Gregor Wentzel
We review the life and remarkable contributions to Physics of Gregor Wentzel.
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arXiv subjects
Reinhard Oehme
Publications and source records attributed to Reinhard Oehme.
Superconvergence Relations
For a limited number of matter fields, the discontinuity of the transverse gauge field propagator can satisfy an exact sum rule. With controlled and limited gauge dependence, this supercconvergence relation is of physical interest.
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Superconvergence and Duality
Superconvergence relations for the transverse gauge field propagator can be used in order to show that the corresponding gauge quanta are not elements of the physical state space, as defined by the BRST algebra. With a given gauge group, these relations are valid for a limited region in the number of matter fields, indicating a phase transition at the boundary. In the case of SUSY gauge theories with matter fields in the fundamental representation, the results predicted by superconvergence can be compared directly with those obtained on the basis of duality and the conformal algebra. There is exact agreement.
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Reduction of Coupling Parameters in Quantum Field Theories
A concise survey is given of the general method of reduction in the number of coupling parameters. Theories with several independent couplings are related to a set of theories with a single coupling. The reduced theories may or may not have particular symmetries. A few have asymptotic power series expansions, others contain non-integer powers and/or logarithmic factors. An example is given with two power series solutions, one with N = 2 Supersymmetry, and one with no known symmetry. In a second example, the reduced Yukawa coupling of the superpotential in a dual magnetic supersymmetric gauge theory is uniquely given by the square of the magnetic gauge coupling with a known factor.
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Reduction of Coupling Parameters and Duality
The general method of the reduction in the number of coupling parameters is discussed. Using renormalization group invariance, theories with several independent couplings are related to a set of theories with a single coupling parameter. The reduced theories may have particular symmetries, or they may not be related to any known symmetry. The method is more general than the imposition of invariance properties. Usually, there are only a few reduced theories with an asymptotic power series expansion corresponding to a renormalizable Lagrangian. There also exist `general' solutions containing non-integer powers and sometimes logarithmic factors. As an example for the use of the reduction method, the dual magnetic theories associated with certain supersymmetric gauge theories are discussed. They have a superpotential with a Yukawa coupling parameter. This parameter is expressed as a function of the gauge coupling. Given some standard conditions, a unique, isolated power series solution of the reduction equations is obtained. After reparametrization, the Yukawa coupling is proportional to the square of the gauge coupling parameter. The coefficient is given explicitly in terms of the numbers of colors and flavors. `General' solutions with non-integer powers are also discussed. A brief list is given of other applications of the reduction method.
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Reduction of Dual Theories
In view of the presence of a superpotential, the dual of a gauge theory like SQCD contains two coupling parameters. The method of the Reduction of Couplings is used in order to express the parameter of the superpotential in terms of the dual gauge coupling. In the conformal window and above it, a unique, isolated solution is obtained. The coupling parameter of the superpotential is given simply by f times the square of the gauge coupling. Here f is a function of the the number of colors and the number of flavors, and it is known explicitly. The solution is valid to all orders in the asymptotic expansion, and it is the appropriate choice for the dual theory. The same solution exists in the free magnetic interval. A `general' solution with non-integer powers is discussed, as are some exceptional cases.
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Duality, Superconvergence and the Phases of Gauge Theories
Results about the phase structure of certain N=1 supersymmetric gauge theories, which have been obtained as a consequence of holomorphy and `electric-magnetic' duality, are shown to be in quantitative agreement with corresponding consequences of analyticity and superconvergence of the gauge field propagator. This connection is of interest, because the superconvergence arguments for confinement are not restricted to theories with supersymmetry. The method of reduction in the space of coupling parameters is used in order to define, beyond the matching conditions, an asymptotically free, dual magnetic theory involving Yukawa couplings.
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Asymptotic Limits and Sum Rules for the Quark Propagator
For the structure functions of the quark propagator, the asymptotic behavior is obtained for general, linear, covariant gauges, and in all directions of the complex $k^2$-plane. Asymptotic freedom is assumed. Corresponding previous results for the gauge field propagator are important in the derivation. Except for coefficients, the leading asymptotic terms are determined by one-loop or by two-loop information, and are gauge independent. Various sum rules are derived.
