Why is the vacuum normalised to 1?

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In summary, the conversation discusses the interpretation of the normalisation of states in quantum field theory, specifically in the example of the real scalar field. It is stated that <0|0>=1, which means that the probability of measuring the vacuum state is 1. It is questioned whether this implies that the probabilities of measuring all states add up to an infinite number, or if a probability greater than one corresponds to measuring multiple particles. It is then clarified that in regular quantum mechanics, the probability of measuring a state is not necessarily 1. The conversation ends with a realization that the confusion was a simple mistake.
  • #1
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I'm studying (relativistic) quantum field theory and have a very simple question. Take for example the real scalar field. My notes simply state that <0|0>=1 is a very natural normalisation. If I'm not mistaken, then this implies that the probability of measuring the vacuum state is 1. How is this to be interpreted? If the field has an infinite number of states then will the probabilities add up to an infinite number? Does a probability greater than one correspond to the measurement of more than one particle? I think not because multiple particles correspond to a single state.

Basically, I don't understand how the normalisation of states is to be interpreted in quantum field theory. Can anyone help?
 
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  • #2
<0|0>=1 means that measuring the state |0> will yield the state |0> with probability 1 which is quite intuitive no?

The probability of actually measuring the stat |0> on any arbitrary ket is <0|psi> which is not necessarily 1 no?

This is just based off my knowledge from regular QM. If something changes in QFT then, disregard what I'm saying...
 
  • #3
I'm pretty sure you're right and I was just being stupid. At first I was thinking "shouldn't the probability that you measure nothing (the vacuum) be 0?". You'd think with this being my 4th quantum mechanics course I would know this. Oh well.
 
  • #4
Don't worry, these little confusions happen to the best of us. =)
 

1. Why is the vacuum normalised to 1?

The vacuum is normalised to 1 in order to simplify calculations and measurements in quantum field theory. It is a convenient reference point to compare the energy levels of particles in a vacuum state.

2. What does normalising the vacuum to 1 mean?

Normalising the vacuum to 1 means setting the vacuum state as the baseline or reference point for energy levels in quantum field theory. This allows for easier comparison and analysis of energy levels of particles in a vacuum state.

3. How is the vacuum normalised to 1?

The vacuum is normalised to 1 by defining the vacuum state as the lowest possible energy state. This is done by setting the vacuum energy to 0 and all other energy levels are measured relative to this baseline.

4. What is the significance of normalising the vacuum to 1?

Normalising the vacuum to 1 is significant because it simplifies calculations and measurements in quantum field theory. It allows for a consistent reference point for energy levels, making it easier to compare and analyze different particles and their interactions.

5. Is normalising the vacuum to 1 a common practice in other areas of science?

Yes, normalising to a baseline or reference point is a common practice in many areas of science, including physics, chemistry, and engineering. It allows for easier comparison and analysis of data and helps to establish a standard for measurements.

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