A question about Wick theorem?

In summary, the Wick theorem allows us to combine boson and fermion field operators in quantum field theory. However, in Feynman diagrams, we only consider propagators for boson, fermion, and ghost fields separately, and not for a combination of boson and fermion fields. This is because of the conservation of particle types. The commutator between boson and fermion field operators is zero, resulting in a zero propagator. This leads to the conservation law in quantum field theory.
  • #1
ndung200790
519
0
I think that Wick theorem permits us to contract boson field operator with fermion field operator(?).Because the commutator between fermion and boson field operators is like commutator between two boson field operators.Then why in Feynman diagrams do we only consider propagators of boson,fermion and ghost fields separately,but do not consider ''complex'' propagator of boson and fermion fields?.Is this because the conservation of of particle types.If it is,how can we deduce the conservation law from QFT?
 
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  • #2
Sorry,now I have found the question:the commutator between boson and fermion field operators is simply zero,so that the corresponding propagator is zero.
 

1. What is the Wick theorem?

The Wick theorem is a mathematical tool used in quantum field theory to simplify complicated calculations involving creation and annihilation operators. It allows us to express the expectation value of a product of operators in terms of the expectation values of individual operators.

2. When is the Wick theorem used?

The Wick theorem is used in quantum field theory whenever we need to calculate the expectation value of a product of operators. This often occurs when we are trying to determine the probability amplitude for a particular quantum process.

3. How does the Wick theorem work?

The Wick theorem works by splitting a product of operators into two parts: a normal-ordered part and a contraction part. The normal-ordered part contains all the terms where the creation operators come before the annihilation operators, while the contraction part contains all the terms where the creation and annihilation operators are paired together. The Wick theorem then tells us that the expectation value of the product of operators is equal to the expectation value of the normal-ordered part plus the sum of all the contractions.

4. What are the benefits of using the Wick theorem?

The Wick theorem simplifies complicated calculations in quantum field theory by breaking them down into smaller, more manageable parts. It also helps us to identify the most important contributions to the expectation value, making it easier to interpret the results.

5. Are there any limitations of the Wick theorem?

While the Wick theorem is a useful tool, it does have some limitations. It only applies to systems with a large number of particles, and it assumes that the system is in its ground state. Additionally, it does not work for all types of operators and can sometimes give incorrect results if not used correctly.

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