3D Physics and the Electroweak Phase Transition: Perturbation Theory and Lattice Monte Carlo Analysis

  • K. Kajantie
  • M. Shaposhnikov
Part of the NATO ASI Series book series (NSSB, volume 338)


We know the Lagrangian of the SU(3)×SU(2)×U(l) standard model (SM) and, therefore, also the equilibrium thermodynamics of the quantum system with the spectrum of the SM: it is given by the functional integral
$${e^{ - F/T}} = \int {D\Phi {\mkern 1mu} \exp \left[ { - \frac{1}{\hbar }\int_0^{\beta \hbar } {d\tau } \int {{d^3}} x\pounds\left( {\Phi \left( {\tau ,{\text{x}}} \right)} \right)} \right],}$$
where the symbol Φ denotes generically all the fields of the SM. In a sense the problem of the electroweak (EW) phase transition thus is trivial: just calculate the above functional integral to give the free energy F and all the thermodynamics.




Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    R. Jackiw, Phys. Rev. D9 (1974) 1686ADSGoogle Scholar
  2. [2]
    D. A. Kirzhnitz, JETP Lett. 15 (1972) 529ADSGoogle Scholar
  3. D. A. Kirzhnitz and A. D. Linde, Phys. Lett. 72B (1972) 471ADSGoogle Scholar
  4. [3]
    L. Dolan and R. Jackiw, Phys.Rev. D9 (1974) 3320ADSGoogle Scholar
  5. [4]
    S. Weinberg, Phys.Rev. D9 (1974) 3357ADSGoogle Scholar
  6. [5]
    D.A. Kirzhnitz and A.D. Linde, Ann. Phys. 101 (1976) 195ADSCrossRefGoogle Scholar
  7. A.D. Linde, Nucl. Phys. B216 (1983) 421, Rep. Prog. Phys. 47 (1984) 925MathSciNetADSCrossRefGoogle Scholar
  8. [6]
    M.E. Shaposhnikov. Nucl. Phys. B287 (1987) 757ADSCrossRefGoogle Scholar
  9. A.I. Bochkarev and M.E. Shaposhnikov, Mod. Phys. Lett. 2A (1987) 417ADSGoogle Scholar
  10. [7]
    G.W. Anderson and L.J. Hall, Phys. Rev. D45 (1992) 2685ADSGoogle Scholar
  11. [8]
    K. Enqvist, J. Ignatius, K. Kajantie and K. Rummukainen, Phys. Rev. D45 (1992) 3415ADSGoogle Scholar
  12. [9]
    M.E. Shaposhnikov, Phys. Lett. B277 (1992) 324; B282 (1992) 483(E)ADSGoogle Scholar
  13. [10]
    M. Carrington, Phys. Rev. D45 (1992) 2933ADSGoogle Scholar
  14. [11]
    M. Dine, R. G. Leigh, P. Huet, A. Linde and D. Linde, Phys. Rev. D46 (1992) 550ADSGoogle Scholar
  15. [12]
    C. G. Boyd, D. E. Brahm and S. Hsu, Phys. Rev. D48 (1993) 4963ADSGoogle Scholar
  16. [13]
    M. Quiros, J.R. Espinosa and F. Zwirner, Phys. Lett. B314 (1993) 206ADSGoogle Scholar
  17. [14]
    W. Buchmüller, T. Helbig and D. Walliser, Nucl. Phys. B407 (1993) 387ADSCrossRefGoogle Scholar
  18. [15]
    W. Buchmüller, Z. Fodor, T. Helbig and D. Walliser, DESY Preprint DESY-93-021 (1993), Ann. Phys., to be publishedGoogle Scholar
  19. [16]
    P. Arnold and O. Espinosa, Phys. Rev. D47 (1993) 3546ADSGoogle Scholar
  20. [17]
    A. Hebecker, Z. Phys. C60 (1993) 271ADSGoogle Scholar
  21. [18]
    Z. Fodor and A. Hebecker, DESY preprint DESY 94-025, 1994Google Scholar
  22. [19]
    B. Bunk, E.-M. Ilgenfritz, J. Kripfganz, A. Schiller, Phys. Lett. B284 (1992) 371; Nucl. Phys. B403 (1993) 453ADSGoogle Scholar
  23. [20]
    K. Kajantie, K. Rummukainen and M. Shaposhnikov, Nucl. Phys. B407 (1993) 356ADSCrossRefGoogle Scholar
  24. [21]
    K. Farakos, K. Kajantie, K. Rummukainen and M. Shaposhnikov, CERN Preprint CERN-TH.6973/94, hep-ph 9404201Google Scholar
  25. [22]
    M. Shaposhnikov, Phys. Lett. B316 (1993) 112ADSGoogle Scholar
  26. [23]
    K. Farakos, K. Kajantie, K. Rummukainen and M. Shaposhnikov, CERN Preprint CERN-TH.7244/94, hep-ph 9404234Google Scholar
  27. [24]
    K. Farakos, K. Kajantie, K. Rummukainen and M. Shaposhnikov, CERN Preprint CERN-TH.7220/94, in preparationGoogle Scholar
  28. [25]
    S. Weinberg, Phys. Lett. 91B (1980) 51ADSGoogle Scholar
  29. [26]
    M. Lindner, M. Sher and H. Zaglauer, Phys. Lett. B228 (1989) 139ADSGoogle Scholar
  30. [27]
    A. Jakovác, K. Kajantie and A. Patkos, Helsinki preprint HU-TFT-94-01, hep-ph-9312355Google Scholar
  31. [28]
    M. Reuter and C. Wetterich, Nucl. Phys. B408 (1993) 91ADSCrossRefGoogle Scholar
  32. [29]
    H.J. Herrmann, W. Janke and F. Karsch (eds.), Proc. Workshop on Dynamics of First Order Phase Transitions, Jülich, June 1992 (World Scientific, Singapore, 1992)Google Scholar
  33. [30]
    C. Borgs, R. Kotecký and S. Miracle-Sole, J. Stat. Phys. 62 (1991) 529ADSCrossRefGoogle Scholar
  34. [31]
    A. M. Ferrenberg and R. H. Swendsen, Phys. Rev. Lett. 61 (1988) 2635ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • K. Kajantie
    • 1
  • M. Shaposhnikov
    • 2
  1. 1.Department of Theoretical PhysicsUniversity of HelsinkiFinland
  2. 2.CERN/THGeneve 23Switzerland

Personalised recommendations