# Noncanonical quantum optics

@article{Czachor2000NoncanonicalQO, title={Noncanonical quantum optics}, author={Marek Czachor}, journal={arXiv: Quantum Physics}, year={2000} }

Modification of the right-hand-side of canonical commutation relations (CCR) naturally occurs if one considers a harmonic oscillator with indefinite frequency. Quantization of electromagnetic field by means of such a non-CCR algebra naturally removes the infinite energy of vacuum but still results in a theory which is very similar to quantum electrodynamics. An analysis of perturbation theory shows that the non-canonical theory has an automatically built-in cut-off but requires charge/mass…

## 13 Citations

### A solvable model of interacting photons

- Physics
- 2006

It is a general belief that the relevant models of quantum field theory cannot be solved analytically. It is even not clear how to formulate these models in a mathematically consistent manner. Only…

### Regularization as Quantization in Reducible Representations of CCR

- Physics
- 2004

A covariant quantization scheme employing reducible representations of canonical commutation relations with positive-definite metric and Hermitian four-potentials (an alternative to the Gupta-Bleuler…

### Automatic Regularization by Quantization in Reducible Representations of CCR: Point-Form Quantum Optics with Classical Sources

- Physics
- 2008

Electromagnetic fields are quantized in a manifestly covariant way by means of a class of reducible “center-of-mass N-representations” of the algebra of canonical commutation relations (CCR). The…

### Non-classical correlations in reducible quantum electrodynamics

- PhysicsJournal of Physics Communications
- 2019

The question is discussed whether the momentum of a photon has a quantum uncertainty or whether it is a classical quantity. The latter assumption is the main characteristic of reducible Quantum…

### Quantization of free electromagnetic field: A different approach to the time-like polarization

- Physics
- 2015

A four-dimensional photon polarization space, such that gives a different interpretation of the ladder operators for the time-like degree comparing to the Gupta-Bleuler formulation is presented. This…

### Gauge Transformations of a Relativistic Field of Quantum Harmonic Oscillators

- PhysicsReports on Mathematical Physics
- 2021

### Emergent Coulomb Forces in Reducible Quantum Electrodynamics

- PhysicsFoundations of Science
- 2019

This paper discusses an attempt to develop a mathematically rigorous theory of quantum electrodynamics (QED). It deviates from the standard version of QED mainly in two aspects: it is assumed that…

### Reducible representations of CAR and CCR with possible applications to field quantization

- Mathematics
- 2003

Reducible representations of CAR and CCR are applied to second quantization of Dirac and Maxwell fields. The resulting field operators are indeed operators and not operator-valued distributions.…

### Relativistic EPR-type experiments for photons in the background of reducible representation HOLA algebras

- Physics
- 2015

Relativistic EPR-type experiments for photons in the background of reducible representation algebras are discussed. A model for the four Bell states, such that maintains maximally correlated in two…

## References

SHOWING 1-10 OF 20 REFERENCES

### The Quantum Theory of the Emission and Absorption of Radiation

- Physics
- 1927

The new quantum theory, based on the assumption that the dynamical variables do not obey the commutative law of multiplication, has by now been developed sufficiently to form a fairly complete theory…

### On the Theory of quantum mechanics

- Mathematics
- 1926

The new mechanics of the atom introduced by Heisenberg may be based on the assumption that the variables that describe a dynamical system do not obey the commutative law of multiplication, but…

### Photon scattering from atoms in an atom interferometer: Coherence lost and regained.

- PhysicsPhysical review letters
- 1995

Experiments are discussed here in which this entanglement results from the elastic scattering of a photon from an atom initially in a state with extended spatial coherence inside an atom interferometer.

### Operational Quantum Physics

- Physics
- 2001

Operational Quantum Physics offers a systematic presentation of quantum mechanics which makes exhaustive use of the full probabilistic structure of this theory. Accordingly the notion of an…

### Dispersion cancellation and quantum eraser experiments analyzed in the Wigner function formalism

- Physics
- 1997

We extend the Wigner function formalism for parametric down-conversion experiments presented in a previous paper [Phys. Rev. A 55 3879 (1997)] to experiments involving propagation through a…

### Optics and interferometry with Na2 molecules.

- PhysicsPhysical review letters
- 1995

An intense, pure beam of sodium molecules (Na2) is produced by using light forces to separate the atomic and molecular species in a seeded supersonic beam using diffraction from a microfabricated grating and a molecule interferometer with fully separated beams and high contrast fringes.

### Fourth-order interference in the Wigner representation for parametric down-conversion experiments

- Physics
- 1997

In the Wigner formalism, after giving a general description of a light beam, the theory of parametric down-conversion is developed to second-order in the coupling constant. We then describe the…

### Observation of Interference Between Two Bose Condensates

- PhysicsScience
- 1997

It is demonstrated that Bose condensed atoms are “laser-like”; that is, they are coherent and show long-range correlations and have direct implications for the atom laser and the Josephson effect for atoms.

### The conceptual development of quantum mechanics

- Physics, History
- 1966

Market: Historians of science and students. An enlarged and revised edition of a volume that offers a systematic and comprehensive account of the historical development of quantum mechanics for the…