The problem of reduction of the wave packet of a relativistic charged particle by emission of a photon is studied with help of the path integral approach. A general expression for arbitrary order correlation function of the electromagnetic field is obtained. As a specific example an ultrarelativistic electron circulating in a storage ring is considered. It is shown that the longitudinal width of the electron wave packet defined by characteristic difference of time between registrations of two photons emitted by the electron is of the order of the wave length of the photons.
The problem of reduction of the wave packet of a relativistic charged particle by emission of a photon is studied with help of the path integral approach. A general expression for arbitrary order correlation function of the electromagnetic field is obtained. As a specific example an ultrarelativistic electron circulating in a storage ring is considered. It is shown that the longitudinal width of the electron wave packet defined by characteristic difference of time between registrations of two photons emitted by the electron is of the order of the wave length of the photons.
We consider the development of decoherence between the momentum components of a wave packet of a non relativistic charged particle interacting linearly with the electromagnetic field in equilibrium at temperature T. By adopting from the beginning the electric dipole approximation the Hamiltonian assumes a form analogous to the one used in the context of quantum computing for an ensemble of two level systems. We obtain the characteristic vacuum and thermal decoherence times and we show that decoherence between different momenta is due to the onset of a correlation between each momentum component and the associated transverse photons that are also responsible of mass renormalization.
In this paper we discuss some aspects of the theory of wave packets. We consider a popular noncovariant Gaussian model used in various applications and show that it predicts too slow a longitudinal dispersion rate for relativistic particles. We revise this approach by considering a covariant model of Gaussian wave packets, and examine our results by inspecting a wave packet of arbitrary form. A general formula for the time dependence of the dispersion of a wave packet of arbitrary form is found. Finally, we give a transparent interpretation of the disappearance of the wave function over time due to the dispersion—a feature often considered undesirable, but which is unavoidable for wave packets. We find, starting from simple examples, proceeding with their generalizations and finally by considering the continuity equation, that the integral over time of both the flux and probability densities are asymptotically proportional to the factor 1/| x | 2 in the rest frame of the wave packet, just as in the case of an ensemble of classical particles.
Interactions between charged particles and light occur in real space and time, yet quantum field theory usually describes them in momentum space. Whereas this approach is well suited for calculating emission probabilities and cross sections, it is insensitive to spatial and temporal phenomena such as, for instance, radiation formation, quantum coherence, and wave packet spreading. These effects are becoming increasingly important for experiments involving electrons, photons, atoms, and ions, particularly with the advent of attosecond spectroscopy and metrology. Here, we propose a general method for describing the emission of photons in phase space via a Wigner function. Several effects for Cherenkov radiation are predicted, absent in classical realm or in quantum theory in momentum space, such as a finite spreading time of the photon, finite duration of the flash and a quantum shift of the photon arrival time. The photon spreading time turns out to be negative near the Cherenkov angle, the flash duration is defined by the electron packet size, and the temporal shift can be both positive and negative. The characteristic time scales of these effects lie in the atto- and femtosecond ranges, thereby illustrating atomic origins of these macroscopic phenomena. The near-field distribution of the photon field resembles the electron packet shape, thus making ``snapshots'' of the emitter wave function. Our approach can easily be generalized to the other types of radiation and extended to scattering, decay, and annihilation processes, bringing tomographic methods of quantum optics to particle physics.
The quantum theory of radiation, formulated in wave-mechanical language but in terms of running waves, is shown to lead under suitable conditions to the classical theory of emission by a particle as a first approximation. Non-relativistic mechanics is used, and the limitations of the method are brought out in terms of classical theory. The characteristic quantum phenomenon of the Compton effect requires that the Compton recoil shall exceed the spread in momentum of the particle, and so that the wave-packet shall greatly exceed in diameter the wave-length of the incident radiation; this condition is realizable on any scale of magnitude. For quasi-classical motion just the reverse is required; furthermore, if the motion is to last for a number of waveperiods, the wave-length must greatly exceed mch (m=massoftheparticle). The classical packet-motion arises from combinations between quantum-states of the particle-field system; this fact suggests that the photon is not a fundamental constituent of the field but only one possible aspect of its action. The infinite "zero-energy" associated apparently even with the lowest energy-state of the field implies no electromagnetic field intensities at any point. Whereas for problems on energy or momentum it is customary to represent an incident wave-train by a single typical quantum state, to obtain motional phenomena of classical type a more complete expression such as that given in the paper must be used. The physically empty field likewise corresponds to a mixture of quantum states but without correlation among their amplitudes.
Spontaneous emission of a photon by an atom is described theoretically in three dimensions with the initial wave function of a finite-mass atom taken in the form of a finite-size wave packet. Recoil and wave-packet spreading are taken into account. The total atom-photon wave function is found in the momentum and coordinate representations as the solution of an initial-value problem. The atom-photon entanglement arising in such a process is shown to be closely related to the structure of atom and photon wave packets which can be measured in the coincidence and single-particle schemes of measurements. Two predicted effects, arising under the conditions of high entanglement, are anomalous narrowing of the coincidence wave packets and, under different conditions, anomalous broadening of the single-particle wave packets. Fundamental symmetry relations between the photon and atom single-particle and coincidence wave-packet widths are established. The relationship with the famous scenario of Einstein-Podolsky-Rosen is discussed.
Essentially, we solve the particle-field equations obtained in the matter distribution quantum mechanics. In the framework of this theory, a particle is described by a density amplitude function, we call wave function, as a packet of waves with the time dependent phases proportional to the relativistic Lagrangian. The mass quantization of such a particle, as a distribution of matter, is obtained from the equality of the spatial integral of the density with the mass as a characteristic of the relativistic dynamics of this matter. The particle dynamics, as a motion of a mass spatial distribution, is obtained from the equality of the wave propagation velocities with the distribution coordinate velocities. This description is a physical one, compared to the Schrödinger-Heisenberg description leading to unphysical results as a null velocity for the kinetic energy as a constant of motion, or Zitterbewegung. The description of a particle interaction with an electromagnetic field by additional Lagrangian terms, with a vector potential conjugated to coordinates, as in the Aharonov-Bohm effect, and an electric potential conjugated to time, leads to the Lorentz force, and the Maxwell equations. In the two conjugated spaces, of the coordinates and of the momentum, the dynamics of a quantum particle is described by propagation operators, depending on the coordinate-momentum product, applied to time dependent wave functions satisfying matter-field equations. Unlike the standard Schrödinger or Schrödinger-Dirac equations, depending only on the Hamiltonian operator, instead of the Hamiltonian these equations contain the Lagrangian, which, besides the Hamiltonian, include additional terms with an explicit dependence on velocity, as it is expected in a relativistic theory. We obtain the wave function of a particle-antiparticle system interacting with an electromagnetic field, as a wave packet of spinors propagating in space with finite dimensions, given by the finite definition domain of the density function, in the space of the matter-field momentum, as a constant of motion. We show that an electrically charged quantum particle, rotating in a central electric field, generates a vector potential with a magnetic field perpendicular to the rotational plane and an electric field in this plane. By a quantum transition, a photon is emitted in the particle rotational plane, with the magnetic field perpendicular to this plane, and the electric field contained in this plane. In this framework, the vector potential rotation is correlated to a particle momentum rotation, for the canonical matter-field momentum as a constant of motion, without any electromagnetic field radiated outside.