Издательство: | Книга по требованию |
Дата выхода: | июль 2011 |
ISBN: | 978-6-1338-7235-6 |
Объём: | 100 страниц |
Масса: | 172 г |
Размеры(В x Ш x Т), см: | 23 x 16 x 1 |
High Quality Content by WIKIPEDIA articles! Imaginary time is a concept derived from quantum mechanics and is essential in connecting quantum mechanics with statistical mechanics. Imaginary time is obtained from real time via a Wick rotation by in the complex plane: . It can be shown that at finite temperature T, the Green's functions are periodic in imaginary time with a period of. Therefore their Fourier transforms contain only a discrete set of frequencies called Matsubara frequencies. Another way to see the connection between statistical mechanics and quantum field is to consider the transition amplitude between an initial state I and a final state F. H is the Hamiltonian of the system. If we compare this with the partition function we see that to get the partition function from the transition amplitudes we can replace , set F = I = n and sum over n. This way we don't have to do twice the work by evaluating both the statistical properties and the transition amplitudes. Finally by using a Wick rotation one can show that the Euclidean quantum field theory in (D + 1)-dimensional spacetime is nothing but quantum statistical mechanics in D-dimensional space.
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