The vertices might be connected by a bosonic or fermionic propagator.

where signifies the normal-product of the operators and takes care of the possible sign change when commuting the fermionic operators to bring them together for a contraction ( a propagator ).

# A fermionic propagator is represented by a solid line connecting two points ;

The minimal coupling between torsion and Dirac spinors generates a spin-spin interaction which is significant in fermionic matter at extremely high densities.

* A baryon, such as the proton or neutron, contains three fermionic quarks and is therefore a fermion ;

# A fermionic field is represented by a solid line attached to the point with an arrow toward the point ;

# A fermionic field is represented by a solid line attached to the point with an arrow from the point ;

Another problem for easy definition is that much of the rest mass of ordinary matter derives from the invariant mass contributed to matter by particles and kinetic energies which have no rest mass themselves ( only 1 % of the rest mass of matter is accounted for by the rest mass of its fermionic quarks and electrons ).

In nonrelativistic quantum mechanics all particles are either bosons or fermions ; in relativistic quantum theories also " supersymmetric " theories exist, where a particle is a linear combination of a bosonic and a fermionic part.

One may notice from this that applying a fermionic creation operator twice gives zero, so it is impossible for the particles to share single-particle states, in accordance with the exclusion principle.

The minimal coupling between torsion and Dirac spinors generates a repulsive spin – spin interaction which is significant in fermionic matter at extremely high densities.

A fermionic condensate is similar to the Bose-Einstein condensate but composed of fermions.

Vacuum energy is the zero-point energy of all the fields in space, which in the Standard Model includes the electromagnetic field, other gauge fields, fermionic fields, and the Higgs field.

It is the quantum mechanical version of an ideal gas, for the case of fermionic particles.

Here is the operator which symmetrizes or antisymmetrizes a tensor, depending on whether the Hilbert space describes particles obeying bosonic or fermionic statistics.

In the Einstein – Cartan theory, however, the minimal coupling between torsion and Dirac spinors generates a repulsive spin – spin interaction which is significant in fermionic matter at extremely high densities.

Along with the standard twistor degrees of freedom, a supertwistor contains N fermionic scalars, where N is the number of supersymmetries.

The polariton is a bosonic quasiparticle, and should not be confused with the polaron, a fermionic one, e. g. an electron plus attached phonon cloud.

In the nonsupersymmetric version the action is invariant under a similar Z < sub > 2 </ sub > symmetry because the matter fields are all fermionic and thus must appear in the action in pairs, while the Higgs fields are bosonic.

The fermionic superpartner of the axion is called the axino, the scalar superpartner is called the saxion.

The minimal coupling between torsion and Dirac spinors generates a spin-spin interaction which is significant in fermionic matter at extremely high densities.

The smallest superspace is a point which contains neither bosonic nor fermionic directions.

Other trivial examples include the n-dimensional real plane R < sup > n </ sup >, which is a vector space extending in n real, bosonic directions and no fermionic directions.

The bosonic part of the supersymmetry algebra is the Poincaré algebra, while the fermionic part is constructed using spinors of Grassmann numbers.

In this matrix theory, particles are represented by non-commuting matrices, and the matrix elements of bosonic and fermionic particles are ordinary complex numbers and non-commuting Grassman numbers, respectively.

The fermionic annihilation operators c and creation operators are defined by their actions on a Fock state thus

As before, the fermionic relations are the same, with the commutators replaced by anticommutators.

This theory can be straightforwardly quantized by treating bosonic and fermionic sectors as free.

Supersymmetry reduces the size of the quantum corrections by having automatic cancellations between fermionic and bosonic Higgs interactions.

* cosmic string loop stabilised by a fermionic supercurrent: vorton

For a state of half-integer spin the argument can be circumvented by having fermionic statistics.

Defining as a general annihilation ( creation ) operator that could be either fermionic or bosonic, the real space representation of the operators defines the quantum field operators and by

We will use the following conventions ; the spatial ( both bosonic and fermionic ) indices will be indicated by M, N, ....

A fermionic condensate is a superfluid phase formed by fermionic particles at low temperatures.

The first atomic fermionic condensate was created by Deborah S. Jin in 2003.

When Eric Cornell and Carl Wieman produced a Bose – Einstein condensate from rubidium atoms in 1995, there naturally arose the prospect of creating a similar sort of condensate made from fermionic atoms, which would form a superfluid by the BCS mechanism.

He speculated that fermionic atoms could be coaxed into pairing up by subjecting them to a strong magnetic field.

This is true for bosons, whereas for fermions the commutator must be replaced by the anticommutator, As a consequence, in the fermionic case the number operator has only the eigenvalues 0 and 1.

The classical scaling dimension of an operator O is determined by dimensional analysis from the Lagrangian ( in 4 spacetime dimensions this means dimension 1 for elementary bosonic fields including the vector potentials, 3 / 2 for elementary fermionic fields etc .).

According to, the superconformal algebra in 3 + 1D is given by the bosonic generators,,,, the U ( 1 ) R-symmetry, the SU ( N ) R-symmetry and the fermionic generators,, and.

and the fermionic action is given by