Related papers: Field Theory Methods in Classical Dynamics
A review is given of the canonical reduction of gauge and relativistic particle theories and of a new covariant rest-frame instant form of dynamics according to Dirac's theory of constraints
We perform a reduction from three to two spatial dimensions of the physics of a spin-1/2 fermion coupled to the electromagnetic field, by applying Hadamard's method of descent. We consider first the free case, in which motion is determined…
We give a detailed exposition of the formalism of Kinetic Field Theory (KFT) with emphasis on the perturbative determination of observables. KFT is a statistical non-equilibrium classical field theory based on the path integral formulation…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…
For a linear Dirac field on a globally hyperbolic static space-time the analytic continuation of its Wightman functions (Green functions) to Schwinger functions and back at zero and finite temperature is shown.
Geometric properties of operators of quantum Dirac constraints and physical observables are studied in semiclassical theory of generic constrained systems. The invariance transformations of the classical theory -- contact canonical…
We adopt a covariant formalism to derive exact evolution equations for nonlinear perturbations, in a universe dominated by two scalar fields. These scalar fields are characterized by non-canonical kinetic terms and an arbitrary field space…
The delta-N formalism is considered to calculate the evolution of the curvature perturbation in generalized multi-field inflation models. The result is consistent with the usual calculation of the standard kinetic term. For the calculation…
The dynamical equations which are basic for the description of the dynamics of quantum felds in arbitrary space--time geometries, can be derived from the requirements of a unique deterministic evolution of the quantum fields, the…
We apply the Dirac factorization method to the nonrelativistic harmonic oscillator and, more in general, to Hamiltonians with a generic potential. It is shown that this procedure naturally leads to a supersymmetric formulation of the…
Dirac particle dynamics is encoded as a unitary path summation rule and implemented on a qubit array, where the qubit array represents both spacetime and the fermions contained therein. The unitary path summation rule gives a quantum…
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
As a sequel to our previous work\cite{Feng2020}, we propose in this paper a quantization scheme for Dirac field in de Sitter spacetime. Our scheme is covariant under both general transformations and Lorentz transformations. We first present…
An equation, we call Dirac gamma-equation, is introduced with the help of the mathematical tools connected with the Clifford algebra. This equation can be considered as a generalization of the Dirac equation for the electron. Some features…
The formulation of a relativistic dynamical problem as a system of Hamilton equations by respecting the principles of Relativity is a delicate task, because in their classical form the Hamilton equations require the use of a time…
We provide an introduction to deformation quantisation and discuss the application of the formalism in solving the evolution problem for many-body systems in terms of semiclassical expansion. In any fixed order of expansion over the…
The ``time-evolution operator'' in mechanics is a powerful tool which can be geometrically defined as a vector field along the Legendre map. It has been extensively used by several authors for studying the structure and properties of the…
We review and compare different variational formulations for the Schr\"{o}dinger field. Some of them rely on the addition of a conveniently chosen total time derivative to the hermitic Lagrangian. Alternatively, the Dirac-Bergmann algorithm…
Scalar field systems containing higher derivatives are studied and quantized by Hamiltonian path integral formalism. A new point to previous quantization methods is that field functions and their derivatives with time are considered as…
An investigation of classical fields with fractional derivatives is presented using the fractional Hamiltonian formulation. The fractional Hamilton's equations are obtained for two classical field examples. The formulation presented and the…