The Pin Groups in Physics: C, P, and T

@article{Berg2000ThePG,
  title={The Pin Groups in Physics: C, P, and T},
  author={Marcus Berg and Cecile DeWitt-Morette and Shangjr Gwo and Erik Kramer},
  journal={arXiv: Mathematical Physics},
  year={2000}
}
We review the role in physics of the Pin groups, double covers of the full Lorentz group. Pin(1,3) is to O(1,3) what Spin(1,3) is to SO(1,3). The existence of two Pin groups offers a classification of fermions based on their properties under space or time reversal finer than the classification based on their properties under orientation preserving Lorentz transformations -- provided one can design experiments that distinguish the two types of fermions. Many promising experimental setups give… 

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References

SHOWING 1-10 OF 137 REFERENCES

The Type I D instanton and its M theory origin

The tree-level amplitude for the scattering of two gauge particles constrained to move on the two distinct boundaries of eleven-dimensional space-time in the Horava-Witten formulation of M-theory is

Spin structures in string theory

Local Field Theory and Isospin Invariance. I. Free‐Field Theory of Spinless Bosons

The properties of free‐field theories of spinless bosons are investigated. The self‐conjugate boson field theories of isospin ½, 32, 52, ⋯ are shown to be nonlocal: the energy, isospin, and number

SUPERSTRING THEORY

SYMMETRY DEFECTS AND BROKEN SYMMETRY. CONFIGURATIONS - HIDDEN SYMMETRY

This paper is an introduction to the study of spontaneous symmetry breaking and topological classification of defects. The latter topic has aits foundation in the former one; both subjects requires

String theory.

The current “standard model” of particle physics—which is nearly 25 years old, has much experimental evidence in its favor and is comprised of six quarks, six leptons, four forces, and the as yet unobserved Higgs boson—contains internal indications that it, too, may be just another step along the path toward uncovering the truly fundamental degrees of freedom.

Derivation of the CPT Theorem and the Connection between Spin and Statistics from Postulates of the S-Matrix Theory

The CPT theorem (G. Luders, Kgl. Danske Videnskab. Selskab Mat.-fys. Medd., 28: No. 5(1954)) and the normal connection between spin and statistics are consequences of postulates of the S-matrix

Existence of Majorana fermions for M-branes wrapped in space and time

We show that it is possible to define Majorana (s)pinor fields on M-branes which have been identified under the action of the antipodal map on the adS factor of the throat geometry, or which have

On Spinors in n Dimensions

The matrix which enters in the charge conjugation transformation of the usual spinors in 4‐space is an invariant matrix and is skew symmetric. It is shown that there exists such an invariant matrix C
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