, Nucl. Phys. B508 (1997) 449.

    Article  ADS  Google Scholar 

  17. A. D’Adda and P. Di Vecchia, Phys. Lett. B73 (1978) 162.

    ADS  Google Scholar 

  18. A. D’Adda, R. Horsley, and P. Di Vecchia, Phys. Lett. B76 (1978) 298.

    ADS  Google Scholar 

  19. R. Horsley, Nucl. Phys. B151 (1979) 399.

    Article  ADS  Google Scholar 

  20. S. Rouhani, Nucl. Phys. B182 (1981) 462.

    Article  ADS  Google Scholar 

  21. H. Yamagishi, Phys. Lett. B147 (1984) 425.

    ADS  Google Scholar 

  22. A. Chatterjee and P. Majumdar, Phys. Rev. D30 (1984) 844.

    ADS  Google Scholar 

  23. A. K. Chatterjee and P. Majumdar, Phys. Lett. B159 (1985) 37.

    ADS  MathSciNet  Google Scholar 

  24. A. Uchiyama, Nucl. Phys. B244 (1984) 57.

    Article  ADS  Google Scholar 

  25. A. Uchiyama, Prog. Theor. Phys. 75 (1986) 1214.

    Article  ADS  Google Scholar 

  26. A. Uchiyama, Nucl. Phys. B278 (1986) 121.

    Article  ADS  Google Scholar 

  27. R. K. Kaul and R. Rajaraman, Phys. Lett. B131 (1983) 357.

    ADS  Google Scholar 

  28. C. Imbimbo and S. Mukhi, Nucl. Phys. B247 (1984) 471.

    Article  ADS  MathSciNet  Google Scholar 

  29. E. Witten and D. I. Olive, Phys. Lett. B78 (1978) 97.

    ADS  Google Scholar 

  30. A. J. Niemi and G. W. Semenoff, Phys. Rev. D32 (1985) 471.

    ADS  MathSciNet  Google Scholar 

  31. M. A. Shifman, A. I. Vainshtein, and M. B. Voloshin, Phys. Rev. D59 (1999) 045016.

    ADS  Google Scholar 

  32. A. Losev, M. A. Shifman, and A. I. Vainshtein, Phys. Lett. B522 (2001) 327.

    ADS  MathSciNet  Google Scholar 

  33. B. Moussallam, Phys. Rev. D40 (1989) 3430.

    ADS  Google Scholar 

  34. J. A. Bagger and S. G. Naculich, Phys. Rev. Lett. 67 (1991) 2252.

    Article  ADS  Google Scholar 

  35. J. A. Bagger and S. G. Naculich, Phys. Rev. D45 (1992) 1395.

    ADS  Google Scholar 

  36. R. J. Perry, Nucl. Phys. A467 (1987) 717.

    ADS  Google Scholar 

  37. R. MacKenzie, F. Wilczek, and A. Zee, Phys. Rev. Lett. 53 (1984) 2203.

    Article  ADS  Google Scholar 

  38. G. Ripka and S. Kahana, Phys. Lett. B155 (1985) 327.

    ADS  Google Scholar 

  39. G. Ripka and S. Kahana, Phys. Rev. D36 (1987) 1233.

    ADS  Google Scholar 

  40. R. Johnson and J. Schechter, Phys. Rev. D36 (1987) 1484.

    ADS  Google Scholar 

  41. G. W. Anderson, L. J. Hall, and S. D. H. Hsu, Phys. Lett. B249 (1990) 505.

    ADS  Google Scholar 

  42. S. Dimopoulos, B. W. Lynn, S. B. Selipsky, and N. Tetradis, Phys. Lett. B253 (1991) 237.

    ADS  Google Scholar 

  43. S. G. Naculich, Phys. Rev. D46 (1992) 5487.

    ADS  Google Scholar 

  44. E. D’Hoker and E. Farhi, Nucl. Phys. B248 (1984) 77.

    Article  MathSciNet  Google Scholar 

  45. E. D’Hoker and E. Farhi, Nucl. Phys. B248 (1984) 59.

    Article  MathSciNet  Google Scholar 

  46. S. R. Coleman, Commun. Math. Phys. 31 (1973) 259.

    Article  MATH  ADS  Google Scholar 

  47. E. Farhi, N. Graham, R. L. Jaffe, and H. Weigel, Nucl. Phys. B585 (2000) 443.

    Article  ADS  Google Scholar 

  48. J. Goldstone and F. Wilczek, Phys. Rev. Lett. 47 (1981) 986.

    Article  ADS  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Dept. Physics, Middlebury College, 05753, 515 McCardell Bicentennial Hall, Middlebury, VT, USA

    Noah Graham (Prof)

  2. Universität Tübingen, FB 13 Inst. Theoretische Physik, Auf der Morgenstelle 14, 72076, Tübingen, Germany

    Markus Quandt

  3. Universität Siegen FB Physik, 57068, Emmy Noether Campus, Siegen, Germany

    Herbert Weigel

Authors
  1. Noah Graham
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  2. Markus Quandt
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  3. Herbert Weigel
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Corresponding author

Correspondence to Noah Graham .

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Graham, N., Quandt, M., Weigel, H. (2009). Applications in One Space Dimension. In: Spectral Methods in Quantum Field Theory. Lecture Notes in Physics, vol 777. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00139-0_4

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  • DOI: https://doi.org/10.1007/978-3-642-00139-0_4

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00138-3

  • Online ISBN: 978-3-642-00139-0

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