Le contenu de cette page n’est pas disponible en français. Veuillez nous en excuser.

The Klein Gordon field as a wave function: causality and localization

Playing this video requires the latest flash player from Adobe.

Download link (right click and 'save-as') for playing in VLC or other f4v compatible player.

Download Video

Recording Details

Scientific Areas: 
PIRSA Number: 


Usually in quantum field theory one considers two different interpretations:
1: The field is an infinite number of quantum oscillators, giving rise to a wave functional \Psi(\phi).
2: The positive frequency component of a field, \phi_+(x), is a wave function analogous to standard quantum mechanics.
While interpretation 2 is often only mentioned implicitly it is crucial to standard computations of measurable scattering probabilities.

We extend the interpretation of QFT as relativistic quantum mechanics (option 2) and show how the total Klein Gordon field which consists of positive and negative frequency contributions, \phi = \phi_+ + \phi_- , can be interpreted as a wave function. Our construction manifestly shows that signal propagation in QFT cannot exceed the speed of light. This follows from the replacement of the Feynman propagator by the Wheeler propagator, which is just the time ordered commutator. Our second observation is that interpretation 2 is not consistent if one uses the Newton Wigner position operator, therefore we introduce a more natural bilinear position operator. We show by an explicit example that the bilinear operator, contrary to the Newton Wigner operator, allows relativistic particles to be perfectly localized, precisely as in non relativistic quantum mechanics.