论文标题
量化的谐波振荡器的零点能量可以较低吗？对“暗能”和“暗物质”物理学的可能影响
Can the zero-point energy of the quantized harmonic oscillator be lower? Possible implications for the physics of "dark energy" and "dark matter"
论文作者
论文摘要
Replacing the canonical pair q and p of the harmonic oscillator (HO) by the locally and symplectically equivalent pair angle phi and action variable I implies a qualitative change of the global topological structure of the associated phase spaces: the pair (q,p) is an element of a topologically trivial plane R^2 whereas the pair (phi,I>0) is an element of a topologically non-trivial, infinitely connected,刺穿平面r^2- {0}，其组（1,2）作为其“规范”组。由于其无限覆盖的组，相关量子哈密顿量的所得（“ symbletic”）频谱由{hbar omega（n+b），n = 0,1，...; b在（0,1]}中，与“正统”频谱{Hbar Omega（n+1/2）}相反。 潜在的最重要的含义涉及红外线分子的振动，例如分子氢H_2的那些。 HO的那些符号光谱可以为两个出色的天体拼图提供同时关键，即深色（真空）能量的本质和暗物质的性质：对于前者，因为零点能量B HBAR o o omega的自由电磁波振荡器模式的自由电磁波振荡器模式可以是极小的> 0（b ca. 0（b ca exp exp（-35），用于衡量的深色darkstears darkstearts darkentienty）。以及暗物质问题的关键，因为h_2的两个核或其他原始diatomic分子的两个核的量子零点能量也可以降低，因此也可能导致“黑暗” h_2 Molecules的“黑暗”和“黑暗的ages”，因此可能会导致“黑暗”的“黑暗”和“黑暗的age”。所有结果似乎与宇宙的LambDACDM模型都达到了惊人的一致性。除了实验室实验外，从宇宙的黑暗时代和其他天体物理观察结果中寻找21-CM无线电信号可以帮助探索这些假设的含义。
Replacing the canonical pair q and p of the harmonic oscillator (HO) by the locally and symplectically equivalent pair angle phi and action variable I implies a qualitative change of the global topological structure of the associated phase spaces: the pair (q,p) is an element of a topologically trivial plane R^2 whereas the pair (phi,I>0) is an element of a topologically non-trivial, infinitely connected, punctured plane R^2-{0}, which has the group SO(1,2) as its "canonical" group. Due to its infinitely many covering groups the resulting ("symplectic") spectrum of the associated quantum Hamiltonian is given by {hbar omega (n+b), n =0,1,...; b in (0,1]}, in contrast to the "orthodox" spectrum {hbar omega (n+1/2)}. The potentially most important implications concern the vibrations of diatomic molecules in the infrared, e.g. those of molecular hydrogen H_2. Those symplectic spectra of the HO may provide a simultaneous key to two outstanding astrophysical puzzles, namely the nature of dark (vacuum) energy and that of dark matter: To the former because the zero-point energy b hbar omega of free electromagnetic wave oscillator modes can be extremely small > 0 (b ca. exp(-35) for the measured dark energy density). And a key to the dark matter problem because the quantum zero-point energies of the Born-Oppenheimer potentials in which the two nuclei of H_2 or the nuclei of other primordial diatomic molecules vibrate can be lower, too, and, therefore, may lead to spectrally detuned "dark" H_2 molecules during the "Dark Ages" of the universe and forming WIMPs in the hypothesized sense. All results appear to be in surprisingly good agreement with the LambdaCDM model of the universe. Besides laboratory experiments the search for 21-cm radio signals from the Dark Ages of the universe and other astrophysical observations can help to explore those hypothetical implications.
