# Acceleration in QFT

• I
• accdd

#### accdd

What is acceleration in QFT at the fundamental level?
What causes it?
Is it quantized?
Is there a connection between acceleration in QFT and the equivalence principle?

Delta2

What does "at a fundamental levbel" mean? What would be the answer to your question for ordinary QM?

protonsarecool, accdd and vanhees71
I understood that particles in QFT are quantized excitations of fields, each field has its own particle.
What happens when a particle accelerates? Why does it accelerate? For example, does an electron accelerate because it has been hit by a photon? By a discrete number of them? What is the relationship between acceleration and the equivalence principle?
In NRQM there are potentials and expected values of operators corresponding to observables, in QFT there is no wave function. What's going on?

Delta2
IYou seem to be thinking of "acceleration" meaning a funbction of a particle's trajectory when in has a well-determined position and velocity. It doesn't work like that even in orfinary QM, much less field theory.

protonsarecool and Delta2
I am not an expert in NRQM, I have only studied from Griffiths' book.
If we have a wave function of a particle, is the mean velocity of a large number of experiments prepared in the same way the derivative of the expected value of the wave function? Can we generalize this to acceleration? Where am I going wrong?
What happens in QFT?
Should I study more quantum mechanics before moving to QFT?

Where am I going wrong?
Trying to understand QFT before understanding QM.

If you want to talk about statistical properties of acceleration, not event by event, you will need to specify the condition and measurements much more precisely. Mathematically, if possible.

protonsarecool, accdd and vanhees71
Should I study more quantum mechanics before moving to QFT?
Yes. Especially the Ehrenfest theorem.

protonsarecool, Delta2, Lord Jestocost and 2 others
Is this reasoning correct or wrong?
In NRQM there is a state vector ## \ket \Psi## that has all the information about the system inside. Therefore, one cannot talk about position, velocity, acceleration, etc. The wave function is the state expressed in position basis, and its Fourier transform is the state expressed in momentum basis.
The expected value is the average value we get by repeating the experiment starting from the same initial conditions, and we can calculate them as follows: ##\braket{x}=\braket{\Psi|\hat x|\Psi}## and ##\braket{p}=\braket{\Psi|\hat p|\Psi}##, where ##\hat x## and ##\hat p## are operator associated with position and momentum.
If I want to get a quantity associated with acceleration, should I consider ##\frac{d\braket{p}}{dt}##?
By Ehrenfest's theorem this quantity is: ##\frac{d\braket{p}}{dt}=-\braket{\frac{\partial V}{\partial x}}##
Which under some conditions reproduces Newton's law $$F=ma$$ in classical mechanics.
Is this related to the concept of acceleration in NRQM or am I still getting it wrong?
What happens in QFT when a particle is accelerated?
I'm using a translator, sorry for mistakes.

Last edited:
vanhees71 and Delta2
Is this related to the concept of acceleration in NRQM ... ?
Yes. Another thing that I recommend you to study is NRQM in the Heisenberg picture, with that formalism acceleration in NRQM is even easier to understand.

What happens in QFT when a particle is accelerated?
If you formulate QFT in the Heisenberg picture, then acceleration in QFT is an easy generalization of acceleration in NRQM. See e.g. https://arxiv.org/abs/1605.04143 Eq. (10).

accdd
Really? Then define "acceleration" for a field!

Really? Then define "acceleration" for a field!
$$\frac{\partial^2\phi(x,t)}{\partial t^2}$$