Regularization and renormalization in scattering from Dirac delta potentials

American Journal of Physics

Volumn 66, Issue 12, 1998, Pages 1101-1109

  Mitra, Indrajit ^a   DasGupta, Ananda ^a   Dutta Roy, Binayak ^a  

^a SAHA INSTITUTE OF NUCLEAR PHYSICS   (India)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032349265     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.19051     Document Type: Article

References (34)

1. Regularization and renormalization are discussed in any modern textbook on quantum field theory. See, e.g., M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Addison-Wesley, Reading, MA, 1995); C. Itzykson and J.-B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980). A nice review of regularization schemes is given in T. Muta, Foundations of Quantum Chromodynamics (World Scientific, Singapore, 1987), Sec. 2.4.1.
2. Regularization and renormalization are discussed in any modern textbook on quantum field theory. See, e.g., M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Addison-Wesley, Reading, MA, 1995); C. Itzykson and J.-B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980). A nice review of regularization schemes is given in T. Muta, Foundations of Quantum Chromodynamics (World Scientific, Singapore, 1987), Sec. 2.4.1.
3. Regularization and renormalization are discussed in any modern textbook on quantum field theory. See, e.g., M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Addison-Wesley, Reading, MA, 1995); C. Itzykson and J.-B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980). A nice review of regularization schemes is given in T. Muta, Foundations of Quantum Chromodynamics (World Scientific, Singapore, 1987), Sec. 2.4.1.
4. J. Fernando Perez and F. A. B. Coutinho, "Schrödinger equation in two dimensions for a zero-range potential and a uniform magnetic field: An exactly solvable model," Am. J. Phys. 59, 52-54 (1991).
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8. 4 theory" in P. Ramond, Field Theory: A Modern Primer (Addison-Wesley, Reading, MA, 1990), 2nd ed., Chap. 4.
9. 4 theory" in P. Ramond, Field Theory: A Modern Primer (Addison-Wesley, Reading, MA, 1990), 2nd ed., Chap. 4.
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11. S. K. Adhikari, T. Frederico, and I. D. Goldman, "Perturbative renormalization in quantum few-body problems," Phys. Rev. Lett. 74, 487-491 (1995).
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14. See the discussion and references in Ref. 2.
15. C. Thorn, "Quark confinement in the infinite momentum frame," Phys. Rev. D 19, 639-651 (1979).
16. S. Weinberg, "Nuclear forces from chiral Lagrangians," Phys. Lett. B 251, 288-292 (1990); "Effective chiral Lagrangians for nucleon-pion interactions and nuclear forces," Nucl. Phys. B 363, 3-18 (1991); D. B. Kaplan, M. J. Savage, and M. B. Wise, "Nucleon-nucleon scattering from effective field theory," Nucl. Phys. B 478, 629-659 (1996).
17. S. Weinberg, "Nuclear forces from chiral Lagrangians," Phys. Lett. B 251, 288-292 (1990); "Effective chiral Lagrangians for nucleon-pion interactions and nuclear forces," Nucl. Phys. B 363, 3-18 (1991); D. B. Kaplan, M. J. Savage, and M. B. Wise, "Nucleon-nucleon scattering from effective field theory," Nucl. Phys. B 478, 629-659 (1996).
18. S. Weinberg, "Nuclear forces from chiral Lagrangians," Phys. Lett. B 251, 288-292 (1990); "Effective chiral Lagrangians for nucleon-pion interactions and nuclear forces," Nucl. Phys. B 363, 3-18 (1991); D. B. Kaplan, M. J. Savage, and M. B. Wise, "Nucleon-nucleon scattering from effective field theory," Nucl. Phys. B 478, 629-659 (1996).
19. We generalize C. Thorn's (Ref. 12) treatment from two to D dimensions.
20. 2).
21. K. Huang, Quarks, Leptons and Gauge Fields (World Scientific, Singapore, 1982); R. Jackiw, in M. A. B. Beg Memorial Volume, edited by A. Ali and P. Hoodbhoy (World Scientific, Singapore, 1991).
22. K. Huang, Quarks, Leptons and Gauge Fields (World Scientific, Singapore, 1982); R. Jackiw, in M. A. B. Beg Memorial Volume, edited by A. Ali and P. Hoodbhoy (World Scientific, Singapore, 1991).
23. This condition has been used in Ref. 10.
24. 18 For a proof of Eq. (35) see P. Ramond (Ref. 6), Appendix B.
25. For a proof of Eq. (36) see L. H. Ryder, Quantum Field Theory (Cambridge U.P., Cambridge, 1985), Appendix 9B.
26. See L. S. Brown, Quantum Field Theory (Cambridge U.P., Cambridge, 1992), p. 164.
27. See M. E. Peskin and D. V. Schroeder (Ref. 1), Sec. 7.5.
28. For a pedagogical discussion on the axial anomaly, see K. Huang (Ref. 16), Chap. 11.
29. A. Cabo, J. L. Lucio, and H. Mercado, "On scale invariance and anomalies in quantum mechanics," Am. J. Phys. 66, 240-246 (1998).
30. iπ/2√B, all the three terms on the RHS of (67) are equal.
31. See, e.g., M. E. Peskin and D. V. Schroeder (Ref. 1). Various renormalization schemes are reviewed in Muta (Ref. 1), Sec. 2.4.3.
32. See, e.g., L. I. Schiff, Quantum Mechanics (McGraw-Hill, Singapore, 1968), 3rd ed., See. 37.
33. For proof, see, e.g., M. E. Peskin and D. V. Schroeder (Ref. 1), p. 249.
34. See J. C. Collins, Renormalization (Cambridge U.P., Cambridge, 1984), Secs. 4.2 and 4.3.