Exact properties of the chemical potential-density relation at finite temperature in the Hubbard model

We draw some rigorous conclusions about the functional properties of the $\mu-\rho$ relation in the Hubbard model based on symmetry considerations and unitary transformations. It is shown that the charge susceptibility reaches its local extreme at half-filling. Exact expressions are obtained in two limiting cases

A note on the proof of magnetic flux quantization from ODLRO

It is noticed that the excellent proof of the connection of magnetic flux quantization and off-diagonal long range order (ODLRO) presented recently by Nieh, Su and Zhao suffers from an imperfection, namely, the f-factors in the case of finite translation do not satisfy $f(a)f(b)=f(a+b)$, which was employed in the proof. A corrected proof is proposed to remedy this point.Comment: 6 pages, LATEX, no figure

A Generally Covariant Theory of Quantized Real Klein-Gordon Field in de Sitter Spacetime

We propose in this paper a quantization scheme for real Klein-Gordon field in de Sitter spacetime. Our scheme is generally covariant with the help of vierbein, which is necessary usually for spinor field in curved spacetime. We first present a Hamiltonian structure, then quantize the field following the standard approach. For the free field, the time-dependent quantized Hamiltonian is diagonalized by Bogliubov transformation and the eigen-states at each instant are interpreted as the observed particle states at that instant. The interpretation is supported by the known cosmological red-shift formula and the on-shell condition of 4-momentum for a free field. Though the mathematics is carried out in term of conformal coordinates for the sake of convenience, the whole theory can be transformed into any other coordinates based on general covariance. It is concluded that particle states, such as vacuum states in particular are time-dependent and vacuum states at one time evolves into non-vacuum states at later times. Formalism of perturbational is provided with an extended Dirac picture.Comment: 15 page

A Generally Covariant Theory of Quantized Dirac Field in de Sitter Spacetime

As a sequel to our previous work\cite{Feng2020}, we propose in this paper a quantization scheme for Dirac field in de Sitter spacetime. Our scheme is covariant under both general transformations and Lorentz transformations. We first present a Hamiltonian structure, then quantize the field following the standard approach of constrained systems. For the free field, the time-dependent quantized Hamiltonian is diagonalized by Bogliubov transformation and the eigen-states at each instant are interpreted as the observed particle states at that instant. The measurable energy-momentum of observed particle/antiparticles are the same as obtained for Klein-Gordon field. Moreover, the energy-momentum also satisfies geodesic equation, a feature justifying its measurability. As in \cite{Feng2020}, though the mathematics is carried out in terms of conformal coordinates for the sake of convenience, the whole theory can be transformed into any other coordinates based on general covariance. It is concluded that particle/antiparticle states, such as vacuum states in particular are time-dependent and vacuum states at one time evolves into non-vacuum states at later times. Formalism of perturbational calculation is provided with an extended Dirac picture.Comment: 15 pages. arXiv admin note: text overlap with arXiv:2003.0989