Galilean Lee model of the δ-function potential

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 61, Issue 3, 2000, Pages 327151-327155

  Hagen, C R ^a  

^a UNIVERSITY OF ROCHESTER   (United States)

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EID: 17544397730     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (13)

1. C. R. Hagen, Phys. Rev. Lett. 64, 503 (1990).
2. P. Gosdzinsky and R. Tarrach, Am. J. Phys. 59, 70 (1991).
3. L. R. Mead and J. Godines, Am. J. Phys. 59, 935 (1991).
4. C. M. Bender and L. R. Mead, Eur. J. Phys. 20, 117 (1999).
5. R. M. Cavalcanti, Eur. J. Phys. 20, L33 (1999).
6. Of course one could also construct an appropriate theory in Minkowski space. Since, however, this would require at some point that a nonrelativistic limit be taken, it is clearly desirable to build in that limit at the outset (i.e., to construct a Galilean theory).
7. J-M. Lévy-Leblond, Commun. Math. Phys. 4, 157 (1967).
8. V. Bargmann, Ann. Math. 59, 1 (1954); J-M. Lévy-Leblond, J. Math. Phys. 4, 776 (1963).
9. V. Bargmann, Ann. Math. 59, 1 (1954); J-M. Lévy-Leblond, J. Math. Phys. 4, 776 (1963).
10. It is well to note that this transformation law clearly indicates the crucial role of the Bargmann superselection rule. Only in the case that it is satisfied is the trilinear interaction term (2) Galilean invariant.
11. It should be noted that the bare (i.e., unrenormalized) internal energies of the N and θ fields have been taken to be zero. That this can be done without loss of generality is a consequence of the fact thai ψ can always be replaced by ψe-iU0′, thereby eliminating the internal energy term for each of these fields. That this cannot also be done for the V field is a consequence of the fact that the interaction term constrains the set of allowable gauge transformations.
12. It should be noted that there is a sign error in the corresponding calculation of Ref. [7].
13. Alternatively stated, the local-field theory with U0<0 is a null theory.