Time translation invariance and the vacuum state

  • Thread starter Jim Kata
  • Start date
191
6

Main Question or Discussion Point

I kind of get the connection, but could someone elaborate the necessity for time translation invariance for the existence of a unique vacuum state.
 

Answers and Replies

76
5
Time translation invariance is neither necessary nor sufficient for the existence of a unique vacuum state. The vacuum state can be degenerate (in fact infinite-fold degenerate) without breaking the time-translation invariance. Conversely, if you violate time translations, you can still have a unique vacuum, depending on what the Lagrangian is.

The time translation invariance is directly related to energy conservation. Just like the spatial translation invariance is related to the momentum conservation. Without time translation invariance, the energy is not conserved. Therefore, even if you have a unique vacuum, its energy will not be conserved if the time translation invariance does not hold. In fact the vacuum at t=0 may not be the vacuum state any more at a later time.
 

Related Threads for: Time translation invariance and the vacuum state

  • Last Post
Replies
8
Views
2K
Replies
1
Views
502
Replies
9
Views
2K
Replies
1
Views
495
Replies
7
Views
3K
Replies
1
Views
646
  • Last Post
2
Replies
35
Views
6K
  • Last Post
Replies
2
Views
2K
Top