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Mon, 03 Apr 2000 00:00:00 +0200Mon, 03 Apr 2000 00:00:00 +0200BRST-Invariant Approach to Quantum Mechanical Tunneling
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/883
A new approach with BRST invariance is suggested to cure the degeneracy problem of ill defined path integrals in the path- integral calculation of quantum mechanical tunneling effects in which the problem arises due to the occurrence of zero modes. The Faddeev-Popov procedure is avoided and the integral over the zero mode is transformed in a systematic way into a well defined integral over instanton positions. No special procedure has to be adopted as in the Faddeev-Popov method in calculating the Jacobian of the transformation. The quantum mechanical tunneling for the Sine-Gordon potential is used as a test of the method and the width of the lowest energy band is obtained in exact agreement with that of WKB calculations.Jui-Qing Liang; H. J. W. Müller-Kirsten; F. Zimmerschied; Jiang-Ge Zhoupreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/883Mon, 03 Apr 2000 00:00:00 +0200A new look at the RST model
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/885
The RST model is augmented by the addition of a scalar field and a boundary term so that it is well-posed and local. Expressing the RST action in terms of the ADM formulation, the constraint structure can be analysed completely. It is shown that from the view point of local field theories, there exists a hidden dynamical field 1 in the RST model. Thanks to the presence of this hidden dynamical field, we can reconstruct the closed algebra of the constraints which guarantee the general invariance of the RST action. The resulting stress tensors TSigma Sigma are recovered to be true tensor quantities. Especially, the part of the stress tensors for the hidden dynamical field 1 gives the precise expression for tSigma . At the quantum level, the cancellation condition for the total central charge is reexamined. Finally, with the help of the hidden dynamical field 1, the fact that the semi-classical static soluti on of the RST model has two independent parameters (P,M), whereas for the classical CGHS model there is only one, can be explained.Jui-Qing Liang; H. J. W. Müller-Kirsten; F. Zimmerschied; Jiang-Ge Zhoupreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/885Mon, 03 Apr 2000 00:00:00 +0200Significance of zero modes in path-integral quantization of solitonic theories with BRST invariance
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/886
The significance of zero modes in the path-integral quantization of some solitonic models is investigated. In particular a Skyrme-like theory with topological vortices in (1 + 2) dimensions is studied, and with a BRST invariant gauge fixing a well defined transition amplitude is obtained in the one loop approximation. We also present an alternative method which does not necessitate evoking the time-dependence in the functional integral, but is equivalent to the original one in dealing with the quantization in the background of the static classical solution of the non-linear field equations. The considerations given here are particularly useful in - but also limited to -the one-loop approximation.Jui-Qing Liang; H. J. W. Müller-Kirsten; F. Zimmerschied; Jiang-Ge Zhou; D. H. Tchrakianapreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/886Mon, 03 Apr 2000 00:00:00 +0200