Research PaperNo Access

Faculty of Physics, University of Warsaw ul. Pasteura 5, 02-093 Warsaw, Poland

E-mail Address: marek.lewicki@fuw.edu.pl

and

L. Smaldone

https://orcid.org/0000-0002-6738-5537

Faculty of Physics, University of Warsaw ul. Pasteura 5, 02-093 Warsaw, Poland

Dipartimento di Fisica, Università di Salerno, Via Giovanni Paolo II, 132 84084 Fisciano, Italy

INFN Sezione di Napoli, Gruppo collegato di Salerno, Italy

E-mail Address: lsmaldone@unisa.it

Corresponding author.

Search for more papers by this author

https://doi.org/10.1142/S0217732324500895Cited by:0 (Source: Crossref)

Abstract

The dynamical map represents a fundamental concept in quantum field theory, providing a solution of the field equations in the Fock space of asymptotic fields. In this paper, we show how to express the dynamical map of a scalar field in the language of quantum effective action. This grants us new insights into the study of topological defects in quantum field theory by showing a connection between the usual least-action principle and Umezawa’s boson transformation method.

Keywords:

PACS: 03.70.+k, 11.10.−z, 11.15.Bt, 11.27.+d, 11.30.Qc, 11.90.+t

References

1. C. Itzykson and J. Zuber , Quantum Field Theory, Dover Books on Physics ( Dover Publications, 2012). Google Scholar
2. H. Kleinert , Particles and Quantum Fields ( World Scientific, 2016). Link, Google Scholar
3. S. Schweber , An Introduction to Relativistic Quantum Field Theory ( Dover Publications, 2013). Google Scholar
4. R. Haag , Kong. Dan. Vid. Sel. Mat. Fys. Med. 29 N12, 1 (1955). Google Scholar
5. H. Umezawa, H. Matsumoto and M. Tachiki , Thermo-Field Dynamics and Condensed States ( North-Holland, 1982). Google Scholar
6. H. Umezawa , Advanced Field Theory: Micro, Macro, and Thermal Physics ( AIP, 1993). Google Scholar
7. O. W. Greenberg , Virtues of the Haag expansion in quantum field theory, in 1st Arctic Workshop on Future Physics and Accelerators (World Scientific, Singapore, 1994), pp. 498–520. Google Scholar
8. M. Blasone, P. Jizba and G. Vitiello , Quantum Field Theory and Its Macroscopic Manifestations: Boson Condensation, Ordered Patterns, and Topological Defects ( Imperial College Press, 2011). Link, Google Scholar
9. H. Umezawa , Il Nuovo Cimento A (1965–1970) 40, 450 (1965). Crossref, ADS, Google Scholar
10. H. Matsumoto, N. J. Papastamatiou and H. Umezawa , Nucl. Phys. B 82, 45 (1974). Crossref, Web of Science, ADS, Google Scholar
11. H. Matsumoto, N. Papastamatiou, H. Umezawa and G. Vitiello , Nucl. Phys. B 97, 61 (1975). Crossref, Web of Science, ADS, Google Scholar
12. C. De Concini and G. Vitiello , Nucl. Phys. B 116, 141 (1976). Crossref, Web of Science, ADS, Google Scholar
13. M. Hongoh, H. Matsumoto and H. Umezawa , Prog. Theor. Phys. 65, 315 (1981). Crossref, ADS, Google Scholar
14. M. Wadati, H. Matsumoto, Y. Takahashi and H. Umezawa , Phys. Lett. A 62, 255 (1977). Crossref, Web of Science, ADS, Google Scholar
15. M. Wadati, H. Matsumoto, Y. Takahashi and H. Umezawa , Fortschr. Phys. 26, 357 (1978). Crossref, Web of Science, Google Scholar
16. M. Wadati, H. Matsumoto and H. Umezawa , Phys. Rev. B 18, 4077 (1978). Crossref, Web of Science, ADS, Google Scholar
17. L. Mercaldo, I. Rabuffo and G. Vitiello , Nucl. Phys. B 188, 193 (1981). Crossref, Web of Science, ADS, Google Scholar
18. M. Blasone and P. Jizba , Ann. Phys. 295, 230 (2002). Crossref, Web of Science, ADS, Google Scholar
