By Pierre Mathieu, David Sénéchal, Philippe Francesco

Filling a major hole within the literature, this entire textual content develops conformal box concept from first ideas. The therapy is self-contained, pedagogical, and exhaustive, and encompasses a good deal of historical past fabric on quantum box idea, statistical mechanics, Lie algebras and affine Lie algebras. the various workouts, with a large spectrum of trouble and matters, supplement and in lots of situations expand the textual content. The textual content is hence not just a very good device for lecture room educating but in addition for person examine. meant essentially for graduate scholars and researchers in theoretical high-energy physics, mathematical physics, condensed topic conception, statistical physics, the e-book may also be of curiosity in different parts of theoretical physics and arithmetic. it is going to organize the reader for unique study during this very energetic box of theoretical and mathematical physics.

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**Sample text**

Let us consider the mean-field approximation in which the interactions between the fields cp~ and cp~ = cp are neglected. 27) In cp(x) + const . 31) Let us consider the system in a finite volume. Then (see Sec. 36) is the coordinate of the centre of the mass of the system in the volume V. I Identifying Q with the momentum [;, [P, q] = Iii, one might think that what we have e nco untered is the dynamics of the harmonic oscillator, [;2 mw2q2 H=-+-2m 2 with the "mass" m as k -+ =V and the frequency w = k -+ O.

This substitution reflects the essence of the dynamics III the BCS model. The composite operator 7/lp(x)7/l",(x) describes a condensate of electrons. e. it is assumed that its classical part dominates. 5). In that case the condensate was described by the elementary field rp( x) ; the condensate led to the spontaneous breakdown of particle number conservation. In the BCS model the condensate described by the composite operator 7/lp(x )7/l",(x) leads to the spontaneous breakdown of the U(l) symmetry connected with the conservation of the electric charge.

8. BCS MODEL OF SUPERCONDUCTIVITY We are ready now to discuss the BCS model. We will do this comparing BCS dynamics with those of the Fermi gas with a Majorana mass. 85) T hus, instead of a Majorana term, a four-fermion term appears in LEGS. 57) . 85) describes the interactions of electrons with phonons near th e Fermi surface. 1 l hl'ory. 86) a rather complicated nonlinear equation. 81). This substitution reflects the essence of the dynamics III the BCS model. The composite operator 7/lp(x)7/l",(x) describes a condensate of electrons.