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5
votes
0answers
152 views

Functional integral aproach for Feynman rules

I am familiar with the basic ideas of quantum field theory but I feel uncomfortable when I have to derive Feynman rules by myself for a given action (for example in non-linear sigma models or ...
3
votes
0answers
96 views

Mode operators in the Virasoro algebra

This questions concerns Exercise 2.11 in Polchinski. We are asked to compute the commutator $$L_{m}(L_{-m}|0;0\rangle) - L_{-m}(L_{m} |0;0\rangle)$$ By plugging the mode expansions, we use the ...
3
votes
0answers
1k views

How to prove Wick's Theorem (Zee's eq. I.2 (16)) via Gaussian integration?

I'm working through Zee's QFT in a Nutshell but there's an integral [I.2 (16)] I couldn't quite derive. The problem is to find $$\langle x_i x_j ... x_k x_l\rangle=\frac{\int ... \int dx_1 ... dx_n ...
2
votes
0answers
149 views

Perturbation theory : quadratic external field

I'm trying to derive the explicit form of S-matrix of an interaction Hamiltonian $$H' = \frac{1}{2} \lambda \left[ \int d^3 x \rho({\vec x}) \phi({\vec x}, t)\right]^2\tag{1}$$ Even though the ...
1
vote
0answers
20 views

Correlator $bc$ system

I have da doubt with bc system. Polchinski says (2.5.10) $$ b(z)b(0)~=~O(z). \tag{2.5.10} $$ I tried to compute the correlation function With eom, using eq (2.5.6b) by Polchinki, removing the ...
1
vote
0answers
52 views

How to apply Wick's theorem in 2nd quantization for Spin Density Operators?

I am trying to work out a correlation function consisting of two spin density operators. Once I rewrite everything in 2nd quantized form, I am unsure of how to apply wicks theorem because the paul ...
1
vote
0answers
65 views

Wick theorem applying to partly ordered operator

I symbolize $T$ as the time-ordered operator and $::$ as normal order symbol. I know that in quantum field theory generally we have: $$T\phi_1(x_1)\dots\phi_n(x_n)=:\phi_1(x_1)\dots\phi_n(x_n):+A$$ ...
1
vote
0answers
107 views

Explicit evaluation of a radially ordered product

I am trying to understand the application of the operator product expansion to calculate the radially ordered product in the complex plain of $T_{zz}(z)\partial_w X^{\rho}(w)$ which should result in ...
0
votes
0answers
63 views

Calculation of OPE in Polchinski

Consider Exercise 2.8 in Polchinski's String Theory book. We are asked to compute the weight of $$f_{\mu \nu}:\partial X^{\mu} \bar{\partial}X^{\nu}e^{ik\cdot X}:$$ I have carried out the usual ...
0
votes
0answers
68 views

How to deal with coupled fermion boson operators?

I am a beginner in field theory and I have an exercise where I have a product of coupled fermion boson operators? $$ \hat{b_{l} }^{\dagger}\hat{c_{l^{'}} }^{\dagger}\hat{a_{q} }\hat{b_{l} ...