A theory of dark energy that matches dark matter

In this paper, a theory of dark energy is proposed that matches dark matter. The relativistic quantum mechanics equations reveal that free particles can have negative energies. We think that the negative energy is the dark energy which behaviors as dark photons with negative energies. In this work, the photon number states are extended to the cases where the photon number can be negative integers, called negative integer photon states, the physical meaning of which are that the photons in such a state are of negative energy, i.e., dark photons. The dark photons constitute dark radiation, also called negative radiation. The formulism of the statistical mechanics and thermodynamics of the dark radiation is presented. This version of dark energy is of negative temperature and negative pressure, the latter regarded as responsible for the accelerate expansion of the universe. It is believed that there is a symmetry of energy-dark energy in the universe. In our previous work, the theory of the motion of the matters with negative kinetic energy was presented. In our opinion, the negative kinetic energy matter is dark matter. In the present work, we demonstrate that the dark substances absorb and release dark energy. In this view, the dark matter and dark energy match. Therefore, there is a symmetry of matter-energy match and dark matter-dark energy match in the universe. We present the reasons why the negative kinetic energy systems and negative radiation are dark to us

A generalized scattering theory in quantum mechanics

In quantum mechanics textbooks, a single-particle scattering theory is introduced. In the present work, a generalized scattering theory is presented, which can be in principle applied to the scattering problems of arbitrary number of particle. In laboratory frame, a generalized Lippmann-Schwinger scattering equation is derived. We emphasized that the derivation is rigorous, even for treating infinitesimals. No manual operation such as analytical continuation is allowed. In the case that before scattering N particles are plane waves and after the scattering they are new plane waves, the transition amplitude and transition probability are given and the generalized S matrix is presented. It is proved that the transition probability from a set of plane waves to a new set of plane waves of the N particles equal to that of the reciprocal process. The generalized theory is applied to the cases of one- and two-particle scattering as two examples. When applied to single-particle scattering problems, our generalized formalism degrades to that usually seen in the literature. When our generalized theory is applied to two-particle scattering problems, the formula of the transition probability of two-particle collision is given. It is shown that the transition probability of the scattering of two free particles is identical to that of the reciprocal process. This transition probability and the identity are needed in deriving Boltzmann transport equation in statistical mechanics. The case of identical particles is also discussed.Comment: 35 pages, 3figure

There is no vacuum zero-point energy in our universe for massive particles within the scope of relativistic quantum mechanics

It was long believed that there is a zero-point energy in the form of h\omega/2 for massive particles, which is obtained from Schr\"odinger equation for the harmonic oscillator model. In this paper, it is shown, by the Dirac oscillator, that there is no such a zero-point energy. It is argued that when a particle's wave function can spread in the whole space, it can be static. This does neither violate wave-particle duality nor uncertainty relationship. Dirac equation correctly describes physical reality, while Schr\"odinger equation does not when it is not the nonrelativistic approximation of Dirac equation with a certain model. The conclusion that there is no zero-point energy in the form of h\omega/2 is applied to solve the famous cosmological constant problem for massive particles.Comment: 14 pages, 1 tabl