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Superconvergence, Confinement and Duality
Arguments for the confinement of transverse gauge field excitations, which are based upon superconvergence relations of the propagator, and upon the BRST algebra, are reviewed and applied to supersymmetric models. They are shown to be in agreement with recent results obtained as a consequence of holomorphy and duality in certain $N=1$ SUSY models. The significance of the one loop anomalous dimension of the gauge field in the Landau gauge is emphasized. For the models considered, it is shown to be proportional, with negative relative sign, to the one loop coefficient of the renormalization group function for the {\it dual map} of the original theory.
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Reduction of Coupling Parameters
The general theory of the reduction in the number of coupling parameters is discussed. The method involves renormalization group invariant relations between couplings. It is more general than the imposition of symmetries. There are reduced theories with no known symmetry. The reduction scheme is finding many applications. Discussed in some detail are the construction of gauge theories with ``minimal'' coupling for Yang-Mills and matter fields, and the Gauge-Yukawa Unification within N=1 supersymmetric GUT's.
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Dispersion Relations in Gauge Theories with Confinement
The analytic structure of {\it physical} amplitudes is considered for gauge theories with confinement of excitations corresponding to the elementary fields. Confinement is defined in terms of the BRST algebra. BRST-invariant, local, composite fields are introduced, which interpolate between physical asymptotic states. It is shown that the singularities of physical amplitudes are the same as in an effective theory with only physical fields. In particular, there are no structure singularities (anomalous thresholds) associated with confined constituents, like quarks and gluons. The old proofs of dispersion relations for hadronic amplitudes remain valid in QCD.
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Analytic Structure of Amplitudes in Gauge Theories with Confinement
For gauge theories with confinement, the analytic structure of amplitudes is explored. It is shown that the analytic properties of physical amplitudes are the same as those obtained on the basis of an effective theory involving only the composite, physical fields. The corresponding proofs of dispersion relations remain valid. Anomalous thresholds are considered. They are related to the composite structure of particles. It is shown, that there are no such thresholds in physical amplitudes which are associated with confined constituents, like quarks and gluons in QCD. Unphysical amplitudes are considered briefly, using propagator functions as an example. For general, covariant, linear gauges, it is shown that these functions must have singularities at finite, real points, which may be associated with confined states.
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Asymptotic Limits and Sum Rules for Gauge Field Propagators
For gauge field propagators, the asymptotic behavior is obtained in all directions of the complex $k^2$-plane, and for general, linear, covariant gauges. Asymptotically free theories are considered. Except for coefficients, the functional form of the leading asymptotic terms is gauge-independent. Exponents are determined exactly by one-loop expressions. Sum rules are derived, which generalize the superconvergence relations obtained in the Landau gauge. (To appear in Physics Letters B)
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On the Analytic Structure of Hadronic Amplitudes in QCD
Analytic properties of hadronic amplitudes are discussed within the framework of QCD as formulated on the basis of the BRST algebra. Local, composite fields are introduced for hadrons. Given confinement, it is shown that hadronic amplitudes have no thresholds or structure singularities (anomalous thresholds) which are directly related to the underlying quark-gluon structure. In contrast, general amplitudes of QCD must have singularities in channels with non-zero color quantum number, which can be related to unphysical states.
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Dispersion Relations in Quantum Chromodynamics
Dispersion relations for the scattering of hadrons are considered within the framework of Quantum Chromodynamics. It is argued that the original methods of proof remain applicable. The setting and the spectral conditions are provided by an appropriate use of the BRST cohomology. Confinement arguments are used in order to exclude quarks and gluons from the physical subspace. Local, BRST-invariant hadron fields are considered as leading terms in operator product expansions for products of fundamental fields. The hadronic amplitudes have neither ordinary nor anomalous thresholds which are directly associated with the underlying quark-gluon-structure. Proofs involving the Edge of the Wedge Theorem and analytic completion are discussed briefly.
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