Lorentz Covariance and Matthews' Theorem for Derivative - Coupled Field Theories
Dec, 197436 pages
Published in:
- Phys.Rev.D 11 (1975) 848
Report number:
- Print-74-1656 (HARVARD)
Citations per year
Abstract: (APS)
The canonical quantization of scalar-field Lagrangians involving at most first derivatives of the fields ("first-order" Lagrangian) or second derivatives ("second-order") is discussed. A direct, but necessarily perturbative, quantization procedure for a general first-order Lagrangian is used to show that such theories yield a Lorentz-invariant S matrix to low orders of perturbation theory provided a covariant regularization scheme (e.g., dimensional or Pauli-Villars—but not a high-momentum cutoff) is employed. Matthews's theorem is verified in this context—the naive Feynman rules are valid. Second-order Lagrangians, quadratic in second but arbitrary in first derivatives, are shown to satisfy Matthews's theorem to all orders of perturbation theory and to be equivalent to first-order theories with Pauli-Villars regularization, thereby yielding a proof of Matthews's theorem for an arbitrary Pauli-Villars—regulated first-order theory. It is shown that for spectral reasons second- (and presumably, higher-) order theories are unacceptable physically. Finally, the canonical quantization of a second-order gauge theory is performed explicitly; the results show that (a) the naive Faddeev-Popov prescription remains valid in the presence of higher derivatives, and (b) the spectral pathology of second-order theories persists in gauge theories.- FIELD THEORY: GAUGE
- S-MATRIX
- PERTURBATION THEORY
- RENORMALIZATION
- INVARIANCE: LORENTZ
- ANALYTIC PROPERTIES
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