MATHEMATICAL PROBLEMS OF RELATIVISTIC PHYSICS; WITH AN APPENDIX ON GROUP REPRESENTATIONS IN HILBERT SPACE. Volume 2

1963 ◽  
Author(s):  
Irving E. Segal ◽  
George W. Mackey
Keyword(s):  
Hilbert Space ◽  
Group Representations ◽  
Mathematical Problems ◽  
Space Volume

scholarly journals QUANTUM GROUP-TWISTED TENSOR PRODUCTS OF C*-ALGEBRAS

2014 ◽  
Vol 25 (02) ◽  
pp. 1450019 ◽  
Author(s):  
RALF MEYER ◽  
SUTANU ROY ◽  
STANISŁAW LECH WORONOWICZ
Keyword(s):  
Hilbert Space ◽  
Tensor Product ◽  
Quantum Group ◽  
Quantum Groups ◽  
Tensor Products ◽  
Group Representations ◽  
Basic Properties ◽  
C Algebras ◽  
Twisted Tensor Product

We put two C*-algebras together in a noncommutative tensor product using quantum group coactions on them and a bicharacter relating the two quantum groups that act. We describe this twisted tensor product in two equivalent ways, based on certain pairs of quantum group representations and based on covariant Hilbert space representations, respectively. We establish basic properties of the twisted tensor product and study some examples.

scholarly journals CLASSIFYING REPORTED AND "MISSING" RESONANCES ACCORDING TO THEIR P and C PROPERTIES

2000 ◽  
Vol 15 (10) ◽  
pp. 1435-1451 ◽  
Author(s):  
M. KIRCHBACH
Keyword(s):  
Hilbert Space ◽  
Spin States ◽  
Particle Data Group ◽  
Group Representations ◽  
Opposite Parity ◽  
Quantum Numbers ◽  
Lower Spin ◽  
Missing Resonances ◽  
Lorentz Group Representations ◽  
Data Group

The Hilbert space ℋ3q of the three quarks with one excited quark is decomposed into Lorentz group representations. It is shown that the quantum numbers of the reported and "missing" resonances fall apart and populate distinct representations that differ by their parity or/and charge conjugation properties. In this way, reported and "missing" resonances become distinguishable. For example, resonances from the full listing reported by the Particle Data Group are accommodated by Rarita–Schwinger (RS) type representations [Formula: see text] with k=1, 3, and 5, the highest spin states being J=3/2-, 7/2+, and 11/2+, respectively. In contrast to this, most of the "missing" resonances fall into the opposite parity RS fields of highest-spins 5/2-, 5/2+, and 9/2+, respectively. Rarita–Schwinger fields with physical resonances as lower-spin components can be treated as a whole without imposing auxiliary conditions on them. Such fields do not suffer the Velo–Zwanziger problem but propagate causally in the presence of electromagnetic fields. The pathologies associated with RS fields arise basically because of the attempt to use them to describe isolated spin-J=k+½ states, rather than multispin-parity clusters. The positions of the observed RS clusters and their spacing are well explained trough the interplay between the rotational-like [Formula: see text]-rule and a Balmer-like [Formula: see text]-behavior.

Quantization and Group Representations

1977 ◽  
Vol 29 (6) ◽  
pp. 1264-1276 ◽  
Author(s):  
R. Cressman
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Phase Space ◽  
Mechanical System ◽  
Correspondence Principle ◽  
Classical Mechanics ◽  
Quantum Mechanical ◽  
Group Representations ◽  
Additional Requirement ◽  
Adjoint Operators

A quantization of a fixed classical mechanical system is firstly an association between quantum mechanical observables (preferably self-adjoint operators on Hilbert space) and classical mechanical observables (i.e. real-valued functions on phase space). Secondly, a quantization should permit an interpretation of the correspondence principle that ‘classical mechanics is the limit of quantum mechanics as Planck's constant approaches zero'. With these two underlying precepts, Section 2 states the four basic requirements, I to IV, of a quantization along with an additional requirement V that characterizes the subclass of special quantizations.

Hilbert Space

1993 ◽  
Author(s):  
J. R. Retherford
Keyword(s):  
Hilbert Space
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