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How negative energy solution has positive energy in lab?

  1. Jul 28, 2013 #1
    In QFT equations, there are not only positive energy solutions, but negative ones as well.

    Dirac had the hole theory. But the sea may have infinite charges and gravity effects.
    And then QFT textbooks just explain the negative solution as anti-particle.

    But in the lab, we measure the energies of particle and anti-particle.
    Both have positive energies.

    So my question is, how to explain that
    anti-particle has negative energy eigen value,
    but in lab observed positive energy?

    If anti-matter had negative energy,
    particle-antiparticle annihilation
    will cancel each other's energies out
    as Energy+(-Energy)=0.
    But in fact we observed Energy+Energy=2 Energy(of gamma).

  2. jcsd
  3. Jul 28, 2013 #2


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    Staff: Mentor

    In QFT, both particles and antiparticles have positive energy. This solves the issue with Dirac's equation.
  4. Jul 28, 2013 #3


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    Science Advisor

    In the original interpretation of the Dirac equation as a single-particle wave equation, negative energy solutions did appear. Dirac's hole theory attempted to remedy this, but lasted only a year or two before it was shown to be inconsistent by Heisenberg.

    In QFT, Ψ is no longer a wavefunction, it's an annihilation operator. And its negative-frequency part is reinterpreted, not as annihilating a negative energy particle but as creating a positive energy antiparticle. The Hilbert space for QFT contains no negative energy states, only positive energy particles and positive energy antiparticles.
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