- #1
Stevo
- 114
- 1
As I understand, QFT is formulated on a Minkowski background spacetime. This spacetime is not dynamical.
So, what a priori reason is there for formulating QFT on a flat background spacetime? Is it a question of empirical evidence? Or of mathematical utility? Or both, something else? I have heard/read that a transformation from one classical background spacetime to another does not necessarily correspond to a unitary transformation, and so we have inequivalent quantum theories. Is this true? Is there a restriction on what background spacetimes we are able to formulate our QFT on?
What is the predominant view of the ontology of this background spacetime in QFT? If there is a fixed inertial reference frame, then we are granting ontological significance to the spacetime and its individual points. This conflicts with general covariance. If the background spacetime was not fixed, or at least we could choose any reference frame from an equivalence class, in what sense could the background spacetime be regarded as not real, as a fictitious mathematical entity?
Edit:
If the background spacetime is regarded as real, is it regarded as a container space, in that it can be colocated with the dynamic objects of QFT? Ie: An object can be located at a spacetime point, but different spacetime points can not be located at the same spacetime point.
So, what a priori reason is there for formulating QFT on a flat background spacetime? Is it a question of empirical evidence? Or of mathematical utility? Or both, something else? I have heard/read that a transformation from one classical background spacetime to another does not necessarily correspond to a unitary transformation, and so we have inequivalent quantum theories. Is this true? Is there a restriction on what background spacetimes we are able to formulate our QFT on?
What is the predominant view of the ontology of this background spacetime in QFT? If there is a fixed inertial reference frame, then we are granting ontological significance to the spacetime and its individual points. This conflicts with general covariance. If the background spacetime was not fixed, or at least we could choose any reference frame from an equivalence class, in what sense could the background spacetime be regarded as not real, as a fictitious mathematical entity?
Edit:
If the background spacetime is regarded as real, is it regarded as a container space, in that it can be colocated with the dynamic objects of QFT? Ie: An object can be located at a spacetime point, but different spacetime points can not be located at the same spacetime point.
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