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Quantal foundation of the nucleon exchange transport theory
ABSTRACTS OF PAPERS TO APPEAR IN FUTURE ISSUES
245
of Minimal Replacement for the PoincarP Group. DOMINIC G. B. EDELEN. Center for the Application of Mathematics, Lehigh University, Bethlehem, Pennsylvania 18015.
The Geometry
The constructs of this paper rest on two elementary facts: (1) the Poincare group PI0 is the maximal group of isometries of Minkowski space-time M,; (2) P,, has a faithful matrix representation as a subgroup of GL(5, R) that maps an afBne set into itself. Local action of P,, and Yang-Mills minimal replacement are shown to induce a well-defined minimal replacement operator that maps the tensor algebra over M4 onto the tensor algebra over a new space-time U,. The natural frame and coframe fields of M4 go over into a canonical system of frame and coframe fields of U4 with both translation and Lorentz-rotation parts. The coframe fields define soldering l-form tields for U, that give rise to the standard geometric quantities through the Cartan equations of structure. This leads to unique determinations of all relevant connection coefficients and the associated 2-forms of curvature and torsion that involve the compensating l-forms for local action of both the translation and the Lorentz-rotation sectors. The metric tensor of U4, that is induced by the minimal replacement operator, is shown to satisfy the Ricci lemma; U, is necessarily a RiemannCartan space. This space admits gauge covariant constant basis fields for the Lie algebra of the Lorentz group and for the Dirac algebra. The induced basis for the Dirac algebra evaluates the images of Dirac operators under minimal replacement, while the induced basis for the Lie algebra of L(4, R) serves to show that the holonomy group of U, is the Lorentz group. The minimal replacement operator is extended to include the case of a total gauge group that is the direct product of the Poincare group and a Lie group of internal symmetries of matter fields. This provides a precise method of lifting any action integral of the matter fields from M, up to U, so that invariance properties are retained when the total group acts locally. The natural representations afforded by minimal replacement result in curvature being evaluated in terms of first order derivatives of the compensating fields that share many properties in common with the Dirac derivation algebra for spin fields. Direct interpretations of the compensating tields are obtained from the geodesic equations. Tensor Field in Superstring Theory. R. ROHM. Physics Department 45248, California Institute of Technology, Pasadena, California 91125; AND E. WITTEN. Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08544.
The Antisymmelric
We discuss various aspects of the role of the antisymmetric tensor field in superstring theory, including the quantization law obeyed by its field strength and its role in topological defects and in vacuum configurations. Foundation of the Nucleon Exchange Transport Theory. J. RANDRUP. Nordita, Blegdamsvej 11, DK-2100 Copenhagen 0, Denmark and Nuclear Science Division, Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720.
Quanta1
The central elements of the nucleon exchange transport theory are discussed within a fully quanta1 framework in order to elucidate the principal characteristics, validity, and limitations of the theory. Special consideration is given to the mean rate of energy dissipation and the penetrability coefficient.
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245
of Minimal Replacement for the PoincarP Group. DOMINIC G. B. EDELEN. Center for the Application of Mathematics, Lehigh University, Bethlehem, Pennsylvania 18015.
The Geometry
The constructs of this paper rest on two elementary facts: (1) the Poincare group PI0 is the maximal group of isometries of Minkowski space-time M,; (2) P,, has a faithful matrix representation as a subgroup of GL(5, R) that maps an afBne set into itself. Local action of P,, and Yang-Mills minimal replacement are shown to induce a well-defined minimal replacement operator that maps the tensor algebra over M4 onto the tensor algebra over a new space-time U,. The natural frame and coframe fields of M4 go over into a canonical system of frame and coframe fields of U4 with both translation and Lorentz-rotation parts. The coframe fields define soldering l-form tields for U, that give rise to the standard geometric quantities through the Cartan equations of structure. This leads to unique determinations of all relevant connection coefficients and the associated 2-forms of curvature and torsion that involve the compensating l-forms for local action of both the translation and the Lorentz-rotation sectors. The metric tensor of U4, that is induced by the minimal replacement operator, is shown to satisfy the Ricci lemma; U, is necessarily a RiemannCartan space. This space admits gauge covariant constant basis fields for the Lie algebra of the Lorentz group and for the Dirac algebra. The induced basis for the Dirac algebra evaluates the images of Dirac operators under minimal replacement, while the induced basis for the Lie algebra of L(4, R) serves to show that the holonomy group of U, is the Lorentz group. The minimal replacement operator is extended to include the case of a total gauge group that is the direct product of the Poincare group and a Lie group of internal symmetries of matter fields. This provides a precise method of lifting any action integral of the matter fields from M, up to U, so that invariance properties are retained when the total group acts locally. The natural representations afforded by minimal replacement result in curvature being evaluated in terms of first order derivatives of the compensating fields that share many properties in common with the Dirac derivation algebra for spin fields. Direct interpretations of the compensating tields are obtained from the geodesic equations. Tensor Field in Superstring Theory. R. ROHM. Physics Department 45248, California Institute of Technology, Pasadena, California 91125; AND E. WITTEN. Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08544.
The Antisymmelric
We discuss various aspects of the role of the antisymmetric tensor field in superstring theory, including the quantization law obeyed by its field strength and its role in topological defects and in vacuum configurations. Foundation of the Nucleon Exchange Transport Theory. J. RANDRUP. Nordita, Blegdamsvej 11, DK-2100 Copenhagen 0, Denmark and Nuclear Science Division, Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720.
Quanta1
The central elements of the nucleon exchange transport theory are discussed within a fully quanta1 framework in order to elucidate the principal characteristics, validity, and limitations of the theory. Special consideration is given to the mean rate of energy dissipation and the penetrability coefficient.
Primed
m Belgium