Related papers: On The Quantization Of Constraint Systems: A Lagra…
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…
This work studies the spatial derivatives of decoupling fields to strongly coupled forward-backward stochastic differential equations in a Brownian setting. We formally deduce the backward dynamics of the first and higher spatial…
Application of the path-integral approach to continuous measurements leads to effective Lagrangians or Hamiltonians in which the effect of the measurement is taken into account through an imaginary term. We apply these considerations to…
We investigate the gravitational effect on Landau levels. We show that the familiar infinite Landau degeneracy of the energy levels of a quantum particle moving inside a uniform and constant magnetic field is removed by the interaction of…
The main goal of these lectures is to introduce and review the Hamiltonian formalism for classical constrained systems and in particular gauge theories. Emphasis is put on the relation between local symmetries and constraints and on the…
Proofs are given that the quantum-mechanical description of the LC -circuit with a time dependent external source can be readily established by starting from a more general discretization rule of the electric charge. For this purpose one…
In this paper we present a unified Lagrangian--Hamiltonian geometric formalism to describe time-dependent contact mechanical systems, based on the one first introduced by K. Kamimura and later formalized by R. Skinner and R. Rusk. This…
Quantum simulation is known to be capable of simulating certain dynamical systems in continuous time -- Schrodinger's equations being the most direct and well-known -- more efficiently than classical simulation. Any linear dynamical system…
We provide a detailed comparison of the different approaches available for the quantization of a totally constrained system with a constraint algebra generating the non-compact $SL(2,\mathbb{R})$ group. In particular, we consider three…
We analyze constrained superfields in supergravity. We investigate the consistency and solve all known constraints, presenting a new class that may have interesting applications in the construction of inflationary models. We provide the…
In the past, the possibility to employ (scalar) material reference systems in order to describe classical and quantum gravity directly in terms of gauge invariant (Dirac) observables has been emphasised frequently. This idea has been picked…
The effective approach to quantum dynamics allows a reformulation of the Dirac quantization procedure for constrained systems in terms of an infinite-dimensional constrained system of classical type. For semiclassical approximations, the…
We give a partial review of what is known so far on stability of periodically driven quantum systems versus regularity of the bounded driven force. In particular we emphasize the fact that unbounded degeneracies of the unperturbed…
The constrained Hamiltonian systems admitting no gauge conditions are considered. The methods to deal with such systems are discussed and developed. As a concrete application, the relationship between the Dirac and reduced phase space…
A generally covariant system can be deparametrized by means of an ``extrinsic'' time, provided that the metric has a conformal ``temporal'' Killing vector and the potential exhibits a suitable behavior with respect to it. The quantization…
A systematic way of generating sets of local boundary conditions on the gauge fields in a path integral is presented. These boundary conditions are suitable for one--loop effective action calculations on manifolds with boundary and for…
Problems involving rolling without slipping or no sideways skidding, to name a few, introduce velocity-dependent constraints that can be efficiently treated by the method of Lagrange multipliers in the Lagrangian formulation of the…
Recently proposed quantization in field theory based on an analogue of Hamiltonian formulation which treats space and time on equal footing (the so-called De Donder-Weyl theory) is applied to General Relativity in metric variables. We…
A variant of the usual Lagrangian scheme is developed which describes both the equations of motion and the variational equations of a system. The required (prolonged) Lagrangian is defined in an extended configuration space comprising both…
Controlled Lagrangian and matching techniques are developed for the stabilization of relative equilibria and equilibria of discrete mechanical systems with symmetry as well as broken symmetry. Interesting new phenomena arise in the…