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aFor a discussion of broken symmetry in condensed matter physics, see P. W. Anderson, Basic Notions of Condensed Matter Physics (Benjamin-Cummings, Menlo Park, CA, 1984), 2. For its role in particle physics, see K. Huang, Quarks, Leptons, and Gauge Fields (Wodd Scientific, Singapore, 1982), s 3,4. bWeinberg-Salam model of unified electro-weak interactions. cQuantum chromodynamics with massless quarks.

mode," wherein the "photon" acquires a mass dynamically, and the would-be Goldstone excitation becomes the longitudinal degree of freedom of the massive "photon." An example of this is the Meissner effect in superconductivity, in which the photon mass corresponds to the inverse penetration depth. We offer a list of broken symmetry phenomena in condensed matter physics and particle physics in Table 16.5. In defining spontaneously broken symmetry, we have assumed that a system can exist in only one ground state, even if it possesses many equivalent ones. This is obvious in classical mechanics, but not in quantum mechanics. In the latter case one can legitimately ask, "Why can't the system exist in a linear combination of different ground states " The answer is that, to make a transition from one ground state to another. one needs an operator that simultaneously changes the states of all the particles in the system. Such an operator does not exist in the thermodynamic limit, when the number of particles tends to infinity. In this limit, therefore, the different ground states generate separate Hilbert spaces, and transitions among them are forbidden. One says that there is a "super selection rule" insulating the ground states from one another. If a superposition is made of two different ground states, then no physical measurement can determine the relative phase of the two states; one would have two separate systems that can never communicate with each other. Thus, such a superposition does not correspond to any experimental situation.

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see broad market changes, such as the softening of ascending prices when comparing the rst trendline here with the second.

(11.131)

where v'(N)

r=::---1

(-I~r~+I)

(11.132)

kT{ v [

~ (1 + r )] -

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~ (1 -

We have covered a tremendous amount of ground in this chapter. We ve learned how to construct and interpret trendlines in many different circumstances. We can see how to make use of them to measure resistance and support levels and to judge when a trend has changed. Now we will add to this knowledge in the next chapter by learning about trendline pairs that make up the much rarer, but still very useful, channel pattern.

r)]}

(11.133)

:r{N[~(I+r)] -v[~(1-r)]} 2

where v[x] =:: v(x) and A = V2'17n 2jmkT, the thermal wavelength. The low-temperature and high-temperature approximations for v(Nxj2) are obtainable from (11.24) and (11.12), respectively. They are

1 x) : : : x 2/ [1 _ '12 (kT)2_ ] 17

X 4/3

(:~ 1)

(11.134)

In this chapter we are going to undertake two different but related subjects: chart resizing and drawn channels. A channel is a drawn object that consists of two parallel trendlines, so many of the same principles you learned in 7 apply. First, though, we will examine charting resizing since it is relevant not just to channels but to almost all drawn objects.

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(1 + r )2/3

r )1/3

(11.135)

(11.136)

Equation (11.135) is invariant under a change of sign of r. This is to be expected; in the absence of field, no absolute meaning can be attached to "up" or "down."

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