# 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…

## 17 Citations

### Reflections on the matter of 3D N=1 vacua and local Spin(7) compactifications

- Mathematics, PhysicsPhysical Review D
- 2022

We use Higgs bundles to study the 3d N = 1 vacua obtained from M-theory compactified on a local Spin(7) space given as a four-manifoldM4 of ADE singularities with further generic enhancements in the…

### Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups

- Mathematics
- 2017

We study three-dimensional gauge theories based on orthogonal groups. Depending on the global form of the group these theories admit discrete $\theta$-parameters, which control the weights in the sum…

### Topological quantum field theory and quantum gravity

- Physics
- 2014

This thesis is broadly split into two parts. In the first part, simple state sum models for minimally coupled fermion and scalar fields are constructed on a 1-manifold. The models are independent of…

### Notes on Ramond-Ramond spinors and bispinors in double field theory

- Chemistry
- 2022

: The Ramond-Ramond sector of double ﬁeld theory (DFT) can be described either as an O ( D, D ) spinor or an O ( D − 1 , 1) × O (1 , D − 1) bispinor. Both formulations may be related to the standard…

### Symmetries, Anomalies and Duality in Chern-Simons Matter Theories

- Physics
- 2018

This thesis investigates the properties of quantum field theory with Chern-Simons interaction in three spacetime dimension. We focus on their symmetries and anomalies. We find many theories exhibit…

### Aspects of Twistor Geometry and Supersymmetric Field Theories within Superstring Theory

- Mathematics
- 2006

There are two major topics within string theory to which the results presented in this thesis are related: non-anticommutative field theory on the one hand and twistor string theory on the other…

### Cyclic Structures of Cliffordian Supergroups and Particle Representations of Spin+(1, 3)

- Mathematics
- 2012

Supergroups are defined in the framework of $${\mathbb{Z}_2}$$Z2 2-graded Clifford algebras over the fields of real and complex numbers, respectively. It is shown that cyclic structures of complex…

### Cobordism conjecture, anomalies, and the String Lamppost Principle

- Mathematics
- 2020

We consider consequences of triviality of cobordism classes and anomaly cancellation in supergravity theories in $d>6$. We argue that this leads to the existence of certain defects which we call…

### Aspects of Twistor Geometry and Supersymmetric Field Theories within Superstring Theory

- Mathematics
- 2006

In this thesis, we report on results in non-anticommutative field theory and twistor string theory, trying to be self-contained. We first review the construction of non-anticommutative N=4 super…

## References

SHOWING 1-10 OF 137 REFERENCES

### The Type I D instanton and its M theory origin

- Physics
- 2000

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…

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

- Physics
- 1968

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…

### SYMMETRY DEFECTS AND BROKEN SYMMETRY. CONFIGURATIONS - HIDDEN SYMMETRY

- Physics
- 1980

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.

- PhysicsProceedings of the National Academy of Sciences of the United States of America
- 1998

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

- Physics
- 1962

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

- Physics
- 1998

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

- Mathematics
- 1962

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…