The relativistic mechanics in a nonholonomic setting : a unified approach to particles with non-zero mass and massless particles

ROSSI, Olga and Jana MUSILOVÁ. The relativistic mechanics in a nonholonomic setting : a unified approach to particles with non-zero mass and massless particles. Journal of Physics A: Mathematical and Theoretical. Velká Británie: IOP Publishing, 2012, vol. 45, No 25, p. 1-27. ISSN 1751-8113. Available from: https://dx.doi.org/10.1088/1751-8113/45/25/255202.

Basic information

• Original name: The relativistic mechanics in a nonholonomic setting : a unified approach to particles with non-zero mass and massless particles
• Name in Czech: Neholonomní relativistická mechanika: jednotný přístup k částicím s nenulovou hmotností a nehmotným částicím
• Authors: ROSSI, Olga (203 Czech Republic) and Jana MUSILOVÁ (203 Czech Republic, guarantor, belonging to the institution).
• Edition: Journal of Physics A: Mathematical and Theoretical, Velká Británie, IOP Publishing, 2012, 1751-8113.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10301 Atomic, molecular and chemical physics
• 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: 1.766
• RIV identification code: RIV/00216224:14310/12:00057386
• Organization unit: Faculty of Science
• Doi: http://dx.doi.org/10.1088/1751-8113/45/25/255202
• UT WoS: 000305395200007
• Keywords (in Czech): Lagrangián; neholonomní vazby; redukované Chetaevovy rovnice; vazební síla; Lorentzova síla; Dickeho síla; tachyony; částice s nulovou hmotností
• Keywords in English: Lagrangian; nonholonomic constraint; reduced Chetaev equations; constraint force;Lorentz force; Dicke force; tachyons; particles with zero mass
• Tags: AKR, rivok
• Tags: International impact, Reviewed

Abstract

A new approach to relativistic mechanics is proposed, suitable to describe in a unified way dynamics of different kinds of relativistic particles. Mathematically it is an application of a geometric theory of nonholonomic systems on fibred manifolds. We propose a setting based on a naturally constructed Lagrangian and a constraint on the four-velocity of a particle that allows a unified approach to particles with any (positive/negative/zero) square of mass. The corresponding equations of motion are obtained and discussed. In particular, new forces are found (different from the usual Lorentz force type term), arising due to the nonholonomic constraint. A possible meaning and relation with forces previously proposed by Dicke is discussed. In particular, equations of motion of massless particles and of tachyons are studied and the corresponding dynamics are investigated.

Abstract (in Czech)

Nový přístup k relativistické mechanice, vhodný pro jednotný popis dynamiky různých typů relativistických částic. Metematicky se jedná o aplikaci geometrické teorie neholonomních systémů na fibrovaných varietách. Popis je založen na přirozeně konstruovaném Lagrangiánu a vazbě pro čtyřrychlost částice, což umožňuje jednotný přístup k částicím s libovolnou (kladnou/zápornou/nulovou) hmotností. Jsou odvozeny a diskutovány příslušné pohybové rovnice. Jsou nalezeny nové síly (odlišné od standardní síly Lorentzova typu), které jsou indukovány neholonomní vazbou. Je diskutována možná souvislost s tzv. Dickeho silou. Jsou studovány také pohybové rovnice pro nehmotné částice a tachyony.

Links

• GA201/09/0981, research and development project: Name: Globální analýza a geometrie fibrovaných prostorů

Investor: Czech Science Foundation, Global analysis and the geometry of fibred spaces