6
votes
2answers
163 views

Decoupling of Holomorphic and Anti-holomorphic parts in 2D CFT

This maybe a very naive question. I have just started studying CFT, and I am confused by why we have two separate parts of everything in CFT (operator algebras and hilbert space), the holomorphic ...
6
votes
1answer
89 views

A question about a complex integration in Peskin's QFT textbook

In page 27 (2.52), the integration is $$\int_{-\infty}^{\infty}dp \frac{p e^{ipr}}{\sqrt{p^2+m^2}}$$ He says that there are two branch cuts starting from $\pm im$ But I learn in complex analysis ...
5
votes
2answers
114 views

Can we treat $\psi^{c}$ as a field independent from $\psi$?

When we derive the Dirac equation from the Lagrangian, $$ \mathcal{L}=\overline{\psi}i\gamma^{\mu}\partial_{\mu}\psi-m\overline{\psi}\psi, $$ we assume $\psi$ and ...
16
votes
2answers
632 views

Why treat complex scalar field and its complex conjugate as two different fields?

I am new to QFT, so I may have some of the terminology incorrect. Many QFT books provide an example of deriving equations of motion for various free theories. One example is for a complex scalar ...
3
votes
2answers
394 views

Global phase symmetry for complex scalar field theory

I have started to study QFT. And I have some difficulties in such classical situation. Suppose i want to calculate $\frac{\partial \mathcal{L}}{\partial (\partial_\mu \phi)}\phi$ for lagrangian ...
1
vote
1answer
68 views

Nonequilibrium themal QFT

Wick rotation to thermal of QFT in Minkowski space to thermal QFT, which is after this transformation analogue to statistical mechanics, does only describe equilibrium statistical mechanics. On page ...
6
votes
2answers
314 views

Complex coordinates in CFT

The Setup: Let's say we want to study a Euclidean $\mathrm{CFT}_2$ on $\mathbb R^2$ with coordinates $\sigma^1$ and $\sigma^2$ and metric $ds^2 = (d\sigma^1)^2+(d\sigma^2)^2$. It seems to me that ...
2
votes
1answer
192 views

Why can you re-write the functional measure of a real-valued field $\phi(x)$ as $\mathcal{D}\phi=\prod_{k_n^0>0}dRe \phi(k_n) d Im \phi(k_n)$?

This happens in Peskin and Schroeder, An Introduction to QFT, on page 285. They set out to calculate correlation functions for the free real-valued Klein-Gordon field $\phi(x)\in \mathbb{R}$. They ...