Abstract
A systematic procedure is proposed for inclusion of Stueckelberg fields. The procedure begins with the involutive closure when the original Lagrangian equations are complemented by all the lower order consequences. The Stueckelberg field is introduced for every consequence included into the closure. The generators of the Stueckelberg gauge symmetry begin with the operators generating the closure of original system. These operators are not assumed to be a generators of gauge symmetry of any part of the original action, nor are they supposed to form an on shell integrable distribution. With the most general closure generators, the consistent gauge invariant theory is iteratively constructed, without obstructions at any stage. The Batalin–Vilkovisky form of inclusion of the Stueckelberg fields is worked out and the existence theorem for the Stueckelberg action is proven.
Highlights
In 1938, Stueckelberg proposed [1] to reformulate the Proca action for the massive vector field in a gauge invariant way by introducing the scalar field
Once the Stueckelberg fields are included as the parameters of gauge transformations of the invariant part of the action, their own gauge symmetry is defined as the composition of original gauge transformations
The Hamiltonian scheme of including Stueckelberg fields proceeds from involutive closure of variational equations, in particular the number of conversion variables coincides with the number of constraints
Summary
In 1938, Stueckelberg proposed [1] to reformulate the Proca action for the massive vector field in a gauge invariant way by introducing the scalar field. C (2021) 81:472 results in the gauge invariant theory of massive spin one with reducible gauge symmetry parameterized by antisymmetric tensor Another commonly used scheme of inclusion of Stueckelberg fields is the method of conversion of the Hamiltonian second class constrained systems into the first class ones. The Hamiltonian scheme of including Stueckelberg fields proceeds from involutive closure of variational equations, in particular the number of conversion variables coincides with the number of constraints. The second class constraints are unrelated, in general, to any integrable distribution, and the Hamiltonian conversion methods do not employ any predefined transformations of the original fields. The main subject of this article is to work out a method of inclusion the Stueckelberg fields which proceeds from the involutive closure of Lagrangian equations.
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