Fetching the paper…

Reading the bibliography…

2019

Lifting Spacetime's Poincar\'e Symmetries

Glasser, Alexander S., Qin, Hong

Original
PDF
Post on X

Understand

In the following work, we pedagogically develop 5-vector theory, an evolution of scalar field theory that provides a stepping stone toward a Poincar\'e-invariant lattice gauge theory.

Defining a continuous flat background via the four-dimensional Cartesian coordinates $\{x^a\}$, we `lift' the generators of the Poincar\'e group so that they transform only the fields existing upon $\{x^a\}$, and do not transform the background $\{x^a\}$ itself.
To facilitate this effort, we develop a non-unitary particle representation of the Poincar\'e group, replacing the classical scalar field with a 5-vector matter field.
We further augment the vierbein into a new $5\times5$ f\"unfbein, which `solders' the 5-vector field to $\{x^a\}$.

Lifting Spacetime's Poincar\'e Symmetries · Around

Built on

J. G. Fletcher, Reviews of Modern Physics 32
1960
Earlier work this paper cites.
T. W. B. Kibble, Physical Review 155
1967
Earlier work this paper cites.
J. N. Goldberg, in General Relativity and Gravitation , Vol. 1 (Plenum Press, New York, 1980) pp. 469–489
1980
Earlier work this paper cites.

Similar

P. J. Olver, Applications of Lie Groups to Differential Equations , 2nd ed., Graduate Texts in Mathematics, Vol. 107 (Springer-Verlag New York, 1993)
1993
Cited alongside, same era.
S. M. Carroll, Spacetime and Geometry: An Introduction to General Relativity (Pearson, 2003)
2003
Cited alongside, same era.
D. K. Wise, Classical and Quantum Gravity 27
2010
Cited alongside, same era.

Then

Y. Kosmann-Schwarzbach, in The Noether Theorems: Invariance and Conservation Laws in the Twentieth Century , Sources and Studies in the History of Mathematics and Physical Sciences, edited by Y. Kosmann-Schwarzbach and B. E. Schwarzbach (Springer New York, New York, NY, 2011) pp. 55–64
Original
2011
Later among the works it cites.
A. S. Glasser and H. Qin, Restoring Poincaré Symmetry to the Lattice (in preparation, 2019)
2019
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…