We show that the recently demonstrated absence of the usual discontinuity for massive spin 2 with a Λ term is an artifact of the tree approximation, and that the discontinuity reappears at one loop.
The DeWitt expansion of the matrix element M xy = x| exp −[ 1 2 (p − A) 2 + V ]t |y , (p = −i∂) in powers of t can be made in a number of ways. For x = y (the case of interest when doing one-loop calculations) numerous approaches have been employed to determine this expansion to very high order; when x = y (relevant for doing calculations beyond one-loop) there appear to be but two examples of performing the DeWitt expansion. In this paper we compute the off-diagonal elements of the DeWitt expansion coefficients using the Fock-Schwinger gauge. Our technique is based on representing M xy by a quantum mechanical path integral. We also generalize our method to the case of curved space, allowing us to determine the DeWitt expansion ofM xy = x| exp 1t|y by use of normal coordinates. By comparison with results for the DeWitt expansion of this matrix element obtained by the iterative solution of the diffusion equation, the relative merit of different approaches to the representation of M xy as a quantum mechanical path integral can be assessed. Furthermore, the exact dependence ofM xy on some geometric scalars can be determined. In two appendices, we discuss boundary effects in the one-dimensional quantum mechanical path integral, and the curved space generalization of the Fock-Schwinger gauge.
We consider several renormalizable, scale free models in three space-time dimensions which involve scalar and spinor fields. The Yukawa couplings are bilinear in both the spinor and scalar fields and the potential is of sixth order in the scalar field. In a model with a single scalar field and a complex Fermion field in three Euclidean dimensions, the couplings in the theory are both asymptotically free. This property is not retained in 2 + 1 dimensional Minkowski space, as we illustrate by considering a renormalizable scale-free supersymmetric model. This is on account of the different properties of the Dirac matrices in Euclidean and Minkowski space. We also examine a model in 2 + 1 dimensional Minkowski space in which two species of Fermions, associated with the two unitarily inequivalent representations of the 2 × 2 Dirac matrices, couple in two different ways to two distinct scalar fields. There are two types of Yukawa couplings in this model, and either one or the other of them can be asymptotically free (but not both simultaneously).
The standard formulation of a massive Abelian vector field in 2 + 1 dimensions involves a Maxwell kinetic term plus a Chern-Simons mass term; in its place we consider a Chern-Simons kinetic term plus a Stueckelberg mass term. In this latter model, we still have a massive vector field, but now the interaction with a charged spinor field is renormalizable (as opposed to superrenormalizable). By choosing an appropriate gauge-fixing term, the Stueckelberg auxiliary scalar field decouples from the vector field. The one-loop spinor self-energy is computed using operator regularization, a technique which respects the three-dimensional character of the antisymmetric tensor cap,. This method is used to evaluate the divergent part of the vector self-energy to two-loop order; it is found to vanish showing that the / 3 function is zero to two-loop order. The canonical structure of the model is examined using the Dirac constraint formalism.PACS number(s): ll.lO. Kk, ll.lO.Gh, 11.15.Bt
By considering N=2 superconformal algebra in d=2 dimensions, we construct an N=2 superconformal algebra in d=1 dimension. An N=1 superconformally invariant action for a particle is constructed. It is not what is obtained by dimensional reduction of the action for a superconformally invariant string.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.
Copyright © 2025 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.