Mathematical analysis as required by a tachyonic observer
We rely on an analysis of initial states of the wave function associated with the simplest relativistic particle—the Weyl neutrino—to construct two series of representations of SL(2,R), or of the twofold cover of this group, by operators acting on scalar functions defined on the real line. The first one, which depends on a parameter p= 0, 1, …, contains the usual onedimensional metaplectic, or oscillator, representation. The second one, a series of representations no longer unitary but, for certain values of the parameter, pseudounitary with respect to some nondegenerate indefinite pseudoscalar product, is built in a comparable way, only exchanging the time coordinate with one of the spatial ones. The first series of representations was originally introduced in connection with automorphic pseudodifferential analysis; the second one is new, except for one value of the (continuous, in this case) parameter ρ, in which case it coincides with the recently introduced anaplectic representation. For each value of the parameter λ (=p or ρ), the basic operators Q and P from the usual Heisenberg pair give way to a new pair (Q, P{sub λ}) and to another analysis of functions on the real line, with as rich a collection of (most of themore »
 Authors:

^{[1]}
 Mathématiques, Université de Reims, Moulin de la Housse, B.P.1039, F51687 Reims Cedex 2 (France)
 Publication Date:
 OSTI Identifier:
 22217995
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Mathematical Physics; Journal Volume: 54; Journal Issue: 9; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COMPARATIVE EVALUATIONS; DIFFERENTIAL EQUATIONS; MINKOWSKI SPACE; NEUTRINOS; OSCILLATORS; RELATIVISTIC RANGE; SCALARS; SYMMETRY; TACHYONS; WAVE FUNCTIONS