dorsal/arxiv
View SchemaGroup Theoretical Quantization of Phase and Modulus Related to Interferences
| Authors | H. A. Kastrup |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0005033 |
| URL | https://arxiv.org/abs/quant-ph/0005033 |
Abstract
Following a recent group theoretical quantization of the symplectic space S={(phi in R mod 2pi, p>0)} in terms of irreducible unitary representations of the group SO(1,2) the present paper proposes an application of those results to the old problem of quantizing modulus and phase in interference phenomena: The self-adjoint Lie algebra generators K_1, K_2 and K_3 of that group correspond to the classical observables p cos(phi), -p sin(phi) and p > 0 the Poisson brackets of which obey that Lie algebra, too. For the irreducible unitary representations of the positive series the modulus operator K_3 has the positive discrete spectrum {n+k, n=0,1,2,...; k > 0}. Self-adjoint operators for cos(phi) and sin(phi) can then be defined as (K_3^{-1}K_1 + K_1 K_3^{-1})/2 and - (K_3^{-1} K_2 + K_2 K_3^{-1})/2 which have the theoretically desired properties for k >0.32. Some matrix elements with respect to number eigenstates and with respect to coherent states are calculated. One conclusion is that group theoretical quantization may be tested by quantum optical experiments.
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"abstract": "Following a recent group theoretical quantization of the symplectic space\nS={(phi in R mod 2pi, p\u003e0)} in terms of irreducible unitary representations of\nthe group SO(1,2) the present paper proposes an application of those results to\nthe old problem of quantizing modulus and phase in interference phenomena: The\nself-adjoint Lie algebra generators K_1, K_2 and K_3 of that group correspond\nto the classical observables p cos(phi), -p sin(phi) and p \u003e 0 the Poisson\nbrackets of which obey that Lie algebra, too. For the irreducible unitary\nrepresentations of the positive series the modulus operator K_3 has the\npositive discrete spectrum {n+k, n=0,1,2,...; k \u003e 0}. Self-adjoint operators\nfor cos(phi) and sin(phi) can then be defined as (K_3^{-1}K_1 + K_1 K_3^{-1})/2\nand - (K_3^{-1} K_2 + K_2 K_3^{-1})/2 which have the theoretically desired\nproperties for k \u003e0.32. Some matrix elements with respect to number eigenstates\nand with respect to coherent states are calculated. One conclusion is that\ngroup theoretical quantization may be tested by quantum optical experiments.",
"arxiv_id": "quant-ph/0005033",
"authors": [
"H. A. Kastrup"
],
"categories": [
"quant-ph",
"hep-th",
"math-ph",
"math.MP",
"physics.optics"
],
"title": "Group Theoretical Quantization of Phase and Modulus Related to Interferences",
"url": "https://arxiv.org/abs/quant-ph/0005033"
},
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