content_image/367148.jpg content_image/367150.jpg content_image/367149.jpg content_image/367155.jpg content_image/367152.jpg content_image/367154.jpg content_image/367153.jpg content_image/367151.jpg
as before, defining the transformed fields by φ u = U $^{u}$η$^{u}$( 0 $_{1}$) , one gets (recall that the reference vector ( 0 $_{1}$) is chosen once and for all) 

<img src='content_image/367148.jpg'>

from which we deduce that under the action of the gauge group SU (2) one has 

Defining in the same way φ s = U $^{s}$η$^{s}$( 0 $_{1}$) one gets 

<img src='content_image/367150.jpg'>

<img src='content_image/367149.jpg'>

U s can be uniquely written as a product of U with an element of SU (2) : 

with 

Finally, under the action of the gauge group U (1) one has 

The field U ∈ SU (2) then supports the (commuting) actions of SU (2) and U (1) respec- tively by left multiplication and by right multiplication in SU (2) . Here U (1) is embedded (through s ) into SU (2) in the σ$_{3}$ -direction of the group SU (2) . 

̂ Using the new variables U and η in place of φ , a straightforward computation leads to 

where 

<img src='content_image/367155.jpg'>

<img src='content_image/367152.jpg'>

<img src='content_image/367154.jpg'>

<img src='content_image/367153.jpg'>

<img src='content_image/367151.jpg'>

