Gauge invariance in simple mechanical systems. (18th June 2015)

• Record Type: Journal Article
• Authors: Barbero G, J Fernando; Prieto, Jorge; J S Villaseñor, Eduardo
• Is Part Of: European journal of physics. Volume 36:Number 5(2015:Sep.)
• Publication Date: 2015-06-18
• Subjects: gauge symmetries -- Hamiltonian formulation -- singular mechanical models; Physics -- Periodicals; Physics -- Study and teaching (Higher) -- Europe -- Periodicals; 530
• DOI: 10.1088/0143-0807/36/5/055005
• Languages: English
• ISSNs: 0143-0807

Abstract

Abstract: This article discusses and explains the Hamiltonian formulation for a class of simple gauge invariant mechanical systems consisting of point masses and idealized rods. The study of these models may be helpful to advanced undergraduate or graduate students in theoretical physics to understand, in a familiar context, some concepts relevant to the study of classical and quantum field theories. We use a geometric approach to derive the Hamiltonian formulation for the model considered in the paper: four equal masses connected by six ideal rods. We obtain and discuss the meaning of several important elements, in particular, the constraints and the Hamiltonian vector fields that define the dynamics of the system, the constraint manifold, gauge symmetries, gauge orbits, gauge fixing, and the reduced phase space.