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The spin of a particle may be used to define a handedness, or helicity, for that particle, which, in the case of a massless particle, is the same as chirality. A symmetry transformation between the two is called parity transformation. Invariance under parity transformation by a Dirac fermion is called chiral symmetry.
In loop quantum gravity (LQG), a spin network represents a "quantum state" of the gravitational field on a 3-dimensional hypersurface. The set of all possible spin networks (or, more accurately, "s-knots" – that is, equivalence classes of spin networks under diffeomorphisms) is countable; it constitutes a basis of LQG Hilbert space.
In particle physics, chiral symmetry breaking generally refers to the dynamical spontaneous breaking of a chiral symmetry associated with massless fermions. This is usually associated with a gauge theory such as quantum chromodynamics, the quantum field theory of the strong interaction, and it also occurs through the Brout-Englert-Higgs mechanism in the electroweak interactions of the standard ...
It has a physical interpretation as the space of massless particles with spin. It is the projectivisation of a 4-dimensional complex vector space , non-projective twistor space T {\displaystyle \mathbb {T} } , with a Hermitian form of signature (2, 2) and a holomorphic volume form .
Ashtekar variables correspond to the choice = (the negative of the imaginary number, ), is then called the chiral spin connection. The reason for this choice of spin connection, was that Ashtekar could much simplify the most troublesome equation of canonical general relativity – namely the Hamiltonian constraint of LQG .
Chiral higher-spin gravity [4] [5] is a unique higher-spin theory with propagating massless fields that is not plagued by non-localities. It is the smallest nontrivial extension of the graviton with massless higher-spin fields in four dimensions.
(It is a non-trivial result of quantum field theory [2] that the exchange of even-spin bosons like the pion (spin 0, Yukawa force) or the graviton (spin 2, gravity) results in forces always attractive, while odd-spin bosons like the gluons (spin 1, strong interaction), the photon (spin 1, electromagnetic force) or the rho meson (spin 1, Yukawa ...
(The name heterotic SO(32) is slightly inaccurate since among the SO(32) Lie groups, string theory singles out a quotient Spin(32)/Z 2 that is not equivalent to SO(32).) Chiral gauge theories can be inconsistent due to anomalies. This happens when certain one-loop Feynman diagrams cause a quantum mechanical breakdown of the gauge symmetry.