By Kleinert.

It's the objective of this ebook to debate an easy method through Feynman direction quintessential formulation during which the transformation to collective fields quantities to merechanges of integration variables in useful integrals. After the transformation, the trail formula will back be discarded. The ensuing box concept is quantizedin the normal type and the basic quanta at once describe the collective excitations

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By A. Zichichi, p. 172. [5] See for example: A. A. Abrikosov, L. P. Gorkov, I. E. P. Kadanoff, G. Baym, Quantum Statistical Mechanics, Benjamin, New York (1962); A. Fetter, J. D. Walecka, Quantum Theory of Many-Paricle Systems, McGraw-Hill, New York (1971). L. Stratonovich, Sov. Phys. Dokl. 2, 416 (1958), J. Hubbard, Phys. Rev. Letters 3, 77 (1959); B. M¨ uhlschlegel, J. Math. Phys. 3, 522 (1962); J. Langer, Phys. Rev. 134, A 553 (1964); T. M. Rice, Phys. Rev. 140 A 1889 (1965); J. Math. Phys. 8, 1581 (1967); A.

Low. Temp. 23, 751 (1976). [31] D. Rainer, J. W. Serene, Phys. Rev. B13, 4745 (1976); Y. Kuroda, A. D. S. Nagi, J. Low Temp. Phys. 25, 569 (1976). 38 2 Relativistic Fields [32] For a review see: D. R. Bes, R. A. Broglia, Lectures delivered at “E. Fermi” Varenna Summer School, Varenna, Como. Italy, 1976. For recent studies: D. R. Bes, R. A. Broglia, R. Liotta, B. R. Mottelson, Phys. Letters 52B, 253 (1974); 56B, 109 (1975), Nuclear Phys. B A260, 127 (1976). See also: R. W. Richardson, J. Math. Phys.

Such discussions are standard and will not be repeated here [7]. 4 n is the number density: n = 2 d3 pF /(2π)3 = p3F /3π 2 . H. 1 General Formulation There is a collective field complementary to the plasmon field which describes dominant collective excitations in many systems such as type II superconductors, 3 He, excitonic insulators, etc. 1) as1 [8] exp − i ×e 2 i 2 dxdx dxdx ψ ∗ (x)ψ ∗ (x )ψ(x )ψ(x)V (x, x ) = const × D∆(x, x )D∆∗ (x, x ) 1 −∆∗ (x,x )ψ(x)ψ(x )−ψ ∗ (x)ψ ∗ (x )∆(x,x ) |∆(x,x )|2 V (x,x ) .

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