Question

Show that the Dirac equation (9.7.12) with $m>0$ is linked by a unitary transformation to the one with $m<0$. The map between the two hamiltonians establishes the duality relation of the Ising model in its fermionic formulation.

   Show that the Dirac equation (9.7.12) with $m>0$ is linked by a unitary transformation to the one with $m<0$. The map between the two hamiltonians establishes the duality relation of the Ising model in its fermionic formulation.
Statistical Field Theory: An Introduction to Exactly Solved Models in Statistical Physics
Statistical Field Theory: An Introduction to Exactly Solved Models in Statistical Physics
Giuseppe Mussardo 1st Edition
Chapter 9, Problem 3 ↓

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The Dirac equation in its simplest form is given by: \[ i \hbar \frac{\partial \psi}{\partial t} = \left( -i \hbar c \vec{\alpha} \cdot \nabla + \beta mc^2 \right) \psi \] where \( \psi \) is the wave function, \( \vec{\alpha} \) and \( \beta \) are the Dirac  Show more…

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Show that the Dirac equation (9.7.12) with $m>0$ is linked by a unitary transformation to the one with $m<0$. The map between the two hamiltonians establishes the duality relation of the Ising model in its fermionic formulation.
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