# The Dirac equation in $2+1$ dimensional gravity with classical electromagnetic background, the gravitational Aharonov-Bohm effect and coupled waveguide arrays.

@article{Koke2019TheDE, title={The Dirac equation in \$2+1\$ dimensional gravity with classical electromagnetic background, the gravitational Aharonov-Bohm effect and coupled waveguide arrays.}, author={Christian Koke and C. Noh and D. G. Angelakis}, journal={arXiv: Quantum Physics}, year={2019} }

The main objective of this work is to present an implementation of the Dirac equation, coupled to classical gravitational and $U(1)$ background fields, in $2+1$ dimensions in a waveguide array. We study the Dirac equation in such backgrounds, make some assumptions on the metric and the vector potential and argue that the restrictions allow for a wide array of physical spacetimes, such as all vacuum solutions of Einstein's field equations and all static spacetimes. Next, we develop a method that… Expand

#### References

SHOWING 1-10 OF 48 REFERENCES

Quantum fields in curved spacetime

- 1997

For the O(N) field theory with λΦ4 self-coupling, we construct the twoparticle-irreducible (2PI), closed-time-path (CTP) effective action in a general curved spacetime. From this we derive a set of… Expand

Quantum fields in curved space-times

- Mathematics
- Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- 1975

The problem of obtaining a quantum description of the (real) KleinGordon system in a given curved space-time is discussed. An algebraic approach is used. The *-algebra of quantum operators is… Expand

Cosmic Strings and Other Topological Defects

- Physics
- 1985

Preface 1. Introduction 2. Phase transitions in the early universe 3. Topological defects 4. String field theory 5. Superconducting strings 6. String dynamics 7. String gravity 8. String interactions… Expand

Introduction to quantum field theory

- Physics
- 1995

Even the uninitiated will know that Quantum Field Theory cannot be introduced systematically in just four lectures. I try to give a reasonably connected outline of part of it, from second… Expand

Opt

- 2017

Many graphics and vision problems can be expressed as non-linear least squares optimizations of objective functions over visual data, such as images and meshes. The mathematical descriptions of these… Expand

Geometry

- 2017

• Use a scale or scale factor to find a measurement. • Find actual lengths and areas from a scale drawing, using a scale factor. • Create multiple scale drawings from the original model or drawing,… Expand

APPL

- 2001

Statistical packages have been used for decades to analyze large datasets or to perform mathematically intractable statistical methods. These packages are not capable of working with random variables… Expand

Ann

- 2005

Aaron Beck’s cognitive therapy model has been used repeatedly to treat depression and anxiety. The case presented here is a 34-year-old female law student with an adjustment disorder with mixed… Expand

E

- P. S. Shellard, Cosmic strings and other topological defects; Cambridge University Press
- 2000

E

- P. S. Shellard, Cosmic strings and other topological defects; Cambridge University Press
- 2000