Vacuum in Quantum Field theory is not empty

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SUMMARY

The vacuum in Quantum Field Theory (QFT) is not an empty space but a dynamic system characterized by fluctuations and the potential for particle-antiparticle pair production. This process occurs due to the collision of energetic electromagnetic radiation, aligning with Einstein's energy-mass equivalence. The vacuum state, denoted as |0⟩, is a no-particle state, while physical particles are described by "dressed" states |vac⟩ and |one⟩, which are eigenstates of the Hamiltonian. Misconceptions about the vacuum being "nothing" stem from a misunderstanding of these concepts, as the vacuum is defined as the lowest energy state with non-vanishing average values for certain observables.

PREREQUISITES
  • Understanding of Quantum Field Theory (QFT) principles
  • Familiarity with particle-antiparticle pair production
  • Knowledge of the Heisenberg Uncertainty Principle
  • Basic grasp of Hamiltonian mechanics in quantum systems
NEXT STEPS
  • Explore the Casimir Effect and its implications in QFT
  • Study the role of the Heisenberg Uncertainty Principle in particle creation
  • Learn about the concept of "dressed" versus "bare" particles in QFT
  • Investigate the mathematical formulation of the Hamiltonian in quantum systems
USEFUL FOR

Physicists, quantum field theorists, and students of theoretical physics seeking to deepen their understanding of the nature of the vacuum and particle dynamics in Quantum Field Theory.

  • #31
Nick666 said:
Is space similar to an empty set in math ?

No. Space is like R^3 the set of all ordered triples of real numbers.
 
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  • #32
And the real numbers corespond to what?
 
  • #33
points in space.
 
  • #34
And the points corespond to ?
 
  • #35
Nick666 said:
And the points corespond to ?


In my opinion, we need to distinguish two things: "vacuum" and "position space".

Vacuum (or "empty space") is an example of a physical system from which all particles has been removed. It is simply a no-particle physical system. So, vacuum is somewhat analogous to the "empty set"

Position space is a linear 3-dimensional space R^3 which is a common set of eigenvalues of three commuting components of the position operator. Points in this space enumerate possible values that can be obtained by measuring the observable called "position". Position-space wavefunctions are defined on this space. This is an abstract space, similar to the momentum space or any other common set of eigenvalues of commuting operators in quantum mechanics.

Eugene.
 
Last edited:
  • #36
Nick666 said:
And the points corespond to ?

The ordered triples of real numbers.
 

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