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fxdung
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When we apply creation operator in vacuum we certainly have one particle,similarly for annihilation operator.Then what is stand for chance(probability) in QFT?
The Born rule doesn't only give the average number of particles but even more information, namely with which probability you find ##N## particles, ##N \in \mathbb{N}_0##. If you have an ##N##-particle Fock state, you find with probability 1 ##N## particles (with an idealized detector of course).atyy said:Probability in QFT is still given using the Born rule. You can use the number operator as the observable in the Born rule, eg. section 4.6 http://hitoshi.berkeley.edu/221b/QFT.pdf. When you use that in the Born rule, you get the average number of particles that will be measured for the state.
There is an analogous formalism in the simple harmonic oscillator.
https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2016/video-lectures/part-2/number-operator-and-commutators/
fxdung said:Can we know explicitly the form of /x1,x2,...xn> or /1p,2p,...,np> in QFT,then we can calculate the probability of that state?
fxdung said:Classical EM field equal expectation: <n_k/E/n_k>, here <n_k/=/0_k>+/1_k>+...
What is similar expression for static EM field?(Because it seems to me <n_k/ for static EM field were /0_k> so corresponding expectation were 0)
In quantum field theory (QFT), probability refers to the likelihood of a particular outcome or event occurring in a physical system. It is a fundamental concept that is used to describe the behavior of particles and their interactions.
In QFT, probability is calculated using mathematical equations known as probability amplitudes. These amplitudes take into account the wave-like nature of particles and their interactions, and allow for the calculation of the likelihood of a particular outcome.
In QFT, probability and uncertainty are closely related. The uncertainty principle states that it is impossible to know both the exact position and momentum of a particle at the same time. This uncertainty is reflected in the probabilistic nature of QFT, where the exact outcome of a particle's behavior cannot be predicted with certainty.
Yes, probability is a key tool in making predictions in QFT. By calculating the probability amplitudes for different outcomes, scientists can make predictions about the behavior of particles and their interactions in a given physical system. However, due to the probabilistic nature of QFT, these predictions can only be made with a certain degree of uncertainty.
In classical physics, probability is often seen as a measure of our lack of knowledge about a system. In QFT, however, probability is an inherent feature of the quantum world and is not simply a result of our limited understanding. Additionally, in classical physics, probabilities are typically calculated using statistical methods, whereas in QFT, they are calculated using mathematical equations and probability amplitudes.