Related papers: Gauge Fixing in the Chain by Chain Method
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…
The equivalence of the chain method and Hamilton-Jacobi formalism is demonstrated. The stabilization algorithm of Hamilton-Jacobi formalism is clariffied and two examples are presented in details.
We describe how geometrical methods can be applied to a system with explicitly time-dependent second-class constraints so as to cast it in Hamiltonian form on its physical phase space. Examples of particular interest are systems which…
We review the Dirac formalism for dealing with constraints in a canonical Hamiltonian formulation and discuss gauge freedom and display constraints for gauge theories in a general context. We introduce the Dirac bracket and show that it…
The gauge symmetries of a general dynamical system can be systematically obtained following either a Hamiltonean or a Lagrangean approach. In the former case, these symmetries are generated, according to Dirac's conjecture, by the first…
The way of finding all the constraints in the Hamiltonian formulation of singular (in particular, gauge) theories is called the Dirac procedure. The constraints are naturally classified according to the correspondig stages of this…
The Hamiltonian description for a wide class of mechanical systems, having local symmetry transformations depending on time derivatives of the gauge parameters of arbitrary order, is constructed. The Poisson brackets of the Hamiltonian and…
Recently, there were works claiming that path integral quantisation of gauge theories necessarily requires relaxation of Lagrangian constraints. As has also been noted in the literature, it is of course wrong since there perfectly exist…
The {\it {gauge - fixing} } and {\it gaugeless } methods for reducing the phase space in the generalized Hamiltonian dynamics are compared with the aim to define the class of admissible gauges . In the gaugeless approach, the reduced phase…
When a Hamiltonian system is subject to constraints which depend explicitly on time, difficulties can arise in attempting to reduce the system to its physical phase space. Specifically, it is non-trivial to restrict the system in such a way…
It is shown that when the gauge algebra is with root system the canonical Hamiltonian commutes with the constraints. Two other simple propositions concerning gauge fixing are proved too.
In a Hamiltonian system with first class constraints observables can be defined as elements of a quotient Poisson bracket algebra. In the gauge fixing method observables form a quotient Dirac bracket algebra. We show that these two algebras…
Gauge fixing is a useful tool to simplify calculations. It is also valuable to combine different methods, in particular lattice and continuum methods. However, beyond perturbation theory the Gribov-Singer ambiguity requires further gauge…
We describe in detail how to eliminate nonphysical degrees of freedom in the Lagrangian and Hamiltonian formulations of a constrained system. Two important and distinct steps in our method are the fixing of ambiguities in the dynamics and…
We look at and compare two different methods developed earlier for inducing gauge invariances in systems with second class constraints. These two methods, the Batalin-Fradkin method and the Gauge Unfixing method, are applied to a number of…
We present a pseudoclassical mechanics model which exhibits gauge symmetry and time-reparametrization invariance. As such, first- and second-class constraints restrict the phase space, and the Hamiltonian weakly vanishes. We show that the…
We describe an approach to fix the gauge degrees of freedom in tensor networks, including those with closed loops, which allows a canonical form for arbitrary tensor networks to be realized. Additionally, a measure for the internal…
A gauge independent method of obtaining the reduced space of constrained dynamical systems is discussed in a purely lagrangian formalism. Implications of gauge fixing are also considered.
Systems under holonomic constraints are classified within the generalized Hamiltonian framework as second-class constraints systems. We show that each system of point particles with holonomic constraints has a hidden gauge symmetry which…
We show that any theory with second class constraints may be cast into a gauge theory if one makes use of solutions of the constraints expressed in terms of the coordinates of the original phase space. We perform a Lagrangian path integral…