Time translation invariance and the vacuum state

Click For Summary
SUMMARY

The discussion clarifies that time translation invariance is neither necessary nor sufficient for the existence of a unique vacuum state in quantum field theory. It emphasizes that a vacuum state can be degenerate, even infinitely so, without violating time translation invariance. Conversely, a unique vacuum can exist despite violations of time translation invariance, depending on the specific Lagrangian employed. The relationship between time translation invariance and energy conservation is highlighted, indicating that without it, energy conservation is compromised, potentially altering the vacuum state over time.

PREREQUISITES
  • Understanding of quantum field theory concepts
  • Familiarity with Lagrangian mechanics
  • Knowledge of time translation invariance and its implications
  • Basic principles of energy conservation in physics
NEXT STEPS
  • Research the implications of Lagrangian formulations in quantum field theory
  • Study the role of symmetries in physics, particularly time and spatial translation invariance
  • Explore the concept of vacuum states in various quantum field theories
  • Investigate the relationship between conservation laws and symmetries in physics
USEFUL FOR

Physicists, particularly those specializing in quantum field theory, theoretical physicists exploring symmetries, and students seeking to understand the foundational principles of energy conservation and vacuum states.

Jim Kata
Messages
197
Reaction score
10
I kind of get the connection, but could someone elaborate the necessity for time translation invariance for the existence of a unique vacuum state.
 
Physics news on Phys.org
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.
 

Similar threads

Graduate Bubble nucleation and metastable vacuum
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Tunneling from a True Vacuum to a False One: Is it Possible for the Higgs Field?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Supplementary material for standard model
  • · Replies 11 ·
Replies
11
Views
2K
Graduate Show Lagrangian is invariant under a Lorentz transformation without using generators
  • · Replies 3 ·
Replies
3
Views
1K
High School How Does Quantum Turbulence Affect Plasma in a Tokamak?
  • · Replies 2 ·
Replies
2
Views
10K
Undergrad Translation-Invariant Operators on Lebesgue Spaces
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Is the 2-qubit singlet state invariant under bilateral projections?
  • · Replies 8 ·
Replies
8
Views
974
Undergrad Is Vacuum Decay from a False to True State Impossible or Just Unlikely?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Vacuum Transitions and Lorentz Symmetry Breaking
  • · Replies 8 ·
Replies
8
Views
2K
High School False Vacuum: Understanding its Impact on the Stability of the Universe
  • · Replies 6 ·
Replies
6
Views
2K