19. L. Leplae and H. Umezawa , J. Math. Phys. 10, 2038 (1969). Crossref, Web of Science, ADS, Google Scholar
20. L. Leplae, F. Mancini and H. Umezawa , Phys. Rev. B 2, 3594 (1970). Crossref, Web of Science, ADS, Google Scholar
21. H. Tze and Z. Ezawa , Phys. Lett. B 55, 63 (1975). Crossref, Web of Science, ADS, Google Scholar
22. M. Wadati, H. Matsumoto and H. Umezawa , Phys. Rev. D 18, 1192 (1978). Crossref, Web of Science, ADS, Google Scholar
23. A. Iorio and L. Smaldone , Int. J. Mod. Phys. D 32, 2350063 (2023). Link, Web of Science, ADS, Google Scholar
24. A. Iorio and L. Smaldone , J. Phys. Conf. Ser. 2533, 012030 (2023). Crossref, Google Scholar
25. R. Mańka, J. Kuczyński and G. Vitiello , Nucl. Phys. B 276, 533 (1986). Crossref, Web of Science, ADS, Google Scholar
26. R. Mańka and G. Vitiello , Ann. Phys. 199, 61 (1990). Crossref, Web of Science, ADS, Google Scholar
27. M. S. Swanson , J. Math. Phys. 22, 777 (1981). Crossref, Web of Science, ADS, Google Scholar
28. C.-N. Yang and D. Feldman , Phys. Rev. 79, 972 (1950). Crossref, Web of Science, ADS, Google Scholar
29. W. Greiner, D. Bromley and J. Reinhardt , Field Quantization ( Springer, 2013). Google Scholar
30. L. H. Ryder , Quantum Field Theory, 2nd edn. ( Cambridge Univ. Press, 1996). Crossref, Google Scholar
31. W. Greiner and J. Reinhardt , Quantum Electrodynamics, Physics and Astronomy Online Library ( Springer, 2003). Crossref, Google Scholar
32. A. Jevicki and C.-K. Lee , Phys. Rev. D 37, 1485 (1988). Crossref, Web of Science, ADS, Google Scholar
33. F. T. Brandt, A. Das, J. Frenkel and A. J. da Silva , Phys. Rev. D 59, 065004 (1999). Crossref, Web of Science, ADS, Google Scholar
34. J. Goldstone , Nuovo Cimento 19, 154 (1961). Crossref, Web of Science, ADS, Google Scholar
35. J. Goldstone, A. Salam and S. Weinberg , Phys. Rev. 127, 965 (1962). Crossref, Web of Science, ADS, Google Scholar
36. M. Peskin and D. Schroeder , An Introduction To Quantum Field Theory, Frontiers in Physics ( Avalon Publishing, 1995). Google Scholar
37. O. Cheyette , Phys. Rev. Lett. 55, 2394 (1985). Crossref, Web of Science, ADS, Google Scholar
38. L.-H. Chan , Phys. Rev. Lett. 57, 1199 (1986). Crossref, Web of Science, ADS, Google Scholar
39. I. Buchbinder, S. Odintsov and L. Shapiro , Effective Action in Quantum Gravity ( Taylor & Francis, 1992). Google Scholar
40. S. Coleman and E. Weinberg , Phys. Rev. D 7, 1888 (1973). Crossref, Web of Science, ADS, Google Scholar
41. H. Matsumoto, N. Papastamatiou and H. Umezawa , Nucl. Phys. B 97, 90 (1975). Crossref, Web of Science, ADS, Google Scholar
42. Z. F. Ezawa and H. C. Tze , Nucl. Phys. B 96, 264 (1975). Crossref, Web of Science, ADS, Google Scholar
43. T. Vachaspati and A. Vilenkin , Phys. Rev. D 31, 3052 (1985). Crossref, Web of Science, ADS, Google Scholar
44. M. Sakellariadou , Phys. Rev. D 42, 354 (1990). Crossref, Web of Science, ADS, Google Scholar
45. R. A. Battye and E. P. S. Shellard , Nucl. Phys. B 423, 260 (1994). Crossref, Web of Science, ADS, Google Scholar
46. A. Vilenkin and E. Shellard , Cosmic Strings and Other Topological Defects, Cambridge Monographs on Mathematical Physics ( Cambridge Univ. Press, 1994). Google Scholar
47. C. Nash and S. Sen , Topology and Geometry for Physicists ( Academic Press, 1988). Google Scholar
48. G. Acquaviva, A. Iorio and L. Smaldone , Ann. Phys. 434, 168641 (2021). Crossref, Web of Science, Google Scholar