Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Classical Physics
Quantum Physics
Quantum Interpretations
Special and General Relativity
Atomic and Condensed Matter
Nuclear and Particle Physics
Beyond the Standard Model
Cosmology
Astronomy and Astrophysics
Other Physics Topics
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Classical Physics
Quantum Physics
Quantum Interpretations
Special and General Relativity
Atomic and Condensed Matter
Nuclear and Particle Physics
Beyond the Standard Model
Cosmology
Astronomy and Astrophysics
Other Physics Topics
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Physics
High Energy, Nuclear, Particle Physics
Conformal symmetry, qed and qcd
Reply to thread
Message
[QUOTE="samalkhaiat, post: 6008496, member: 35381"] Any field theory with conserved symmetric and traceless energy-momentum tensor is conformally invariant. This happens in theories with no dimension-full parameters (coupling constants). However, in QFT’s, quantization introduce a scale (the UV-cut off) and coupling “constants” run with energy. This introduces a scale which breaks conformal symmetry. But, as it is always the case, classical symmetry casts a shadow on the quantum theory and, therefore, remains a powerful predictive tool. This happens even in ordinary QM: In atomic physics, we continue to label the states [itex]Y_{lm}(\theta , \phi)[/itex] by the eigen value [itex]l[/itex] of the [itex]SO(3)[/itex]-Casimir even though the spin-orbit coupling breaks rotational symmetry. To fully appreciate the predictive power of the conformal group in QFT’s you need to be familiar with RG and [itex]\beta[/itex]-function: the topology of RG flow is controlled by fixed points. Fixed points are those points in the (coupling parameter)-space that have vanishing [itex]\beta[/itex]-function. If [itex]\beta[/itex] is zero, clearly the coupling is a constant, i.e., it is scale invariant and does not change with energy scale. A fixed point [itex]g_{\ast}[/itex] of the RG, therefore, corresponds to a scale-invariant (and as far as we are currently understand, conformally-invariant) QFT. [/QUOTE]
Insert quotes…
Post reply
Forums
Physics
High Energy, Nuclear, Particle Physics
Conformal symmetry, qed and qcd
Back
Top