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R. N. Mohapatra
11.4 Spontaneous Symmetry Breaking
In 1960 and 1961, Yoichiro Nambu and Jeffery Goldstone, respectively, discovered a profound theorem which arises when symmetry is broken spontaneously
(case (2) above). A simple way to illustrate this possibility is as follows: suppose
you have a straight stick standing vertically; to an ant sitting on top of this stick,
the area around the stick looks the same to it. The stick (and the ant sitting
on it) has a symmetric environment, called rotational symmetry. However,
because of gravity, such a standing stick will quickly fall to the ground. Then
the space around it does not look the same anymore to the ant. The rotational
symmetry is now said to be spontaneously broken. This is a crude example
of what “spontaneous symmetry breaking” in Quantum Field Theory means.
There is no explicit symmetry breaking in this case.
Some other pedagogical examples of spontaneous symmetry breaking are
the following: suppose there is a round banquet table with glasses arranged
at every seat for guests. All the guests sit down. They could pick either glass
on the left or right. So before any guest picks up a glass, the table is left–
right symmetric but as soon as one guest picks up a glass (say from the right
side) to drink from it, all the remaining guests have to pick their glasses also
from the right side. The left–right symmetry is spontaneously broken. Another
example is that there are two roads emerging from a single road like a fork
and are symmetrical with respect to the approaching car. The person in the
car approaching the fork sees a left–right symmetric situation but as soon as
he/she picks one of the forked roads, the symmetry is broken spontaneously.
The analog of these possibilities can be written in terms of Quantum Field
Theory.
11.5 Higgs Mechanism
The idea of spontaneous symmetry breaking was implemented in the context
of symmetries which are space-time dependent, in the year 1964. It was
proposed by a group of six physicists and is generally known nowadays as
the Higgs mechanism, after one of its proponents, Peter Higgs. The Higgs
mechanism has the property which gives mass to the massless gauge bosons
of gauge theory. This can be used to give masses to the W and Z boson,
making the weak force short range. The same mechanism is responsible for
all the masses of the standard model particles, i.e. gauge bosons and fermions.
R. N. Mohapatra
11.4 Spontaneous Symmetry Breaking
In 1960 and 1961, Yoichiro Nambu and Jeffery Goldstone, respectively, discovered a profound theorem which arises when symmetry is broken spontaneously
(case (2) above). A simple way to illustrate this possibility is as follows: suppose
you have a straight stick standing vertically; to an ant sitting on top of this stick,
the area around the stick looks the same to it. The stick (and the ant sitting
on it) has a symmetric environment, called rotational symmetry. However,
because of gravity, such a standing stick will quickly fall to the ground. Then
the space around it does not look the same anymore to the ant. The rotational
symmetry is now said to be spontaneously broken. This is a crude example
of what “spontaneous symmetry breaking” in Quantum Field Theory means.
There is no explicit symmetry breaking in this case.
Some other pedagogical examples of spontaneous symmetry breaking are
the following: suppose there is a round banquet table with glasses arranged
at every seat for guests. All the guests sit down. They could pick either glass
on the left or right. So before any guest picks up a glass, the table is left–
right symmetric but as soon as one guest picks up a glass (say from the right
side) to drink from it, all the remaining guests have to pick their glasses also
from the right side. The left–right symmetry is spontaneously broken. Another
example is that there are two roads emerging from a single road like a fork
and are symmetrical with respect to the approaching car. The person in the
car approaching the fork sees a left–right symmetric situation but as soon as
he/she picks one of the forked roads, the symmetry is broken spontaneously.
The analog of these possibilities can be written in terms of Quantum Field
Theory.
11.5 Higgs Mechanism
The idea of spontaneous symmetry breaking was implemented in the context
of symmetries which are space-time dependent, in the year 1964. It was
proposed by a group of six physicists and is generally known nowadays as
the Higgs mechanism, after one of its proponents, Peter Higgs. The Higgs
mechanism has the property which gives mass to the massless gauge bosons
of gauge theory. This can be used to give masses to the W and Z boson,
making the weak force short range. The same mechanism is responsible for
all the masses of the standard model particles, i.e. gauge bosons and fermions.