tom.stoer said:Just a second: there is a big difference between the 'x' in QM and the 'x' in QFT. 'x' in QM is an operator, whereas 'x' in QFT is a continuous index.
Even though it is true in the standard formulation of QFT, I think there is a way to reformulate QFT such that x becomes an operator just as in many-particle QM. See Sec. 3 oftom.stoer said:Just a second: there is a big difference between the 'x' in QM and the 'x' in QFT. 'x' in QM is an operator, whereas 'x' in QFT is a continuous index.
referframe said:I have read that, in QFT, unlike QM, there is no position probability density function because position is not considered an observable.
Then how is a position measurement represented/modeled in QFT?
As always, thanks in advance.
Position representation in QFT (Quantum Field Theory) is a mathematical framework used to describe the behavior of quantum particles in terms of position coordinates. It is based on the principles of quantum mechanics and special relativity, and allows for the calculation of probabilities of a particle's position at a given time.
In QFT, position is typically represented by a wave function, which describes the probability of finding a particle at a specific position in space. This wave function is a complex-valued function that varies over time, and can be used to calculate the expectation values of position and momentum for a particle.
Position representation in QFT is significant because it allows for the prediction and calculation of the behavior of quantum particles. It also allows for the study of interactions between particles and the effects of external forces on their motion.
Position representation differs from other representations in QFT, such as momentum representation, in that it focuses on the position coordinates of a particle rather than its momentum. It also takes into account the wave nature of particles, whereas other representations may not.
One limitation of position representation in QFT is that it does not take into account the uncertainty principle, which states that it is impossible to know both the exact position and momentum of a particle simultaneously. Additionally, it may not be applicable in certain scenarios, such as when dealing with particles that have no definite position, such as photons.