Register to reply

How does interacting Lagrangian have form of product of fields?

by ndung200790
Tags: fields, form, interacting, lagrangian, product
Share this thread:
ndung200790
#1
Nov27-10, 10:16 PM
P: 520
Please teach me this problem:
It seem that following Haag's theorem there not exist quantized equation of motion for interacting fields.So I dont understand how to know the form of interacting Lagrangian has form of product of fields(example Lagrangian of Fermi field interacting with electromagnetic field).
Thank you very much for advance.
Phys.Org News Partner Physics news on Phys.org
On-chip topological light: First measurements of transmission and delay
A two-stage trap for single protons leads to measurement of their magnetic properties
Unexpected phenomenon discovered at the surface of a transition metal oxide material
strangerep
#2
Nov28-10, 01:39 AM
Sci Advisor
P: 1,910
Quote Quote by ndung200790 View Post
[...] I dont understand how to know the form of interacting Lagrangian has form of product of fields(example Lagrangian of Fermi field interacting with electromagnetic field).
It just comes from quantizing the classical theory.

It seem that following Haag's theorem there not exist quantized equation of motion
for interacting fields.
That's not quite what Haag's theorem says. The free representation and the interacting
representation are both constructed to be Poincare representations, but Haag's theorem
basically means you can't (rigorously, nonperturbatively) express the latter in terms of
the former. Getting around the manifestations of this is one of the reasons for
renormalization.
ndung200790
#3
Nov28-10, 09:17 PM
P: 520
So,how to derive phi-4 interacting Lagrangian and Yukawa interaction,because there are not coresponding classical theory.
Please give me a favour to explain again.
Thank you very much.

dextercioby
#4
Nov29-10, 09:45 AM
Sci Advisor
HW Helper
P: 11,896
How does interacting Lagrangian have form of product of fields?

There are some rules you should follow in the absence of gauge invariance when it comes to building interaction terms. One of this is locality, namely the power of the fields be finite. And then you can use the concept of relevance judged by whether the interacting theory is normalizable in 4D or not. By this judgement, we rule out the phi-3,5,6,.. theories in 4D either because they're not normalizable, or, if they are, they have no physical application so far. That's why we-re left with the phi-4 case which is normally thoroughly analyzed in the serious books.


Register to reply

Related Discussions
Equation of motion for interacting fields Advanced Physics Homework 2
Interacting Spins , Heisenberg Hamiltonian , Tensor product Atomic, Solid State, Comp. Physics 5
Basics of interacting fields Quantum Physics 14
Direct Product Basis for Interacting Systems Quantum Physics 6
Interacting magnetic fields Earth 3