Coset Decompositions of Space Groups: Applications to Domain Structure Analysis

Left- and double-coset decompositions of space groups are systematically analysed by putting the emphasis on the introduction of special auxiliary groups. An algorithm is tailored to exploit the specific structure of space groups. The new results are, amongst others, an efficient alternative method to determine for space groups minimal sets of double-coset representatives and a general formula that gives the structure and number of left cosets that are contained in double cosets. Left-coset and double-coset decompositions of space groups are exploited in domain structure analysis

PC software for crystallographic space groups and its application in symmetry analysis of domain structures

An integrated package of programs has been developed to investigate the structures and representations of crystallographic space groups. The programs, written in PASCAL and C, are made user friendly by additional programs using the Oakland C-scape Interface Management System. A Microsoft Windows version of the software is currently being developed using Borland Delphi. For a given phase transition the software identifies all domain states and finds inter alia (i) symmetry groups of all domain states in algebraic form as a conjugate subgroup stratum, (ii) all operations that transform a given domain state into another domain state, (iii) classes of crystallographically equivalent domain pairs, (iv) symmetry groups of ordered and unordered domain pairs. As an illustrative example software results for the triply commensurate charge-density-wave domain states in the 2H polytype TaSe 2 are presented

Non-Linear Canonical Transformations in Classical and Quantum Mechanics

$p$-Mechanics is a consistent physical theory which describes both classical and quantum mechanics simultaneously through the representation theory of the Heisenberg group. In this paper we describe how non-linear canonical transformations affect $p$-mechanical observables and states. Using this we show how canonical transformations change a quantum mechanical system. We seek an operator on the set of $p$-mechanical observables which corresponds to the classical canonical transformation. In order to do this we derive a set of integral equations which when solved will give us the coherent state expansion of this operator. The motivation for these integral equations comes from the work of Moshinsky and a variety of collaborators. We consider a number of examples and discuss the use of these equations for non-bijective transformations.Comment: The paper has been improved in light of a referee's report. The paper will appear in the Journal of Mathematical Physics. 24 pages, no figure

Equivalence of induced representations

Equivalence of induced representations for finite groups is considered in order to determine those equivalence classes of space group representations which are linked by complex conjugation