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Register a new userRadiation-reaction in classical offshell electrodynamics: I. The above mass-shell case
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Offshell electrodynamics based on a manifestly covariant off-shell relativistic dynamics of Stueckelberg, Horwitz and Piron, is five-dimensional. In this paper, we study the problem of radiation reaction of a particle in motion in this framework. In particular, the case of above-mass-shell is studied in detail, where the renormalization of the Lorentz force leads to a system of non-linear differential equations for 3 Lorentz scalars. The system is then solved numerically, where it is shown that the mass-shell deviation scalar $ve$ either smoothly falls down to 0 (this result provides a mechanism for the mass stability of the off-shell theory), or strongly diverges under more extreme conditions. In both cases, no runaway motion is observed. Stability analysis indicates that the system seems to have chaotic behavior in the divergent case. It is also shown that, although a motion under which the mass-shell deviation $ve$ is constant but not-zero, is indeed possible, but, it is unstable, and eventually it either decays to 0 or diverges.
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In previous paper derivations of the Green function have been given for 5D off-shell electrodynamics in the framework of the manifestly covariant relativistic dynamics of Stueckelberg (with invariant evolution parameter $tau$). In this paper, we reconcile these derivations resulting in different explicit forms, and relate our results to the conventional fundamental solutions of linear 5D wave equations published in the mathematical literature. We give physical arguments for the choice of the Green function retarded in the fifth variable $tau$.
The rotating reference system, two-point correlation functions, and energy density are used as the basis for investigating thermal effects observed by a detector rotating through random classical zero-point radiation. The RS consists of Frenet -Serret orthogonal tetrads where the rotating detector is at rest and has a constant acceleration vector. The CFs and the energy density at the rotating reference system should be periodic with rotation period because CF and energy density measurements is one of the tools the detector can use to justify the periodicity of its motion. The CFs have been calculated for both electromagnetic and massless scalar fields in two cases, with and without taking this periodicity into consideration. It turned out that only periodic CFs have some thermal features and particularly the Plancks factor with the temperature T= h w /k . Regarding to the energy density of both electromagnetic and massless scalar field it is shown that the detector rotating in the zero-point radiation observes not only this original zero-point radiation but, above that, also the radiation which would have been observed by an inertial detector in the thermal bath with the Planks spectrum at the temperature T. This effect is masked by factor 2/3(4 gamma^2-1) for the electromagnetic field and 2/9 (4 gamma ^2-1) for the massless scalar field, where the Lorentz factor gamma=(1 - v^2 / c^2)^(1/2). Appearance of these masking factors is connected with the fact that rotation is defined by two parameters, angular velocity w and the radius of rotation, in contrast with a uniformly accelerated linear motion which is defined by only one parameter, acceleration a. Our calculations involve classical point of view only and to the best of our knowledge these results have not been reported in quantum theory yet.
A non-existence theorem of classical electrodynamics in odd-dimensional spacetimes is shown to be invalid. The source of the error is pointed out, and is then demonstrated during the derivation of the fields generated by a uniformly moving point source.
The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a flat Riemannian metric tensor while the imaginary part represents a symplectic two-form. The immersion of classical manifolds in the complex projective space associated with the Hilbert space allows to pull-back tensor fields related to previous ones, via the immersion map. This makes available, on these selected manifolds of states, methods of usual Riemannian and symplectic geometry. Here we consider these pulled-back tensor fields when the immersed submanifold contains separable states or entangled states. Geometrical tensors are shown to encode some properties of these states. These results are not unrelated with criteria already available in the literature. We explicitly deal with some of these relations.
We deal with the reversible dynamics of coupled quantum and classical systems. Based on a recent proposal by the authors, we exploit the theory of hybrid quantum-classical wavefunctions to devise a closure model for the coupled dynamics in which both the quantum density matrix and the classical Liouville distribution retain their initial positive sign. In this way, the evolution allows identifying a classical and a quantum state in interaction at all times. After combining Koopmans Hilbert-space method in classical mechanics with van Hoves unitary representations in prequantum theory, the closure model is made available by the variational structure underlying a suitable wavefunction factorization. Also, we use Poisson reduction by symmetry to show that the hybrid model possesses a noncanonical Poisson structure that does not seem to have appeared before. As an example, this structure is specialized to the case of quantum two-level systems.
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