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By Meghnad Saha

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Math. Phys. 23, 1852. (1982). Grassmann variables Chandlin, D. , Nuovo Cim. 4, 231 (1956). Berezin, F. A. (1966). Method of Second Quantization (Academic Press, New York). McLerran, L. , Rev. Mod. Phys. 58, 1021 (1986). 3 Interactions and diagrammatic techniques Unfortunately it is not possible to carry out the functional integration in closed form when the Lagrangian contains terms that are more than quadratic in the fields. The reader is invited to verify this. Thus, it is important to develop approximation techniques.

70) is over the Dirac indices. 81). The boson line in the first diagram carries zero frequency and momentum and gives rise to the factor D0 (0, 0) = m−2 . 62). 2. The new aspects are: 1 There is a factor T n [d3 p/(2π)3 ]G0 (ωn , p) for each fermion line. 2 There is a factor g at each vertex. 3 There is a trace over Dirac indices for each closed fermion loop as well as a minus sign coming from the Grassmann nature of the fermion field. 68)) arise from the fact that the scalar field φ develops a nonzero thermal average.

For bosons we argued that we must take ωn = 2πnT in order that φ(x, τ ) be periodic, which followed from the trace operation in the partition function. 85) Tτ φ(x, where θ is the step-function. 86) implies that φ(y, 0) = φ(y, β) and hence ωn = 2πnT . 90) This implies that and hence This antiperiodicity required of fermion fields is in no way inconsistent with the trace operation in the partition function. The trace only means that the system returns to its original state after a “time” β. 89) describes the same physical state as the left-hand side.

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A treatise on heat: Including kinetic theory of gasses [sic], thermodynamics and recent advances in statistical thermodynamics by Meghnad Saha


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