Hunting the ghosts of a ‘strictly quantum field’: the Klein–Gordon equation

Wavepackets representing relativistic quantum particles injected into a halfspace, from a source that is switched on at a definite time, are represented by superpositions of plane waves that must include negative frequencies. Propagation is causal: it is a consequence of analyticity that at time t no part of the wave has travelled farther than ct, corresponding to the front of the signal. Nevertheless, interference fringes behind the front travel superluminally. For Klein-Gordon and Dirac wavepackets, the spatially integrated density increases because current is injected at the boundary. Even in the simplest causal model, understanding the shape of the wave after long times is an instructive exercise in the asymptotics of integrals, illustrating several techniques at a level suitable for graduate students; different spatial features involve contributions from a pole and from two saddle points, the uniform asymptotics for the pole close to a saddle, and the coalescence of two saddles into the Sommerfeld precursor immediately behind the front.

Section: Klein-gordon Particlesmentioning

confidence: 99%

Causal wave propagation for relativistic massive particles: physical asymptotics in action

Berry

2012

“…Also without joining Teller's extreme position it is unquestionable that, in the transition between classical and quantum domains, something notable happens: classical images of the field in terms of continuous functions performable in space-time are seriously compromised since they are grounded on the idea of superposition of plane waves, each of them taken with its 'weight' factor (the coefficient representing the amplitude of each plane wave). Nevertheless, 2 An investigation of the problems raised by canonical quantization for teaching QFT at university level was developed in [6] by focusing on the Klein-Gordon equation. 3 The choice between Hilbert and Fock is related to the choice between a non-relativistic and relativistic quantum field theories.…”

Section: Conceptual Analysis: Problematic Aspectsmentioning

confidence: 99%

“…The mathematical tool of fiber bundles seems to be effective in removing such a 'dyscrasia': if, for example, a one-dimensional physical space is considered, a one-dimensional vectorial space can be linked to each point of the space (graphically, it corresponds to a series of lines that are perpendicular to the unique space dimension we are considering). What happens is that, as usual, for each point of the physical space, a vector representing the amplitude of the electric field is given but, by means of this representation, it is clear that the oscillation happens in the fiber space and not in the physical one 6 .…”

Section: Implications Of the Analysis For Teachingmentioning

confidence: 99%

What is what we call the ‘quantum field’? Answering from a teaching perspective by taking the foundations into account

Bertozzi¹

2013

Within physics education research a number of teaching proposals aimed at introducing elements of particle physics into secondary-school and introductory-university-level courses have been produced in recent years. Many of them face the problem of introducing the notion of the quantum field, which has a central role in contemporary physics. In this paper two representative examples are discussed; it is shown that both of them take the standard approach to introducing quantum field theory at university level (the ‘canonical quantization approach’) as their reference and that at the same time they introduce some ideas regarding quantum fields that are problematic when recent studies of the foundations of quantum field theory are taken into account. Starting from recent reformulations of quantum field theory, a different perspective to the notion of the quantum field is presented and a certain number of original insights that seem to be promising from a teaching perspective are emphasized.

“…In the third group reports discuss systems of coupled oscillators, like the one described in this report. These systems in their continuous limit are described by the Klein-Gordon equation, and are therefore sometimes called Klein-Gordon strings [14][15][16][17]. The reports discuss the use of the systems as classical analogies or visualisation tools for quantum phenomena related to the Klein-Gordon equation.…”

Section: Introductionmentioning

confidence: 99%

Propagation of polarised mechanical waves in an anisotropic medium

Faletič

Čepič

2018

During the propagation in an anisotropic medium, linearly polarized light in general becomes elliptically polarized. One can detect the polarization state of the transmitted light, but not the evolution of the polarization state during the propagation inside the material. We present a mechanical model where this evolution can be observed. The anisotropic medium is modelled by a series of coupled anisotropic oscillators. An oscillator consists of a bead hanging on an elastic string, and is coupled to neighbouring oscillators with stronger springs. When the system is excited in the plane perpendicular to the springs, the trajectories of the oscillating beads indicate the polarization state of the excitation at their respective positions. We analyze the model analytically, numerically and experimentally.