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The spin and the strange twists of fermions

Of all the known physical quantities as spin is generally regarded as the most "quantum-mechanical." The word spin comes from the English "spin", meaning turn or rotate, and refers to a physical property of particles (1) subatomic, by which all elementary particle has an angular momentum intrinsic fixed value. Is a characteristic of the particle such as mass or electric charge, and a magnitude that remains as does the energy or momentum.

Unlike what happens with the angular momentum of macroscopic objects, which are used, which can take many different values \u200b\u200bdepending on the actions to which subjects see the magnitude of the spin of a particle is always the same for this particular type of particle. It is only the spin axis direction that can vary, but in a very strange way.

For an electron, proton or neutron spin quantity is always 1 / 2 of minimum value of time allowed (H) . Precisely why this amount of angular momentum would not be permitted for an object composed of a number of orbiting particles without any of them were turning on itself. Spin can only appear because it is an intrinsic property of the particle itself, ie not arising from the orbital motion of its parts around its center.

A particle like the electron, has an odd multiple spin ħ / 2 (h / 2, 3h / 3, 5h / 2, etc) is called a fermion, and presents a curious rarity: a full 360 º rotation transforms its state vector is not in itself but in the negative of itself, require therefore a rotation of 720 º to stay the same as before rotation. Most particles Nature are fermions, the remaining particles for which the spin is an integer multiple of h (h, 2h, 3h, 4h, etc.) are called bosons. Under a rotation of 360 º the state vector becomes a boson itself, not its negative.

If we take a particle of spin 1 / 2, for example the electron, the space of possible quantum-mechanical states turns out to be two dimensional, so we can take a base of only two states can be represented as [above> and [down below, for the first spin clockwise tour around the direction vertically upwards and the second is in the same way down. the same way as in a Euclidean plane any vector is a linear superposition of two orthonormal bases in question, in this case occurs as any possible state of the electron spin is a linear superposition , eg

w [up> + z [Down> where w, z complex numbers. Since the physical state represented remains unchanged if we multiply the two components by a non-zero complex number, the ratio z / q is the significant complex number that represents the state of the particle.


This complex number is represented on a Riemann sphere called, as shown in Fig. In Ecuador the same singular points are 1, -1, i-i.



The Riemann sphere plays a crucial role in any two-state quantum system, describing all possible quantum states. For a particle of spin 1 / 2, geometric role is particularly evident since the field points correspond to possible spatial directions for the axis of rotation. In other situations, the role of the Riemann sphere of possibilities is much more hidden, with a much less clear with the geometry space.


The strange turn of 720 ° of the electron to stay the same is quite a paradox. In many cases it seems that quantum mechanics phenomena has completely illogical, but to analyze every situation completely normal for us in the light of this amazing theory we note that without unexplained. The very cohesion of matter, as we know, or the existence of the four fundamental forces no sense. In the latter case at its foundations, paradoxically, is the very principle of uncertainty. A principle of "cumbersome" It seems that only measure is to prevent infinite accuracy.


(1) It is recognized that a "particle" may have individual parts that it can be treated as a whole quantum mechanical simple, with a well defined total angular momentum.