Conformal weights of the vertex operator

In summary, conformal weights are a measure of how a vertex operator behaves under conformal transformations and are calculated using the Virasoro algebra. They have physical significance as they correspond to the energy and momentum of a particle and determine scaling behavior. Negative conformal weights are possible and are related to other properties of a vertex operator, such as its conformal spin and scaling dimension.
  • #1
maverick280857
1,789
4
Hi,

I'm trying to prove that the conformal weight of the bosonic vertex operator [itex]:e^{ik\cdot X}:[/itex] is [itex]\left(\frac{\alpha'k^2}{4},\frac{\alpha'k^2}{4}\right)[/itex].

I've done some algebra but I think I am making some mistake with a factor of 2 somewhere because I get a 1/2 instead of a 1/4. My attempt is detailed in the attachment.

Can someone please tell me what is wrong here? Its probably a dumb thing, but I don't see it.

Thanks!
 

Attachments

  • Vertex Operator OPE.pdf
    340 KB · Views: 312
Physics news on Phys.org
  • #2
To the moderator: this should probably be moved to the "Beyond the Standard Model" subforum. Apologies for the inconvenience!
 

Related to Conformal weights of the vertex operator

What are conformal weights and why are they important?

Conformal weights are a way of measuring the transformation properties of a vertex operator under conformal transformations. They are important because they provide information about how a vertex operator behaves under different transformations, which is crucial in understanding the underlying structure of a quantum field theory.

How are conformal weights calculated?

Conformal weights are calculated by using the Virasoro algebra, which is a set of mathematical rules that describe how conformal transformations act on vertex operators. The conformal weight is then determined by the eigenvalue of a specific operator in the Virasoro algebra.

What is the physical significance of conformal weights?

Conformal weights have physical significance because they correspond to the energy and momentum of a particle in a quantum field theory. They also determine the scaling behavior of a vertex operator, which is important in studying the behavior of a quantum system at different length scales.

Can conformal weights be negative?

Yes, conformal weights can be negative. In fact, negative conformal weights are common in theories with complex or non-unitary representations. They can also arise when studying conformal field theories in higher dimensions.

How are conformal weights related to other properties of a vertex operator?

Conformal weights are related to other properties of a vertex operator, such as its conformal spin and scaling dimension. These properties are all interconnected and provide a complete description of how a vertex operator behaves under conformal transformations.

Similar threads

A Renormalisation of the Fermionic triangle loop
    • High Energy, Nuclear, Particle Physics
Replies
1
Views
1K
A Scalar decay to one-loop in Yukawa interaction
    • Quantum Physics
Replies
4
Views
1K
A The μ in dimensional regularization
    • High Energy, Nuclear, Particle Physics
Replies
4
Views
1K
I Scattering of a scalar particle and a Fermion
    • High Energy, Nuclear, Particle Physics
Replies
2
Views
2K
A Yang-Mills 3 boson Lagrangian term in Peskin and Schroeder
    • High Energy, Nuclear, Particle Physics
Replies
7
Views
2K
I Calculation of ideal ignition temperature for a D-T fusion reaction
    • High Energy, Nuclear, Particle Physics
Replies
3
Views
879
I Fourier Transform of Photon Emission Hamiltonian
    • Quantum Physics
Replies
4
Views
891
I Trig Manipulations I'm Not Getting
    • General Math
Replies
1
Views
418
A Creation and annihilation operator
    • Quantum Physics
Replies
3
Views
919
I Lindbladian Jump Operators Condition
    • Quantum Physics
Replies
0
Views
721

Hot Threads

Recent Insights

Back
Top