Free The Higgs Boson: Searching for the God Particle by Scientific American Editors Page A

determined. The Higgs field can be represented as an arrow superposed on the other isotopic-spin indicators in the imaginary internal space of a hadron.
What distinguishes the arrow of the Higgs field is that it has a fixed length,
established by the vacuum value of the field. The orientation of the other isotopic-spin arrows can then be measured with respect to the axis defined by the Higgs field. In this way a proton can be distinguished from a neutron.
    It might seem that the introduction of the Higgs field would spoil the gauge symmetry of the theory and thereby lead again to insoluble infinities. In actuality,
however, the gauge symmetry is not destroyed but merely concealed.
The symmetry specifies that all the laws of physics must remain invariant when the isotopic-spin arrow is rotated in an arbitrary way from place to place. This implies that the absolute orientation of the arrow cannot be determined, since any experiment for measuring the orientation would have to detect some variation in a physical quantity when the arrow was rotated. With the inclusion of the Higgs field the absolute orientation of the arrow still cannot be determined because the arrow representing the Higgs field also rotates during a gauge transformation. All that can be measured is the angle between the arrow of the Higgs field and the other isotopic-spin arrows, or in other words their relative orientations.
    The Higgs mechanism is an example of the process called spontaneous symmetry breaking, which was already well established in other areas of physics.
The concept was first put forward by Werner Heisenberg in his description of ferromagnetic materials. Heisenberg pointed out that the theory describing a ferromagnet has perfect geometric symmetry in that it gives no special distinction to any one direction in space. When the material becomes magnetized, however,
there is one axis–the direction of magnetization–that can be distinguished from all other axes. The theory is symmetrical but the object it describes is not. Similarly, the Yang-Mills theory retains its gauge symmetry with respect to rotations of the isotopic-spin arrow,
but the objects described–protons and neutrons–do not express the symmetry.
    How does the Higgs mechanism lend mass to the quanta of the Yang-Mills field? The process can be explained as follows. The Higgs field is a scalar quantity,
having only a magnitude, and so the quantum of the field must have a spin of zero. The Yang-Mills fields are vectors,
like the electromagnetic field, and are represented by spin-one quanta. Ordinarily a particle with a spin of one unit has three spin states (oriented parallel,
antiparallel and transverse to its direction of motion), but because the Yang-Mills particles are massless and move with the speed of light they are a special case; their transverse states are missing.
If the particles were to acquire a mass,
they would lose this special status and all three spin states would have to be observable. In quantum mechanics the accounting of spin states is strict and the extra state must come from somewhere;
it comes from the Higgs field.
Each Yang-Mills quantum coalesces with one Higgs particle; as a result the Yang-Mills particle gains mass and a spin state, whereas the Higgs particle disappears. A picturesque description of this process has been suggested by Abdus Salam of the International Center for Theoretical Physics in Trieste:
the massless Yang-M ills particles "eat"
the Higgs particles in order to gain weight, and the swallowed Higgs particles become ghosts.
    In 1971, Veltman suggested that I investigate the renormalization of the pure Yang-Mills theory. The rules for constructing the needed Feynman diagrams had already been formulated by Faddeev, Popov, Fradkin and Tyutin,
and independently by Bryce S. DeWitt of the University of Texas at Austin and Stanley Mandelstam of the University of California at Berkeley. I could adapt to the task the powerful methods for