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I would like to know how is it expressed antiparticles' energy. According to Tipler-Mosca's Modern Physics,

Spin-$\frac{1}{2}$ particles are described by the Dirac equation, which is an extension of the Schrödinger equation that includes special relativity. One feature of Paul Dirac’s theory, proposed in 1927, is the prediction of the existence of antiparticles. In special relativity, the energy of a particle is related to the mass and the momentum of the particle by $E=\pm \sqrt{(pc)^2+(m_0c^2)^2} $. We usually choose the positive solution and dismiss the negative-energy solution with a physical argument. However, the Dirac equation requires the existence of wave functions that correspond to the negative-energy states.

So,

  1. Do antiparticles have negative energies? Specifically, wich sign must we give to those energies when checking if energy is conserved at a reaction involving antiparticles?
  2. Are their energies just equal to their respective ordinary particles' energies buy with the opposite sign, given by $E=- \sqrt{(pc)^2+(m_0c^2)^2} $?
  3. What about particles with spins different from $\frac{1}{2}$ (i.e., bosons and other fermions)?
Quaerendo
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  • Related: https://physics.stackexchange.com/q/28583/123208 Also see https://en.wikipedia.org/wiki/Dirac_sea – PM 2Ring Jan 29 '20 at 12:42
  • What book(s) are you reading? it's just that most texts available on the internet do explain the varying interpretation of negative energy results, for example Griffiths, Sakuri, Ryder, Tong and many more. –  Jan 29 '20 at 12:51
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    Anti-particles don't have negative energy. If they did, then a particle and an anti-particle annihilating would product zero net energy. – rghome Jan 29 '20 at 14:34
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    The proper way to understand antiparticles is using quantum field theory, not just the Dirac equation. In QFT a single electron-positron field can describe $N_e$ electrons and $N_p$ positrons. The Dirac equation is just a relativistic single-particle wave equation. In QFT both electrons and positrons have positive energy. – G. Smith Jan 29 '20 at 18:47

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