Steven Weinberg offers a way to explain inflation

[oldman]

In electromagnetism the operative running constant is alpha (approx. = 1/137) that relates charge to attraction and distance. Charge does not have to run, because alpha runs.

Thanks for this correction.

What I think is an intriguing question is what is meant by "fundamental".

It's not as simple an issue as some people may imagine. ...
So I can't answer your question about are there any really fundamental, not merely effective, physical theories. But glad you asked. Maybe someone else will put it into perspective for both of us.

I hope so. But I suspect that it depends on "times that are a-changing", as Bob Dylan once sang, so that any answer may not be final. Perhaps Newton's gravity was once viewed as quite fundamental. It still is in atyy's sense:

A fundamental theory is one that does not predict its own breakdown

Maybe a lifetime ago General Relativity was formulated as a fundamental theory of gravity. There seem to be doubts nowadays.

 

[marcus]

... any answer may not be final. Perhaps Newton's gravity was once viewed as quite fundamental. It still is in atyy's sense:

A fundamental theory is one that does not predict its own breakdown

Maybe a lifetime ago General Relativity was formulated as a fundamental theory of gravity. There seem to be doubts nowadays.

It begins to seem as if accurately predicting its own limitations ("effective" in Atyy's sense) is a VIRTUE to be appreciated in a theory.

General Relativity has its Penrose et al singularity theorems. The particle Standard Model has (correct me if I am wrong) Landau poles---blow-up points---which can be shifted around but not entirely avoided. Both theories illuminate their own limitations.

 

[DarMM]

Sorry, in message #150 reply to atyy, I should clear up what I meant by "Yes" in the first line. I meant yes Asymptotic freedom needs a critical point and no it cannot do with a limit cycle.

 

[atyy]

Sorry, in message #150 reply to atyy, I should clear up what I meant by "Yes" in the first line. I meant yes Asymptotic freedom needs a critical point and no it cannot do with a limit cycle.

Do theories with a limit cycle have a physical interpretation?

 

[DarMM]

Do theories with a limit cycle have a physical interpretation?

No, one needs a critical point to have a continuum limit. So a renormalization group flow which exhibits a limit cycle is simply another theory without a continuum limit. No different from a theory without a limit cycle which doesn't approach the critical point.

 

[atyy]

http://arxiv.org/abs/nucl-th/0303038
An Infrared Renormalization Group Limit Cycle in QCD
Eric Braaten (Ohio State U.), H.-W. Hammer

http://arxiv.org/abs/0803.2911
The impact of bound states on similarity renormalization group transformations
Stanislaw D. Glazek, Robert J. Perry

 

[DarMM]

http://arxiv.org/abs/nucl-th/0303038
An Infrared Renormalization Group Limit Cycle in QCD
Eric Braaten (Ohio State U.), H.-W. Hammer

http://arxiv.org/abs/0803.2911
The impact of bound states on similarity renormalization group transformations
Stanislaw D. Glazek, Robert J. Perry

The second paper is not related to field theory, so I'll only talk about the first.
The paper is concerned with the infrared behaviour of the theory, in that specific case I'm not familiar with the meaning of limit cycles.
However asymptotic safety is related to the ultraviolet behaviour of a field theory and obtaining a continuum limit. For this you need a critical point, a limit cycle would not do, as it wouldn't provide a diverging lattice correlation. So for the ultraviolet the theory cannot make do with a limit cycle.

However maybe I haven't understood what you are asking, providing the links on their own without commentary doesn't indicate what you are trying to say.

 

[atyy]

But don't we just need all the couplings to be finite for arbitrary energies?