Can a Lagrangian in QFT be Renormalizable?

In summary, the conversation discusses the concept of renormalizability in quantum field theory, specifically in relation to a term in the Lagrangian for a scalar field theory. It is mentioned that a term with a mass dimension greater than 5 is considered non-renormalizable, and that this is the case for gravity and the Fermi model of weak interactions. The speaker also notes that a coupling with negative mass dimension is not perturbatively renormalizable and instead requires an energy cutoff.
  • #1
Giuseppe Lacagnina
3
1
Possibly very silly question in QFT. Consider the Lagrangian for a scalar field theory.
A term like

g/φ^2

should be renormalizable on power counting arguments. The mass dimension of g should be

2 (D-1)

where D is the number of space-time dimensions.Does this make sense?
 
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  • #2
Isn't there a rule where if the mass dimension is greater than 5, the term is non-renormalizable?
2(D-1)=6, if D=4.
 
  • #3
As far as I know, a lagrangian term is not perturbatively renormalizable if it involves a coupling with negative mass dimension.
Like it happens for gravity or the Fermi model of weak interactions, which works as an effective theory with an energy cutoff.
 

Related to Can a Lagrangian in QFT be Renormalizable?

1. What is a Lagrangian in quantum field theory (QFT)?

A Lagrangian in QFT is a mathematical function that describes the dynamics of a quantum field. It encapsulates the interactions and behavior of particles in a quantum field theory.

2. What does it mean for a Lagrangian in QFT to be renormalizable?

In QFT, the term "renormalizable" refers to the ability of a Lagrangian to produce finite and meaningful results when calculating physical quantities. A renormalizable Lagrangian allows for the removal of infinities that arise in perturbative calculations, resulting in well-defined and predictive theories.

3. Why is it important for a Lagrangian in QFT to be renormalizable?

If a Lagrangian is not renormalizable, it means that the theory it describes is not well-defined and cannot make meaningful predictions. Renormalizability is an important criteria for a theory to be considered valid and useful in describing the physical world.

4. Can any Lagrangian in QFT be made renormalizable?

No, not all Lagrangians in QFT can be made renormalizable. Renormalizability is a property that some Lagrangians possess naturally, while others require additional modifications or "renormalization procedures" to achieve renormalizability.

5. How does the concept of renormalization tie into the overall understanding of quantum field theory?

Renormalization is a key concept in QFT, as it allows for the reconciliation of infinities that arise in perturbative calculations. It also provides a way to connect the microscopic description of particles and fields to the macroscopic world we observe. Without renormalization, many important predictions and calculations in QFT would not be possible.

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