Discover the Basics of Conformal Field Theory: An Introduction for Beginners

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Conformal Field Theory (CFT) is a type of field theory characterized by a conformal symmetry group, which preserves angles but not scales. This symmetry differs from the Poincare group and can be broken during the renormalization process, introducing a length scale known as an anomaly. In two dimensions, the conformal group becomes infinite dimensional, leading to unique properties and behaviors. For further understanding, it is recommended to consult "Conformal Field Theory" by Philippe Di Francesco, particularly chapter 4. Overall, CFT plays a significant role in theoretical physics, especially in quantum field theory contexts.
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Hi there,

Can anyone explain to me what Conformal Field Theory really is in brief summary? I do not mind if anyone wants to go into technical details as I have some basic knowledge of quantum field theory already.

Thank you
 
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I suggest you read "conformal field theory" by Philippe Di Francesco et al, chapter 4. :)

Conformal field theory is basically a field theory with a conformal symmetry group. This group can be seen as the group of all symmetries which only change scales, not angles. Ofcourse, this is another group then the Poincare group. However, as soon as you start to renormalize things this symmetry can be broken, because renormalization introduces a length scale; this is called an anomaly (a classical field theory which is broken as soon as you start to quantize things).

In two dimensions things become also interesting, because then the conformal group becomes infinite dimensional.
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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