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In terms of the Hamiltonian $H$ the antisymmetry follows simply: Majorana fields $\Psi(x,t)$ are real, and they satisfy a real wave equation $$\partial\Psi/\partial t =-iH\Psi,$$ where $iH$ is real, hence $H$ is imaginary. Since $H$ must also be Hermitian, it means that $H^T=-H$ (antisymmetric).

_{More explicitly, $H=\gamma_{\rm M}^\mu \partial_\mu$, with $\gamma_{\rm M}^\mu$ the Dirac matrices in the Majorana representation, for which $\gamma_{\rm M}$ is a purely imaginary $4\times 4$ matrix. The antisymmetry of $H$ becomes manifest if we discretize the derivative operator.}

In terms of the Hamiltonian $H$ the antisymmetry follows simply: Majorana fields $\Psi(x,t)$ are real, and they satisfy a real wave equation $$\partial\Psi/\partial t =-iH\Psi,$$ where $iH$ is real, hence $H$ is imaginary. Since $H$ must also be Hermitian, it means that $H^T=-H$ (antisymmetric).

_{More explicitly, $H=\gamma_{\rm M}^\mu \partial_\mu$, with $\gamma_{\rm M}^\mu$ the Dirac matrices in the Majorana representation, for which $\gamma_{\rm M}$ is a purely imaginary $4\times 4$ matrix. The antisymmetry of $H$ becomes manifest if we discretize the derivative operator so that $H$ becomes a matrix and $H_{nm}=-H_{mn}$.}

In terms of the Hamiltonian $H$ the antisymmetry follows simply: Majorana fields $\Psi(x,t)$ are real, and they satisfy a real wave equation $$\partial\Psi/\partial t =-iH\Psi,$$ where $iH$ is real, hence $H$ is imaginary. Since $H$ must also be Hermitian, it means that $H^T=-H$ (antisymmetric).

In terms of the Hamiltonian $H$ the antisymmetry follows simply: Majorana fields $\Psi(x,t)$ are real, and they satisfy a real wave equation $$\partial\Psi/\partial t =-iH\Psi,$$ where $iH$ is real, hence $H$ is imaginary. Since $H$ must also be Hermitian, it means that $H^T=-H$ (antisymmetric).

_{More explicitly, $H=\gamma_{\rm M}^\mu \partial_\mu$, with $\gamma_{\rm M}^\mu$ the Dirac matrices in the Majorana representation, for which $\gamma_{\rm M}$ is a purely imaginary $4\times 4$ matrix. The antisymmetry of $H$ becomes manifest if we discretize the derivative operator.}

In terms of the Hamiltonian $H$ the antisymmetry follows simply: Majorana fields $\Psi(x,t)$ are real, and they satisfy a real wave equation $$\partial\Psi/\partial t =-iH\Psi,$$ where $iH$ is real. Since $H$ must also be Hermitian, it means that $H^T=-H$ (antisymmetric).

In terms of the Hamiltonian $H$ the antisymmetry follows simply: Majorana fields $\Psi(x,t)$ are real, and they satisfy a real wave equation $$\partial\Psi/\partial t =-iH\Psi,$$ where $iH$ is real, hence $H$ is imaginary. Since $H$ must also be Hermitian, it means that $H^T=-H$ (antisymmetric).