scholarly journals QUANTUM MECHANICALLY INDUCED WESS–ZUMINO TERM IN THE PRINCIPAL CHIRAL MODEL

1998 ◽  
Vol 13 (37) ◽  
pp. 3017-3024 ◽  
Author(s):  
HITOSHI MIYAZAKI ◽  
IZUMI TSUTSUI
Keyword(s):  
Configuration Space ◽  
Critical Value ◽  
Chiral Model ◽  
Quantum Level ◽  
Two Dimensional ◽  
Coupling Constant ◽  
Dirac Monopole ◽  
Principal Chiral Model

It is argued that in the two-dimensional principal chiral model, the Wess–Zumino term may be induced quantum mechanically in a manner analogous to the θ-term in QCD. Our argument is based on the fact that the configuration space of the model has a structure topologically identified as a sphere, and that the Dirac monopole potential, which is induced on the sphere by inequivalent quantizations, appears in the guise of the Wess–Zumino term. Our result suggests that, at the critical value λ2=8π/|k| of the coupling constant, the principal chiral model belongs to the same family of models with the Wess–Zumino–Novikov–Witten model at the quantum level.

Stability of the two-dimensional Brown–Ravenhall operator

2002 ◽  
Vol 132 (5) ◽  
pp. 1133-1144 ◽  
Author(s):  
A. Bouzouina
Keyword(s):  
Critical Value ◽  
Two Dimensional ◽  
Coupling Constant ◽  
Kato Inequality

We prove that the two-dimensional Brown–Ravenhall operator is bounded from below when the coupling constant is below a specified critical value—a property also referred to as stability. As a consequence, the operator is then self-adjoint. The proof is based on the strategy followed by Evans et al. and Lieb and Yau, with some relevant changes characteristic of the dimension. Our analysis also yields a sharp Kato inequality.

Stability of the two-dimensional Brown–Ravenhall operator

2002 ◽  
Vol 132 (5) ◽  
pp. 1133-1144 ◽  
Author(s):  
A. Bouzouina
Keyword(s):  
Critical Value ◽  
Two Dimensional ◽  
Coupling Constant ◽  
Kato Inequality

We prove that the two-dimensional Brown–Ravenhall operator is bounded from below when the coupling constant is below a specified critical value—a property also referred to as stability. As a consequence, the operator is then self-adjoint. The proof is based on the strategy followed by Evans et al. and Lieb and Yau, with some relevant changes characteristic of the dimension. Our analysis also yields a sharp Kato inequality.

The Impact of Geometric Variation on Compressor Two-Dimensional Incidence Range

2014 ◽  
Vol 137 (2) ◽  
Author(s):  
Martin N. Goodhand ◽  
Robert J. Miller ◽  
Hang W. Lung
Keyword(s):  
Design Process ◽  
Design Space ◽  
Leading Edge ◽  
Critical Value ◽  
Two Dimensional ◽  
Suction Surface ◽  
Design Intent ◽  
Manufacture Process ◽  
The Impact ◽  
Geometric Variation

An important question for a designer is how, in the design process, to deal with the small geometric variations which result from either the manufacture process or in-service deterioration. For some blade designs geometric variations will have little or no effect on the performance of a row of blades, while in others their effects can be significant. This paper shows that blade designs which are most sensitive are those which are susceptible to a distinct switch in the fluid mechanisms responsible for limiting blade performance. To demonstrate this principle, the sensitivity of compressor 2D incidence range to manufacture variations is considered. Only one switch in mechanisms was observed, the onset of flow separation at the leading edge. This switch is only sensitive to geometric variations around the leading edge, 0–3% of the suction surface. The consequence for these manufacture variations was a 10% reduction in the blade's positive incidence range. For this switch, the boundary in the design space is best defined in terms of the blade pressure distribution. Blade designs where the acceleration exceeds a critical value just downstream of the leading edge are shown to be robust to geometric variation. Two historic designs, supercritical blades and blades with sharp leading edges, though superior in design intent, are shown to sit outside this robust region and thus, in practice, perform worse. The improved understanding of the robust, region of the design space is then used to design a blade capable of a robust, 5% increase in operating incidence range.

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