Covariant Schroedinger operator

JANYŠKA, Josef and Marco MODUGNO. Covariant Schroedinger operator. J. Phys. A: Math. Gen. UK: Institute of Physics Publishing, 2002, vol. 35, No 40, p. 8407-8434. ISSN 0305-4470.

Basic information

• Original name: Covariant Schroedinger operator
• Authors: JANYŠKA, Josef (203 Czech Republic, guarantor) and Marco MODUGNO (380 Italy).
• Edition: J. Phys. A: Math. Gen. UK, Institute of Physics Publishing, 2002, 0305-4470.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10101 Pure mathematics
• Country of publisher: United Kingdom of Great Britain and Northern Ireland
• Confidentiality degree: is not subject to a state or trade secret
• Impact factor: Impact factor: 1.406
• RIV identification code: RIV/00216224:14310/02:00006568
• Organization unit: Faculty of Science
• Keywords in English: Schoedinger operator; general covariance; quantum mechanics
• Tags: general covariance, quantum mechanics, Schoedinger operator

Abstract

We analyse the Schroedinger operator for a quantum scalar particle in a curved spacetime which is fibred over absolute time and is equipped with given spacelike metric, gravitational field and electromagnetic field. We approach the Schroedinger operator by three independent ways: in terms of covariant differentials induced by the quantum connection, via a quantum Lagrangian and directly by the only requirement of general covariance. In particular, in the flat case, our Schroedinger operator coincides with the standard one.

Links

• GA201/02/0225, research and development project: Name: Prodlužování geometrických struktur

Investor: Czech Science Foundation, Prolongation of geometric structures

• MSM 143100009, plan (intention): Name: Matematické struktury algebry a geometrie

Investor: Ministry of Education, Youth and Sports of the CR, Mathematical structures of algebra and geometry