We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 05 November 2011
Abstract
In this paper we show how to eliminate nonphysical degrees of freedom in both the Lagrangian and Hamiltonian formulations of a constrained system. The use of gauge fixing procedures is different in the two cases, but the final result is that the number of degrees of freedom in the two formulations agrees. The two key steps in our method are to use gauge fixing to eliminate ambiguities in the dynamics and to determine the inequivalent initial data. Applications to reparameterization invariant theories are briefly discussed.
Introduction
The degrees of freedom in either the Lagrangian or the Hamiltonian formulation of a singular system are reduced in two stages: reduction from using the natural constraints (with consistency requirements) and reduction through a gauge fixing procedure. In general the number of natural constraints in the Lagrangian formulation differs from the number in the Hamiltonian formulation [1]. In this paper we show how to determine the dynamics and fix the gauge in both formalisms. We believe the Lagrangian discussion is new and useful. The result includes a proof that the final number of degrees of freedom in the two formalisms is the same. Important parts of our methods are the two steps of determining the dynamics and determining the independent initial data.
In section 2 we develop a detailed version of the Hamiltonian gauge fixing procedure. In section 3 we study the Lagrangian gauge fixing procedure and show that the number of degrees of freedom in the Hamiltonian and Lagrangian formalisms are equal.
To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.
