Postulate boson

The force carrier (or exchange ) particles are all bosons. These particles are responsible for carrying the four fundamental forces. This family includes the strong interaction carrier, the gluon the weak interaction carriers, the W and Z° the carrier of the electromagnetic force, the photon and the postulated but unobserved carrier of the gravitational force, the graviton. 

Special attention must be paid in systems of identical particles, where we have to take into account the symmetry postulate of quantum mechanics. This means that the space of states for fermions is the antisymmetric subspace of while the symmetric subspace dK+N refers to bosons. 

Boltzon Postulate. Maxwell-Boltzmann (MB) statistics predict that all energies are a priori equally likely, and that all particles in the system are physically distinguishable (labeled by some number, or shirt patch, "color", or whatever, or picked up by "tweezers"). These MB particles can be called boltzons. If, however, we remove this distinguishability, then we have indistinguishable "corrected boltzons (CB)" [2], whose statistics become very roughly comparable to the statistics of fermions or bosons (see Problem 5.3.10 below). 

According to the symmetrization postulate of quantum mechanics, the spin-space state function of a system of N nondifferentiable nuclei must be invariant under any of the A /2 even permutations IV W performed simultaneously on the space (7 ) and spin (S) particles coordinates. Under odd permutations, the state function of N fermions changes sign while that of N bosons remains invariant. 

The functions now satisfy the relation Tp 1 = . It is accepted by postulate, and subsequent agreement with experiment, that particles with eigenfunctions belonging to the Ai(S) and A2(S) types are the only ones that occur in nature Bosons and Fermions respectively. A more familiar form of Eq. 9.7 is the Slater determinant ... 

Postulate VI has to do with the symmetry of the wave function with respect to different labeling identical particles. If one exchanges the labels of two identical particles (the exchange of all the coordinates of the two particles), then for two identical fermions, the wave function has to change its sign (antisymmetric), while for two identical bosons, the function does not change (symmetry). As a consequence, two identical fermions with the same spin coordinate cannot occupy the same point in space. 

Postulate V says that an elementary particle has an internal angular momentum (spin). One can measure only two quantities the square of the spin length -I- l)h and one of its components where ms = —s, —s -I-1,..., -l-s, with spin quantum number s > 0 characteristic for the type of particle (integer for bosons, half-integer for fermions). The spin magnetic quantum number ms takes 2s -I-1 values. 

Finally, we should note that all that has been said so far is valid for fermionic annihilation and creation operators only. In the case of bosons these operators need to fulfill commutation relations instead of the anticommutation relations. The fulfillment of anticommutation and commutation relations corresponds to Fermi-Dirac and Bose-Einstein statistics, respectively, valid for the corresponding particles. Accordingly, there exists a well-established cormection between statistics and spin properties of particles. It can be shown [65], for instance, that Dirac spinor fields fulfill anticommutation relations after having been quantized (actually, this result is the basis for the antisymmetrization simply postulated in section 8.5). Hence, in occupation number representation each state can only be occupied by one fermion because attempting to create a second fermion in state i, which has already been occupied, gives zero if anticommutation symmetry holds. 

Vector Boson postulated by the unified theory of weak and electromagnetic interactions. 

Postulate vn must be antisymmetric (symmetric) for the exchange of identical fermions (bosons). 

It was not until 1957 that the phenomena of superconductivity was explained by a theory developed by Bardeen, Cooper, and Schreiffer (BCS theory) in which it was postulated that two electrons became loosely bound by exchanging a virtual phonon (another way of saying a cooperative interaction with the lattice ions). By becoming paired with opposite spins, the so-called Cooper pairs act as bosons and are no longer controlled by the Pauli principle therefore, many can exist in the same quantum state. This pairing creates an energy gap about the Fermi level in which no states are available for the Cooper pair to be scattered into hence, they can move through the lattice unimpeded, very much like the superfluid state of liquid He which exhibits zero viscosity. 

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