vanhees71 said:Yes! I never understood why Srednicky deals with ##\phi^3## theory. It's totally useless and physically ill-defined to begin with. Otherwise it's a great book to learn the fundamentals of QFT.
The constraint for renormalizability is that your coupling constants have positive mass dimension, as you get from power counting. ##\phi^3## theory in 1+3 space-time dimensions is superrenormalizable in a formal sense, and you can do formal calculations within perturbation theory. However, it doesn't have a stable ground state and thus is flawed already in the very beginning.
vanhees71 said:Hm, just do QED ;-). Spinor QED is, in my opinion, the simplest theory to deal with. The only problem didactics wise is that it is a U(1) gauge theory and thus you need some more formalism to quantize it properly (best in terms of the path-integral formalism using Feynman-Faddeev-Popov techniques) before you can derive the Feynman rules, compared to a simple toy model like ##phi^4## theory. Also these toy model has its own right in terms of the linear O(N) ##\sigma## model, describing pions and ##\sigma## mesons, employing spontaneous symmetry breaking, etc.
vanhees71 said:The best books on the subject are
Weinberg, Quantum Theory of Fields, Cambridge University Press
However, that's not good as an introduction. My newest favorite is
M. D. Schwartz, Quantum Field Theory and the Standard Model, Cambridge University Press
I learned it during my Diploma Thesis from Ryder and Bailin&Love. The latter is particularly nice, concerning the path-integral formalism.
Srednicky is a good book too. I only don't like his engagement with ##\phi^3## theory. His strength in my opinion is the careful treatment of the LSZ reduction formalism. Of course, he also covers QED and also the entire Standard Model to some extent in Part III.
Dimensional analysis is a mathematical tool used in science to check the consistency of equations and to convert quantities from one unit to another. It involves examining the units of each variable in an equation to ensure that they are consistent and makes use of the fact that physical quantities can be expressed in terms of fundamental dimensions such as length, time, and mass.
Dimensional analysis is used in scientific research to aid in the development of new theories and models. It helps scientists to identify the key variables and their relationships in a system, and to determine the appropriate units for measuring these variables. It is also useful in identifying errors and inconsistencies in equations or experimental data.
A coupling constant is a numerical value that represents the strength of the interaction between two or more particles in a physical system. It is used in quantum field theory to describe the strength of the force between particles, such as the electromagnetic force or the strong nuclear force.
The coupling constant is often expressed in terms of fundamental dimensions, such as length, time, and mass. This allows scientists to use dimensional analysis to check the consistency of equations involving coupling constants and to convert them to different units. Dimensional analysis can also be used to derive relationships between different coupling constants in a system.
Yes, dimensional analysis and coupling constants can be applied to all branches of science. It is particularly useful in physics and chemistry, but can also be applied in biology, engineering, and other fields. Any system that involves physical quantities can benefit from the use of dimensional analysis and coupling constants to ensure consistency and accuracy in equations and measurements.