Similarly, for the imaginary-time operators, ψ ψ ( x , τ τ ) = e K τ τ ψ ψ ( x ) e − − K τ τ ψ ψ ¯ ¯ ( x , τ τ ) = e K τ τ ψ ψ † † ( x ) e − − K τ τ . [Note that the imaginary-time creation operator ψ ψ ¯ ¯ ( x , τ τ ) is not the Hermitian conjugate of the annihilation operator ψ ψ ( x , τ τ ) .]