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Volume 23, Issue 1
Displaying 1-8 of 8 articles from this issue
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J. H. Chabrowski1987 Volume 23 Issue 1 Pages 1-16
Published: 1987
Released on J-STAGE: January 22, 2009
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David Applebaum1987 Volume 23 Issue 1 Pages 17-56
Published: 1987
Released on J-STAGE: January 22, 2009
JOURNAL FREE ACCESSThe stochastic calculus constructed in [2] for fermion Brownian motion is augmented through the inclusion of stochastic integration with respect to the gauge process. The solutions of certain non-commutative stochastic differential equations are used to construct dilations of contraction semigroups on a Hilbert space frak{h}0 and of uniformly continuous, completely positive semigroups on B(frak{h}0). Finally we construct a fermion analogue of the classical Poisson process and investigate some of its properties.View full abstractDownload PDF (2850K) -
Akisato Kubo1987 Volume 23 Issue 1 Pages 57-100
Published: 1987
Released on J-STAGE: January 22, 2009
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Nobuyuki Tose1987 Volume 23 Issue 1 Pages 101-116
Published: 1987
Released on J-STAGE: January 22, 2009
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S. L. Woronowicz1987 Volume 23 Issue 1 Pages 117-181
Published: 1987
Released on J-STAGE: April 24, 2009
JOURNAL FREE ACCESSFor any number ν in the interval [−1, 1] a C*-algebra A generated by two elements α and γ satisfying simple (depending on ν) commutation relation is introduced and investigated.
If ν=1 then the algebra coincides with the algebra of all continuous functions on the group SU(2). Therefore one can introduce many notions related to the fact that SU(2) is a Lie group. In particular one can speak about convolution products, Haar measure, differential structure, cotangent boundle, left invariant differential forms, Lie brackets, infinitesimal shifts and Cartan Maurer formulae. One can also consider representations of SU(2).
For ν<1 the algebra A is no longer commutative, however the notions listed above are meaningful. Therefore A can be considered as the algebra of all “continuous functions” on a “pseudospace SνU(2)” and this pseudospace is endowed with a Lie group structure.
The potential applications to the quantum physics are indicated.View full abstractDownload PDF (5258K) -
Katsuhiro Komiya1987 Volume 23 Issue 1 Pages 183-194
Published: 1987
Released on J-STAGE: January 22, 2009
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Yoshifumi Ando1987 Volume 23 Issue 1 Pages 195-207
Published: 1987
Released on J-STAGE: April 24, 2009
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Kouyemon Iriye1987 Volume 23 Issue 1 Pages 209-213
Published: 1987
Released on J-STAGE: April 24, 2009
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