. . . "\"The\u00A0core of the project will lie in the analysis of the contradiction between the undeniable success of the description of quantum bound states using the so called PT-symmetric operators and an apparently complete failure of this fundamental approach in attempted applications to scattering. The expected\u00A0clarification of this puzzle will start from a consequent\u00A0reevaluation of\u00A0several methodical and mathematical\u00A0fundamentals in\u00A0our theoretical understanding of microscopic world. Not leaving the standard abstract postulates of Quantum Theory we shall concentrate upon their consequent, albeit less traditional interpretation. In it, several well known phenomenological models based on the use of non-Hermitian representations of observables will be re-interpreted,\u00A0\u00A0after a\u00A0suitable non-unitary Dyson's maping, as Hermitian\u00A0 in another space (in this sense their Hermiticity is \"\"hidden\"\", indeed). There will also be numerous applications worked out in the range covering\u00A0 SUSY or relativistic models\u00A0and even some unquantized systems (say, in MHD or cosmology). On the level of methods our approach will involve the structures and methods of linear algebra as well as computer-asssisted symbolic manipulations or complex and functional analysis.\""@en . . "825"^^ . . "0"^^ . "2011-01-01+01:00"^^ . "PT-symmetry; quantum mechanics and field theory; metric operators; solvable models; supersymmetry"@en . . "0"^^ . "2013-12-31+01:00"^^ . "Kryptohermitovsk\u00E9 pojet\u00ED kvantov\u00E9 teorie a jej\u00EDch aplikac\u00ED"@cs . . "825"^^ . . . . "1"^^ . . "The concept of cryptohermiticity in Quantum Theory and its applications"@en . "\"Hlavn\u00EDm p\u0159edm\u011Btem projektu bude naj\u00EDt \u0159e\u0161en\u00ED rozporu mezi nepopirateln\u00FDm \u00FAsp\u011Bchem popisu kvantov\u00FDch v\u00E1zan\u00FDch stav\u016F pomoc\u00ED tzv. PT symetrick\u00FDch oper\u00E1tor\u016F a zd\u00E1nliv\u011B naprost\u00FDm selh\u00E1v\u00E1n\u00EDm tohoto p\u0159\u00EDstupu p\u0159i pokusech o popis rozptylov\u00FDch experiment\u016F. Metodick\u00FDm v\u00FDchodiskem o\u010Dek\u00E1van\u00E9ho \u0159e\u0161en\u00ED bude d\u016Fsledn\u00E9 dopracov\u00E1n\u00ED teoretick\u00FDch a matematick\u00FDch z\u00E1klad\u016F kvantov\u00E9 teorie fyzik\u00E1ln\u00EDho mikrosv\u011Bta. Nehodl\u00E1me p\u0159itom vyj\u00EDt za r\u00E1mec standardn\u00EDch abstraktn\u00EDch postul\u00E1t\u016F kvantov\u00E9 teorie. Soust\u0159ed\u00EDme se pouze na jejich d\u016Fslednou, v\u00A0n\u011Bkter\u00FDch ohledech ov\u0161em pon\u011Bkud netradi\u010Dn\u00ED interpretaci, v\u00A0n\u00ED\u017E budou mnoh\u00E9 zn\u00E1m\u00E9 fenomenologick\u00E9 modely reprezentuj\u00EDc\u00ED pozorovateln\u00E9 veli\u010Diny pomoc\u00ED tzv. nesamosdru\u017Een\u00FDch oper\u00E1tor\u016F reinterpretov\u00E1ny (za pou\u017Eit\u00ED Dysonovy transformace) jako representace \"\"skryt\u011B\"\" (viz. \"\"krypto\"\" v\u00A0n\u00E1zvu projektu) samosdru\u017Een\u00E9. Aplikace budou vypracov\u00E1v\u00E1ny v rozsahu pokr\u00FDvaj\u00EDc\u00EDm nejen modely supersymetrick\u00E9\u00A0\u010Di relativistick\u00E9 ale p\u0159\u00EDpadn\u011B i kosmologick\u00E9 a magnetohydrodynamick\u00E9 (tj. fakticky nekvantovan\u00E9). V metodicko-matematick\u00E9 rovin\u011B se pokus\u00EDme o co nej\u0161ir\u0161\u00ED interdisciplin\u00E1rn\u00ED p\u0159\u00EDstup sahaj\u00EDc\u00ED od pou\u017Eit\u00ED struktur a metod line\u00E1rn\u00ED algebry a po\u010D\u00EDta\u010Dov\u00FDch symbolick\u00FDch manipulac\u00ED a\u017E po komplexn\u00ED a funkcion\u00E1ln\u00ED anal\u00FDzu.\u00A0\u00A0\""@cs . "17"^^ . . "17"^^ . .