Electronic Resource
College Park, Md.
:
American Institute of Physics (AIP)
Journal of Mathematical Physics
27 (1986), S. 2282-2289
ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
Coherent states defined with respect to an irreducible ray representation u: g→ug, g∈G, of an arbitrary locally compact separable group G are examined. It is shown that the following conditions (a)–(d) are equivalent: (a) u admits coherent states, (b) u is square integrable, (c) the W*-system implemented by u is integrable, and (d) u is a subrepresentation of the left regular c-representation, where c is the respective multiplier of u. Furthermore, the group theoretical background of what is called the "P-representation of observables'' associated with coherent states is investigated: It is shown that the P-representation (which corresponds to a covariant semispectral measure) fulfills a certain maximality requirement. The P-representation can be used to represent the quantum system in question on the Hilbert space L2(G,dg) of square-integrable functions (with respect to Haar measure dg) on the kinematical group G.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.527000
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