Full and partial gauge fixing

Abstract

Gauge fixing may be done in different ways. We show that using the chain structure to describe a constrained system, enables us to use either a perfect gauge, in which all gauged degrees of freedom are determined; or an imperfect gauge, in which some first class constraints remain as subsidiary conditions to be imposed on the solutions of the equations of motion. We also show that the number of constants of motion depends on the level in a constraint chain in which the gauge fixing condition is imposed. The relativistic point particle, electromagnetism and the Polyakov string are discussed as examples and perfect or imperfect gauges are distinguished.

Dynamical structure of fields in light cone coordinates

“…In contrast with the conventional coordinates where we deal with two coupled first order differential equations of motion, in light-cone coordinates we have only one differential equation. As we mentioned earlier, imposing the light-cone constraint (12), is equivalent to solving one equation of motion of ordinary coordinates. The original fields can be expanded in terms of the Schrödinger modes a( k, 0) as…”

Constraint structure and Hamiltonian treatment of Nappi-Witten model

“…Then they add up to give the above results. The algebra (13) shows that Ψ 1 (σ, τ ) and Ψ 2 (σ, τ ) are first class constraints. Moreover, from (8) we see that:…”

“…For a "complete gauge fixing" the number of independent gauge fixing conditions should be equal to the number of first class constraints [13]. In this way, we should suggest 5 gauge fixing conditions to fix the gauges generated by the constraints given in (12), and reach a "reduced phase space" of 4 field variables.…”

“…On the other hand, we are still left with the remaining gauges generated by Ψ 1 and Ψ 2 which generate the effect of reparametrization on the variables X a . In fact, since we have fixed the gauge from the middle of the constraint chains, the gauge is fixed partially in the language of reference [13]. In partial gauge fixing the Lagrange multipliers are determined while the variations generated by some of the gauge generators are not fixed.…”

Hamiltonian structure of three-dimensional gravity in Vielbein formalism

“…However, the canonical analysis may have more products. It is also well known that the gauge symmetries of a theory may be better understood in the algebraic structure of first class constraints of the system [13][14][15]. In this regard, there are not so many results in the literature on three dimensional gravity.…”