# Questions tagged [wick-theorem]

A combinatoric procedure in QFT of reducing arbitrary products of creation and annihilation operators to sums of products of pairs of these operators. A string of such operators is rewritten as the normal-ordered product of the string, plus the normal-ordered product after all single contractions among operator pairs, plus all double contractions, etc., plus all full contractions.

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### Wick's Theorem: Why is the vacuum expectation value of uncontracted operators zero?

I'm am right now reading Chapter 4.3 (Wick's Theorem) in Peskin & Schroeder. It is said that In the vacuum expectation value, any term in which there remain uncontracted operators gives zero (...
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### Feynman Propagator in Peskin & Schroeder

To prove Wick's Theorem, Peskin & Schroeder define the contraction of two fields: \begin{align} \text{Contract}[\phi(x)\phi(y)]\equiv \begin{cases} [\phi^+(x),\phi^-(y)] & \text{for }x^0>y^...
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I'm studying Quantum Field Theory and encountered Wick's theorem: for the real Klein Gordon field $\phi(x)$, one has $$T(\phi(x_1)\cdots\phi(x_n)) = N(\phi(x_1)\cdots\phi(x_n) + \text{ all possible ... 1answer 157 views ### Normal order vs Time order for fermions For a conformal field X, Polchinski gives a relation between the time ordering T (or equivalently the radial ordering {\cal R}) of a functional of identical fields and the normal ordering, which ... 2answers 823 views ### Symmetry factor via Wick's theorem Consider the lagrangian of the real scalar field given by$$\mathcal L = \frac{1}{2} (\partial \phi)^2 - \frac{1}{2} m^2 \phi^2 - \frac{\lambda}{4!} \phi^4$$Disregarding snail contributions, the ... 1answer 861 views ### Why is Wick contraction a c-number? It is mentioned in Fetter's Quantum Theory of Many-Particle Systems (in contraction part of section 8 Wick's Theorem), that: contractions are c numbers in the occupation-number Hilbert space, not ... 1answer 676 views ### Time-ordered product of two normal-ordered products of fields Suppose you have a scalar field theory with field operators \phi(x)=\phi(x)_+ + \phi(x)_-  that can be decomposed into terms of annihilation and destruction operators. Let$$ D(x-y) = <0|T(\phi(...
I think that general point of view about central charge in books is considering OPE $T(z) T(w)$ for different field theories and finding that general expression for the most singular term is about to ...