Related papers: Path integral formulation of constrained systems w…
A canonical formalism for higher-derivative theories is presented on the basis of Dirac's method for constrained systems. It is shown that this formalism shares a path integral expression with Ostrogradski's canonical formalism.
The connection between the canonical and the path integral formulations of Einstein's gravitational field is discussed using the Hamilton - Jacobi method. Unlike conventional methods, it is shown that our path integral method leads to…
In this work we analyze systems described by Lagrangians with higher order derivatives in the context of the Hamilton-Jacobi formalism for first order actions. Two different approaches are studied here: the first one is analogous to the…
It is shown that the phase space path integral for a system with arbitrary second class constraints (primary, secondary ...) can be rewritten as a configuration space path integral of the exponent of the Lagrangian action with some local…
We consider the description of second-class constraints in a Lagrangian path integral associated with a higher-order $\Delta$-operator. Based on two conjugate higher-order $\Delta$-operators, we also propose a Lagrangian path integral with…
Path integral expressions for three canonical formalisms -- Ostrogradski's one, constrained one and generalized one -- of higher-derivative theories are given. For each fomalism we consider both nonsingular and singular cases. It is shown…
It is shown that the Dirac approach to Hamiltonization of singular theories can be slightly modified in such a way that primary Dirac constraints do not appear in the process. According to the modified scheme, Hamiltonian formulation of…
Path integral formulation based on the canonical method is discussed. Path integral for Yang-Mills theory is obtained by this procedure. It is shown that gauge fixing which is essential procedure to quantize singular systems by Faddeev's…
Constrained Hamiltonian systems are investigated by using the Hamilton-Jacobi method. Integration of a set of equations of motion and the action function is discussed. It is shown that we have two types of integrable systems: a) ${\it…
D-dimensional constrained systems are studied with stochastic Lagrangian and\break Hamiltonian. It is shown that stochastic consistency conditions are second class constraints and Lagrange multiplier fields can be determined in…
We develop a Hamilton-Jacobi theory for singular lagrangian systems using the Gotay-Nester-Hinds constraint algorithm. The procedure works even if the system has secondary constraints.
This work conducts a Hamilton-Jacobi analysis of classical dynamical systems with internal constraints. We examine four systems, all previously analyzed by David Brown: three with familiar components (point masses, springs, rods, ropes, and…
An equation is obtained to find the Lagrangian for a one-dimensional autonomous system. The continuity of the first derivative of its constant of motion is assumed. This equation is solved for a generic nonconservative autonomous system…
Hamiltonian systems with linearly dependent constraints (irregular systems), are classified according to their behavior in the vicinity of the constraint surface. For these systems, the standard Dirac procedure is not directly applicable.…
The Hamiltonian formulation for the mechanical systems with reparametrization-invariant Lagrangians, depending on the worldline external curvatures is given, which is based on the use of moving frame. A complete sets of constraints are…
We propose a method of quantization based on Hamilton-Jacobi theory in the presence of a random constraint due to the fluctuations of a set of hidden random variables. Given a Lagrangian, it reproduces the results of canonical quantization…
In this paper, the theory of the fractional singular Lagrangian systems is investigated with second order derivatives. The fractional quantization for these systems is examined using the WKB approximation. The Hamilton Jacobi treatment can…
One classical theory, as determined by an equation of motion or set of classical trajectories, can correspond to many unitarily {\em in}equivalent quantum theories upon canonical quantization. This arises from a remarkable ambiguity, not…
We give here a covariant definition of the path integral formalism for the Lagrangian, which leaves a freedom to choose anyone of many possible quantum systems that correspond to the same classical limit without adding new potential terms…
We consider a simple modification of standard phase-space path integrals and show that it leads in configuration space to Lagrangians depending also on accelerations.