Basics Of Statistical Physics (Third Edition) by Muller-kirsten Harald J W;

Author:Muller-kirsten, Harald J W;
Language: eng
Format: epub
Publisher: World Scientific Publishing Company
Published: 2022-01-15T00:00:00+00:00

and determines the quantity Δ, also called Schwinger function [69], from the conditions (observe ( – m2)Δ = 0)***

Verify these conditions (since Δ diverges on the light cone it should be considered as a distribution). (b) Could we take on the left hand side of Eq. (8.54) not the commutator with minus sign but the anticommutator with plus sign? Show that this plus sign leads to a contradiction by setting φ = a + ib ≠ 0, φ* = a − ib (with a = a*, b = b*). Hence the scalar field φ obeys Bose–Einstein statistics (not Fermi–Dirac statistics).

[Hint: Use Δ = 0 for x = x′, t = t′, so that

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