dorsal/arxiv
View SchemaThe connection between conformal group and quantum states of photons
| Authors | Jian Qi Shen |
|---|---|
| Categories | |
| ArXiv ID | physics/0311002 |
| URL | https://arxiv.org/abs/physics/0311002 |
Abstract
This note is concerned with the connections between the conformal group and the quantum states of photons. It is shown that there exist analogies between the photonic quantum states and the conformal group, namely, the time-development operator (with a free Hamiltonian), displacement and squeezing operators of the vacuum state corresponds to the dilatation, translation, proper Lorentz transformations, respectively, and that the three quantum states of photons ({\it i.e.}, Fock state, coherent state and squeezed state) in quantum optics thus bear some analogy to the above three transformations in the conformal group. Based on this comparison, we argue by analogy that if the phase transformation operators acting on a vacuum state (hence the Fock state, coherent state and squeezed state are generated) are truly exactly analogous to the conformal transformations, then a fourth quantum state of photons (referred to as the {\it conformal state}), which corresponds to the {\it special conformal} transformation (acceleration transformation) and will therefore be of special physical interest, can be suggested.
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"abstract": "This note is concerned with the connections between the conformal group and\nthe quantum states of photons. It is shown that there exist analogies between\nthe photonic quantum states and the conformal group, namely, the\ntime-development operator (with a free Hamiltonian), displacement and squeezing\noperators of the vacuum state corresponds to the dilatation, translation,\nproper Lorentz transformations, respectively, and that the three quantum states\nof photons ({\\it i.e.}, Fock state, coherent state and squeezed state) in\nquantum optics thus bear some analogy to the above three transformations in the\nconformal group. Based on this comparison, we argue by analogy that if the\nphase transformation operators acting on a vacuum state (hence the Fock state,\ncoherent state and squeezed state are generated) are truly exactly analogous to\nthe conformal transformations, then a fourth quantum state of photons (referred\nto as the {\\it conformal state}), which corresponds to the {\\it special\nconformal} transformation (acceleration transformation) and will therefore be\nof special physical interest, can be suggested.",
"arxiv_id": "physics/0311002",
"authors": [
"Jian Qi Shen"
],
"categories": [
"physics.optics",
"physics.gen-ph"
],
"title": "The connection between conformal group and quantum states of photons",
"url": "https://arxiv.org/abs/physics/0311002"
},
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