Noncanonical quantum optics

  title={Noncanonical quantum optics},
  author={Marek Czachor},
  journal={arXiv: Quantum Physics},
  • M. Czachor
  • Published 20 March 2000
  • Physics
  • arXiv: Quantum Physics
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… 
A solvable model of interacting photons
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
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
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
  • J. Naudts
  • Physics
    Journal 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
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
Reducible Quantum Electrodynamics. I. The Quantum Dimension of the Electromagnetic Field
In absence of currents and charges the quantized electromagnetic field can be described by wave functions which for each individual wave vector are normalized to one. The resulting formalism involves
Regularization just by quantization -- a new approach to the old problem of infinities in quantum field theory (Draft of lecture notes)
This is the current form of lecture notes on my approach to field quantization. I explain on a simple scalar-field model the physical motivation and show some preliminary applications (field produced
On the Emergence of the Coulomb Forces in Quantum Electrodynamics
A simple transformation of field variables eliminates Coulomb forces from the theory of quantum electrodynamics. This suggests that Coulomb forces may be an emergent phenomenon rather than being
Photon fields in a fluctuating spacetime
We present a model of interacting quantum fields, formulated in a non-perturbative manner. One of the fields is treated semi-classically, the other is the photon field. The model has an
Gauge Transformations of a Relativistic Field of Quantum Harmonic Oscillators
  • J. Naudts
  • Physics
    Reports on Mathematical Physics
  • 2021


The Quantum Theory of the Emission and Absorption of Radiation
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
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.
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
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
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.
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
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
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
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
Output Coupler for Bose-Einstein Condensed Atoms
We have demonstrated an output coupler for Bose condensed atoms in a magnetic trap. Short pulses of rf radiation were used to create Bose condensates in a superposition of trapped and untrapped