All Questions
11
questions
1
vote
0
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72
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Calculating $\langle\hat{\phi_i}\rangle_t$ (Blundell's Quantum field theory) (EDITED) [closed]
I am reading Blundell's Quantum field theory for the Gifted Amateur and stuck at some calculation. In his book p.197, 21.2 Sources in statistical physics, he defined the partition function with the ...
- 323
4
votes
0
answers
189
views
Feynman Rules from Generating Functional
For the following Lagrangian:
$$\mathcal{L}= \overline \psi \left(i \gamma^{\mu}D_{\mu} - m \right)\psi -\frac{1}{2}\left(F_{\mu\nu}\right)^2,$$
I'm trying to find the Feynman rules. I know that the ...
- 1,213
1
vote
0
answers
352
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Complete the square for the generating functional of the Dirac field
Quote Peskin page 302 the Dirac generating function was
$$Z[\bar \eta ,\eta ]=\int D\bar\psi D\psi\exp[i\int dx^4 (\bar\psi (i\gamma^\mu\partial_\mu -m )\psi+\bar\eta \psi+\bar\psi \eta)]$$
could be ...
- 3,256
1
vote
3
answers
549
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Taking functional derivatives of generating functional
I'm learning how to compute functional derivatives of generating funtionals. Suppose I have the generating functional
$$Z[J] = \exp\left\{\int{dy_1 \; dz_1\; J(y_1) \Delta(y_1 - z_1) J(z_1)}\right\}.$$...
- 373
0
votes
1
answer
172
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Closed form of partition function in $0+0$-dimenional $\phi^4$ theory
The problem:
In one of McGreevy's excellent exercises in QFT, we are given the $0+0$ dimensional partition function
$$Z=\int_{-\infty}^{+\infty}dq\ e^{-S(q)}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (1)$$,
...
- 7,720
0
votes
0
answers
132
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Coupled quantum oscillator: Field theory
Consider two masses $m$ connected by a spring with a spring constant $k$. Each mass is also connected to the wall using the same springs. The Hamiltonian is
$$
H = \frac{p_1^2 + p_2^2}{2m} + \frac{k}{...
- 631
6
votes
2
answers
1k
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Correlation Function of One-Dimensional XY Model
From the Harvard lecture notes XY model: particle-vortex duality by Subir Sachdev, the path-integral of 1D XY-model is given by
$$\mathcal{Z}=\int\mathcal{D}\theta\exp{\left\{-\frac{K}{2}\int \!dx~(\...
- 2,923
1
vote
0
answers
431
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Connected Diagrams [duplicate]
The generating functional for the connected part of the Green functions is defined
as
$$iW[j] = \log Z[j].$$
From this the four-point connected Green's function is then given by
$G_c(x_1,x_2,x_3,...
- 445
2
votes
1
answer
612
views
Explicit calculation of the two-point function by path integrals
I need help carrying out the following calculation:
We have the generating functional of free theory:
$$Z[f] = \exp\left(\frac{i}{2} \int d^4xd^4y f(x)f(y)\Delta(x-y)\right) $$
where $f$ is an ...
- 184
1
vote
1
answer
1k
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Calculating the generating functional for the free scalar field explicitly by completing the square
I'm trying to reproduce the calculation resulting in equation (3.12) in the following script:
http://www.desy.de/~jlouis/Vorlesungen/QFTII11/QFTIIscript.pdf
The only difference is that in my notes, ...
- 2,835
1
vote
1
answer
112
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Where does this hyperbolic tangent in Nakahara's text come from?
I don't see why the term with $\tanh$ appears in the equation 1.164
The textbook is the second edition of Geometry, Topology and Physics
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