Quick search Find article
Quick search
Find article

Symmetry representations in the rigged Hilbert space formulation of quantum mechanics

S Wickramasekara and A Bohm

Show affiliations


We discuss some basic properties of Lie group representations in rigged Hilbert spaces. In particular, we show that a differentiable representation in a rigged Hilbert space may be obtained as the projective limit of a family of continuous representations in a nested scale of Hilbert spaces. We also construct a couple of examples illustrative of the key features of group representations in rigged Hilbert spaces. Finally, we establish a simple criterion for the integrability of an operator Lie algebra in a rigged Hilbert space.


PACS

03.65.Fd Algebraic methods

02.30.Tb Operator theory

02.20.Sv Lie algebras of Lie groups

MSC

81R15 Operator algebra methods (See also 46Lxx, 81T05)

47A70 (Generalized) eigenfunction expansions; rigged Hilbert spaces

22E60 Lie algebras of Lie groups (For the algebraic theory of Lie algebras, see 17Bxx)

Subjects

Mathematical physics

Quantum information and quantum mechanics

Dates

Issue 3 (25 January 2002)

Received 29 March 2001, in final form 10 September 2001

Published 11 January 2002



  1. Symmetry representations in the rigged Hilbert space formulation of quantum mechanics

    S Wickramasekara and A Bohm 2002 J. Phys. A: Math. Gen. 35 807

  2. The relative effects of arterial curvature and lumen diameter on wall shear stress distributions in human right coronary arteries

    Barbara M Johnston and Peter R Johnston 2007 Phys. Med. Biol. 52 2531

  3. Calorimetric enthalpies for palladium - hydrogen (deuterium) systems at H(D) contents up to about [H]([D])/[Pd] = 0.86

    Y Sakamoto et al 1996 J. Phys.: Condens. Matter 8 3229

  4. A cone jet-finding algorithm for heavy-ion collisions at LHC energies

    S-L Blyth et al 2007 J. Phys. G: Nucl. Part. Phys. 34 271

  5. Magnetic field surfaces

    Bernard Jancewicz and Piotr Brzeski 2005 Eur. J. Phys. 26 617

  6. Zero temperature correlation functions for the impenetrable fermion gas

    Vadim V Cheianov and M B Zvonarev 2004 J. Phys. A: Math. Gen. 37 2261

  7. Plasma sources based on the propagation of electromagnetic surface waves

    M Moisan and Z Zakrzewski 1991 J. Phys. D: Appl. Phys. 24 1025

  8. Trace for the Loewner equation with singular forcing

    L P Kadanoff and M Kleine Berkenbusch 2005 Nonlinearity 18 937

  9. Krein space quantization in curved and flat spacetimes

    T Garidi et al 2005 J. Phys. A: Math. Gen. 38 245

  10. Theory of symmetry for a rotational relativistic Birkhoff system

    Luo Shao-Kai et al 2002 Chinese Phys. 11 429

Related review articles

What's this?
View review articles related to this research to gain an insight into the key trends in this subject area. Related review articles are selected based on PACS/MSC codes, and are no more than three years old.

  1. Integrable structure of box–ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
  2. Spectral problems in open quantum chaos
  3. Lectures on localization and matrix models in supersymmetric Chern–Simons-matter theories
More

View by subject




Export








Please login to access our web services, or create an account if you don't yet have one.

You must have cookies enabled in your web browser to be able to login.

Username
Password

Forgotten your password? Get a new one here.