Related papers: Canonical formalism and quantization of perturbati…
The canonical structure of theories whose Lagrangian contains higher powers of time derivatives is often obscured by the nonlinear relationship between the velocities and momenta. We use the Dirac formalism and define a generalized Legendre…
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.
A modification of the canonical quantization procedure for systems with time-dependent second-class constraints is discussed and applied to the quantization of the relativistic particle in a plane wave. The time dependence of constraints…
It has been suggested that the chiral symmetry can be implemented only in classical Lagrangians containing higher covariant derivatives of odd order. Contrary to this belief, it is shown that one can construct an exactly soluble…
Shortcomings of Dirac's constrained analysis in the context of fourth order Pais-Uhlenbeck oscillator action and the appearance of badly affected phase-space Hamiltonian for a generalized fourth order oscillator action, following…
We review a perturbative approach to deal with Lagrangians with higher or infinite order time derivatives. It enables us to construct a consistent Poisson structure and Hamiltonian with only first time derivatives order by order in…
Time boundary terms usually added to action principles are systematically handled in the framework of Dirac's canonical analysis. The procedure begins with the introduction of the boundary term into the integral Hamiltonian action and then…
We consider the problem of constrained motion along a conic path under a given external potential function. The model is described as a second-class system capturing the behavior of a certain class of specific quantum field theories. By…
Different routes towards the canonical formulation of a classical theory result in different canonically equivalent Hamiltonians, while their quantum counterparts are related through appropriate unitary transformation. However, for…
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…
We present an approach to the canonical quantization of systems with equations of motion that are historically called non-Lagrangian equations. Our viewpoint of this problem is the following: despite the fact that a set of differential…
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 present a method for constructing a consistent low energy canonical formalism for higher order time-derivative theories, extending the Dirac method to include perturbative Hamiltonian constraints. We apply it to two paradigmatic…
We analyze the canonical treatment of classical constrained mechanical systems formulated with a discrete time. We prove that under very general conditions, it is possible to introduce nonsingular canonical transformations that preserve the…
We consider a class of Lagrangians that depend not only on some configurational variables and their first time derivatives, but also on second time derivatives, thereby leading to fourth-order evolution equations. The proposed higher-order…
One of the less well understood ambiguities of quantization is emphasized to result from the presence of higher-order time derivatives in the Lagrangians resulting in multiple-valued Hamiltonians. We explore certain classes of branched…
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…
The fractional quantization of singular systems with second order Lagrangian is examined. The fractional singular Lagrangian is presented. The equations of motion are written as total differential equations within fractional calculus. Also,…
We develop a Lagrangian approach for constructing a symplectic structure for singular systems. It gives a simple and unified framework for understanding the origin of the pathologies that appear in the Dirac-Bergmann formalism, and offers a…
The alternative version of Hamiltonian formalism for higher-derivative theories is proposed. As compared with the standard Ostrogradski approach it has the following advantages: (i) the Lagrangian, when expressed in terms of new variables…