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Gauge Invariance and the Pauli-Villars Regulator in Lorentz-and CPT-Violating Electrodynamics
| Content Provider | Semantic Scholar |
|---|---|
| Copyright Year | 2004 |
| Abstract | We examine the nonperturbative structure of the radiatively induced Chern-Simons term in a Lorentzand CPT-violating modification of QED. Although the coefficient of the induced Chern-Simons term is in general undetermined, the nonperturbative theory appears to generate a definite value. However, the CPT-even radiative corrections in this same formulation of the theory generally break gauge invariance. We show that gauge invariance may yet be preserved through the use of a Pauli-Villars regulator, and, contrary to earlier expectations, this regulator does not necessarily give rise to a vanishing ChernSimons term. Instead, two possible values of the Chern-Simons coefficient are allowed, one zero and one nonzero. This formulation of the theory therefore allows the coefficient to vanish naturally, in agreement with experimental observations. 1 baltschu@indiana.edu One of the most interesting terms that arises in the study of Lorentzand CPTviolating corrections to the standard model action [1, 2, 3] is the electromagnetic ChernSimons term, with Lagrange density LCS = 1 2 (kCS)μǫ FαβAγ [4, 5, 6]. LCS is not gauge invariant; it changes by a total derivative under a gauge transformation. However, the associated action is gauge invariant, and it generates a modified theory in which photons of different polarizations propagate at different speeds. The resulting birefringence has been searched for in the light from distant galaxies [6, 7, 8], but no such effect has been seen. This constrains kCS to effectively vanish. It is interesting to ask whether the Chern-Simons term may be generated as a radiative correction and, if so, whether the physical term’s effectively vanishing value can be reconciled with the possibility of nonzero Lorentz violation in other sectors of the theory. The relevant Lagrange density for studying these questions is [9] L = − 1 4 F Fμν + ψ̄(i6∂ −m− e6 A−6bγ5)ψ. (1) This theory has the potential to induce a finite radiatively-generated Chern-Simons term, with ∆kCS proportional to b. However, the coefficient of proportionality depends upon the regularization [10, 11, 12]. If the regulator used enforces the gauge invariance of the induced Lagrange density, then ∆kCS must necessarily vanish [13]; however, this is not particularly interesting, because it excludes the existence of a Chern-Simons term a priori. Other regulators lead to different values of ∆kCS, and through a suitable choice, any coefficient of proportionality between the two may be found. This ambiguity has been extensively studied, and several potentially interesting values of ∆kCS have been identified [11, 14, 15, 16, 17, 18]. Most notably, if the theory is defined nonperturbatively in b, then the ambiguity is lessened, and a single value appears to be preferred [10, 11, 14]. However, since this value is nonzero, there is a potential for conflict with the observed vanishing of kCS. We shall continue the analysis of the nonperturbatively-defined theory. While the induced Chern-Simons term itself has been extensively studied, the higher-order, CPT-even corrections to this theory have largely been neglected. In a nonperturbatively defined theory, the terms of all orders in b are tied together, and so information about the CPT-even terms may help clarify the structure of the CPT-odd Chern-Simons term. We have previously demonstrated [19] that the O(b) terms in the photon self-energy may violate the Ward identity that enforces the transversality of the vacuum polarization—pμΠ (p) = 0; however, our calculation was limited to the case of m = 0. We shall demonstrate here that the same result holds in the opposite limit, when |b| ≪ m (which represents the physical regime for all electrically charged elementary particles). This failure of transversality could represent a significant problem for the nonperturbative formulation of the theory. However, this difficulty may be overcome through the use of a Pauli-Villars regulator. Introducing such a regulator changes the nature of the ambiguity in the Chern-Simons term. When the Ward-identity-violating terms are eliminated, we are left with a theory |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/hep-th/0407172v1.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Arabic numeral 0 Biologic Preservation Birefringence CHPT1 wt Allele CPT (file format) Captopril Charge (electrical) Coefficient Electricity Elementary particle Keneth Alden Simons Notiospathius aff. pauli Jo728SB Photons QED (text editor) Rombellin Search - action Vanish (computer science) carnitine O-palmitoyltransferase activity |
| Content Type | Text |
| Resource Type | Article |
