# Spin Frame Transformations and Dirac Equations

@article{Noris2021SpinFT, title={Spin Frame Transformations and Dirac Equations}, author={R. Noris and Lorenzo Fatibene}, journal={International Journal of Geometric Methods in Modern Physics}, year={2021} }

We define spin frames, with the aim of extending spin structures from the category of (pseudo-)Riemannian manifolds to the category of spin manifolds with a fixed signature on them, though with no selected metric structure. Because of this softer requirements, transformations allowed by spin frames are more general than usual spin transformations and they usually do not preserve the induced metric structures. We study how these new transformations affect connections both on the spin bundle and…

## One Citation

### Boundary structure of gauge and matter fields coupled to gravity

- Physics
- 2022

The boundary structure of 3+1-dimensional gravity (in the Palatini–Cartan formalism) coupled to to gauge (Yang–Mills) and matter (scalar and spinorial) fields is described through the use of the…

## References

SHOWING 1-10 OF 19 REFERENCES

### Spinors and diffeomorphisms

- Mathematics
- 1986

We discuss the action of diffeomorphisms on spinors on an oriented manifoldM. To do this, we first describe the action of the diffeomorphism groupD(M) on the set Π =H1 (M,Z2) of inequivalent spin…

### A universal spinor bundle and the Einstein–Dirac–Maxwell equation as a variational theory

- Mathematics
- 2015

Not only the Dirac operator, but also the spinor bundle of a pseudo-Riemannian manifold depends on the underlying metric. This leads to technical difficulties in the study of problems where many…

### Natural and gauge natural formalism for classical field theorie[s] : a geometric perspective including spinors and gauge theories

- Mathematics
- 2003

I The Geometric Setting Introduction.- 1. Fiber Bundles.- 2. Jet Bundles.- 3. Principal Bundles and Connections.- 4. Natural Bundles.- 5. Gauge Natural Bundles.- II The Variational Structure of Field…

### Do Bosons Feel Spin Frames?

- Physics
- 1999

In order to allow a coherent dynamicalspinor-matter coupling in a previous paper of ours weintroduced new variables to describe gravitationalfield, related to spin structures and called spinframes. A…

### Gauge Formalism for General Relativity and Fermionic Matter

- Physics
- 1998

A new formulation for General Relativity is developed; it is a canonical, global and geometrically well posed formalism in which gravity is described using only variables related to spin structures.…

### Metric affine gauge theory of gravity: Field equations, Noether identities, world spinors, and breaking of dilation invariance

- Physics, Mathematics
- 1995

### Spacetime Topology (I) – Chirality and the Third Stiefel–Whitney Class

- Physics
- 2002

The standard model of particle physics poses certain limitations upon the topology of spacetime, most notably by imposing the triviality of an important family of characteristic classes, the…

### Conformal aspects of the Palatini approach in Extended Theories of Gravity

- Physics
- 2006

The debate on the physical relevance of conformal transformations can be faced by taking the Palatini approach into account gravitational theories. We show that conformal transformations are not only…

### Extended Gravity

- Physics
- 2014

Abstract: We shall show equivalence between Palatini-f(R) theories and Brans-Dicke (BD) theories at the level of action principles in generic dimension with generic matter coupling. We do that by…