Local photons (original) (raw)
Related papers
In contrast to wave functions in nonrelativistic quantum mechanics interpreted as probability amplitudes, wave functions in relativistic quantum mechanics have generalized meanings such as charge-density amplitudes, energy-density amplitudes as well as particle-number density amplitudes, etc. Applying electromagnetic field intensities we construct a photon wave function, it corresponds to the (1,0)+(0,1) spinor representation of the electromagnetic field, and can be interpreted as the energy-density amplitude of photons outside a source. In terms of photon wave functions we develop photon wave mechanics, which provides us with a new quantum-mechanical description for photons outside a source.
1 3 O ct 2 01 8 On single-photon wave function
2018
We present in this paper how the single-photon wave function for transversal photons (with the direct sum of ordinary unitary representations of helicity 1 and -1 acting on it) is subsumed within the formalism of Gupta-Bleuler for the quantized free electromagnetic field in the Krein space (i.e. in the ordinary Hilbert space endowed with the Gupta-Bleuler operator η). Rigorous Gupta-Bleuler quantization of the free electromagnetic field is based on a generalization of ours (published formerly) of the Mackey theory of induced representations which includes representations preserving the indefinite Krein inner-product given by the Gupta-Bleuler operator and acting in the Krein space. The free electromagnetic field is constructed by application of the direct sum of (symmetrized) tensor products of a specific indecomposable (but reducible) single-photon representation which is Krein-isometric but non unitary, we call it Lopuszański representation, i. e. we construct the field by applica...
Photon Structure and Wave Function from the Vector Potential Quantization
Photon Structure and Wave Function from the Vector Potential Quantization , 2023
A photon structure is advanced based on the experimental evidence and the vector potential quantization at a single photon level. It is shown that the photon is neither a point particle nor an infinite wave but behaves rather like a local “wave-corpuscle” extended over a wavelength, occupying a minimum quantization volume and guided by a non-local vector potential real wave function. The quantized vector potential oscillates over a wavelength with circular left or right polarization giving birth to orthogonal magnetic and electric fields whose amplitudes are proportional to the square of the frequency. The energy ω and momentum k are carried by the local wave- corpuscle guided by the non-local vector potential wave function suitably normalized.
On single-photon wave function
arXiv (Cornell University), 2016
We present in this paper how the single-photon wave function for transversal photons (with the direct sum of ordinary unitary representations of helicity 1 and-1 acting on it) is subsumed within the formalism of Gupta-Bleuler for the quantized free electromagnetic field in the Krein space (i.e. in the ordinary Hilbert space endowed with the Gupta-Bleuler operator η). Rigorous Gupta-Bleuler quantization of the free electromagnetic field is based on a generalization of ours (published formerly) of the Mackey theory of induced representations which includes representations preserving the indefinite Krein inner-product given by the Gupta-Bleuler operator and acting in the Krein space. The free electromagnetic field is constructed by application of the direct sum of (symmetrized) tensor products of a specific indecomposable (but reducible) single-photon representation which is Krein-isometric but non unitary, we call it Lopuszański representation, i. e. we construct the field by application of the Segal's second quantization functor to the specific Krein-isometric representation. A closed subspace Htr of the single-photon Krein space on which the indefinite Krein-inner-product is strictly positive is constructed such that the Krein-isometric single-photon representation generates modulo unphysical states precisely the action of a representation which preserves the positive inner product on Htr induced by the Krein inner product, and is equal to the direct sum of ordinary unitary representations of helicity 1 and-1 respectively. Two states of single photon Krein space are physically equivalent whenever differ by a state of Krein norm zero and whose projection on Htr, in the sense of the Krein-inner-product, vanishes. In particulart it follows that the results of Bia lynicki-Birula on the single-photon wave function may be reconciled with the micro-local perturbative approach to QED initiated by Stückelberg and Bogoliubov.
Coherence and Quantum Optics VII, 1996
Relativistic invariance of photon wave mechanics 33 Localizability of photons 34 Phase-space description of a photon 36 Hydrodynamic formulation 39 Photon wave function in non-Cartesian coordinate systems and in curved space 40 Photon wave function as a spinor field 42 Photon wave functions and mode expansion of the electromagnetic field 44 Summary 45 References 47
Maxwell equations as the one-photon quantum equation
1999
Maxwell equations (Faraday and Ampere-Maxwell laws) can be presented as a three component equation in a way similar to the two component neutrino equation. However, in this case, the electric and magnetic Gauss's laws can not be derived from first principles. We have shown how all Maxwell equations can be derived simultaneously from first principles, similar to those which have been used to derive the Dirac relativistic electron equation. We have also shown that equations for massless particles, derived by Dirac in 1936, lead to the same result. The complex wave function, being a linear combination of the electric and magnetic fields, is a locally measurable and well understood quantity. Therefore Maxwell equations should be used as a guideline for proper interpretations of quantum theories.
Why photons cannot be sharply localized
Physical Review A, 2009
Photons cannot be localized in a sharply defined region. The expectation value of their energy density and the photon number density can only be approximately localized, leaving an exponential tail. We show that one may sharply localize either electric or magnetic (but not both) footprints of photons, and only momentarily. In the course of time evolution this localization is immediately destroyed. However, the coherent states, like their classical counterparts, can be localized without any limitations. The main tool in our analysis is a set of space-dependent photon creation and annihilation operators defined without any reference to the mode decomposition.
Maximal localizability of photons
Bull. Acad. Pol. Sci., Ser. Sci., Math., Astron. …, 1973
We show that simple geometric requirements lead to a unique position operator for the photon. The different components of the position do not commute. We investigate also the problem of maximal localizability and we draw the conclusion that for every closed curve there is a photon state localized on this curve.