By Victor Nikolaevich Popov
Written through a distinct physicist and best researcher, this quantity describes the speculation and chosen functions of 1 of an important mathematical instruments utilized in the theoreticial research of collective excitations in statistical physics. The textual content deals an creation to practical vital ideas in equilibrium statistical physics, and discusses the expression of partition features and eco-friendly features by way of practical integrals. Sections of the e-book take care of the appliance of sensible integrals in superfluid Bose platforms, platforms with Coulomb interplay, and superfluid Fermi structures. The publication additionally considers the applying of the concept that of Bose-condensation of auxiliary fields to the idea of crystals, heavy atoms and likewise to the idea of version Hamiltonians.
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Extra resources for Functional Integrals and Collective Excitations
Example text
2 ) has the meaning of superlluid density p,. The superfluid density p, is equal to the full density p = P i. at zero temperature. Taking this into account, we will replace p;. by p,, if T #- 0. 2), we took into account only the field functions l/f 0(x r), lf/0(x, r), which had no zeros in the x, r space (more precisely 1/10(x, r)l 2 = p(x, r) was close to p0(k0)). Now let us consider the case when l/f 0(x, r) may vanish at some discrete set of points in the x plane (for a fixed If we go around such a point, the phase variable cp(x, r) acquires an increment 2rrn, where n is an integer.
T plane. The considerations determining the main diagram series for the self energy parts of Green's functions A, B are also applicable if we want to find the main diagram series for the pressure p. 20) where p0 is the pressure of the ideal Bose gas, C0 is the constant (C0 = ). 5), and D is the sum of all connected (vacuum) diagrams. ned factors (1) and (2): D ':I:;; + + 8 O C> + + + c:x:=> + + ... 2 1) + �+ b ... c 6 Low-density Bose gas 35 These diagrams contain either two vertices of the second-order or two independent loops, or one independent loop with either one second-order vertex or two third-order vertices.
In r0a where a is the vortex core radius. This formula is valid for r0 » a. We now express the contribution of those x, y for which I x - y l r0 as a fu nctional integral over the new vector potential function 2mc Ii fJr. np. = (dli(x), dl i(y)) -+ I x - yI : • _ YI < ,0 = = - -, > (8. <>(o;A;)CT;dA; ; J exp ( - J d3x(curl A)2 )nx<>(o;A;)CT;dA; c (mc2 ) 1/2 - np"-- i ,k Ix k q= 2n p ' - (8. 16) (8. 1 7) is a coupling constant. We can prove (8. 16) by making a shift transform ation which cancels the linear term J(jA) d 3 x in the exponent of the integrand in the numerator on the right-hand side of(8.