VOLUME 75, NUMBER 22 PH YS ICAL REVIEW LETTERS 27 NovEMBER 1995

Lavelle and McMullan Reply: Much is known aboutthe charged sectors of quantum electrodynamics (QED).The state space displays rich superselection sectors where,in particular, the velocity of charged particles, like theelectron, labels different sectors [1,2]. The BRST chargecan be used effectively to project out the gauge invariant,physical states, but the resulting state space is an infinitetensor product of these superselection sectors; i.e., theBRST charge is not capable, on its own, of distinguishingbetween these physically distinct sectors. In our Letter [3]we introduced a new, nonlocal, noncovariant symmetrythat projected out the static sector of QED (describedby Dirac's dressed electron). The nonstatic extensionof Dirac's construction are still BRST, and indeed anti-BRST invariant, but are not invariant under our symmetry.As such, our symmetry, in conjunction with BRST, canbe used to extract an irreducible sector of the intricatestructure of QED. Indeed, as one would expect to be ableto recover the other velocity dependent sectors in a similarfashion, we conjecture that our symmetry is but onemember of a whole class of distinct, new, noncovariantsymmetries of QED.

In our presentation of the symmetry, we took greatpains to show that it really is a symmetry of QED. In thepreceding Comment [4] a simplistic argument is presentedin free QED (which is, after all, a trivial theory withoutinteraction or charges and which hence lacks the abovesuperselection sectors) to claim that our symmetry is nomore than "a nonlocal version of standard BRST." Nomatter what the merits of these arguments are for thefree theory, this is manifestly not true for the interactingtheory. The Comment exemplifies the dangers of formal

manipulations of path integrals in nontrivial theories likethe full version of QED.

On a lesser note, we point out that Tang and Finkel-stein's work [5] is not a covariant version of our sym-metry; as far as we are aware this has also never beensuggested by those authors.

Martin Lavelle*Grup de Fisica Teorica and IFAE Edificio CnUniversitat Autonoma de BarcelonaE-08193 Bellaterra, Barcelona, Spain

David McMullan~School of Mathematics and StatisticsUniversity of PlymouthDrake Circus, Plymouth, Devon PL4 8AA, United Kingdom

Received 18 September 1995PACS numbers: 12.20.—m, 11.10.Ef, 11.30.—j

*Electronic address: lavelleifae. es~Electronic address: d.mcmullan plymouth. ac.uk

[1] R. Haag, Local Quantum Physics (Springer-Verlag,Berlin, Heidelberg, 1993).

[2] D. Buchholz, Commun. Math. Phys. 85, 49 (1992).[3] M. Lavelle and D. McMullan, Phys. Rev. Lett. 71, 3758

(1993).[4] V. O. Rivelles, preceding Comment, Phys. Rev. Lett. 75,

4150 (1995).[5] Z. Tang and D. Finkelstein, Phys. Rev. Lett. 73, 3055

(1994).

0031-9007/95/75(22)/4151(1) $06.00 1995 The American Physical Society 4151