By Michael V. Sadovskll

This examine monograph deals an advent to complicated quantum box theoretical ideas for many-particle structures past perturbation thought. a number of schemes for resummation of the Feynman diagrams are defined. The ensuing approximations are in particular compatible for strongly correlated fermion and boson platforms. additionally thought of is the crossover from BCS superconductivity to Bose--Einstein condensation in fermion platforms with powerful beautiful interplay. specifically, a box theoretic formula of "bosonization" is gifted; it's released right here for the 1st time. this technique is utilized to the fractional quantum corridor influence, to the Coulomb plasma, and to a number of precisely solvable versions

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Peierls (1935) and L. D. Landau12 (1937) showed that in one-dimensional systems short-range forces cannot give rise to such a long-range order: thermal ﬂuctuations are so strong that they will always destroy the order. This is the so-called Landau–Peierls instability. Thus, strictly speaking, the sequence of smectic layers cannot show long-range order. A quasi-long-range order can, nevertheless exist. Experiments have revealed that along the direction of the layers the periodicity in the variations of the pair-correlation function is not perfect: the periodic function is multiplied by a function that decreases with a temperature-dependent power of distance.

Strobl, Condensed Matter Physics – Crystals, Liquids, Liquid Crystals, and Polymers, Springer-Verlag, Berlin (2004). 5. B. K. Vainshtein, V. M. Fridkin, and V. L. Indenbom, Modern Crystallography, Volume 2; Structure of Crystals, Third edition, Springer-Verlag, Berlin (2000). 13 Robert F. Curl Jr. (1933–), Sir Harold W. Kroto (1939–), and Richard E. Smalley (1943–2005) were awarded the 1996 Nobel Prize in Chemistry “for their discovery of fullerenes”. 3 The Building Blocks of Solids In what follows, of all condensed phases we shall study only the solid phase in the strictest sense of the word.

Apart from the heaviest elements, throughout the periodic table spin–orbit coupling is less important than ﬂuctuations of the interelectronic Coulomb interaction. Thus in a ﬁrst approximation spin–orbit interaction can be neglected, whereupon the orbital momenta li and spins si of individual electrons add up independently. The resultant angular momentum and spin8 of the atom are then L= li , S= si . , the Hamiltonian without the spin–orbit interaction term), the electronic state is characterized by the quantum numbers L, S, mL , and mS derived from the eigenvalues of the operators L2 , S 2 , Lz , and Sz .