The Lee-Wick Fields out of Gravity

We study the Maxwell-Einstein theory in the framework of effective field theories. We show that the modified one-loop renormalizable Lagrangian due to quantum gravitational effects contains a Lee-Wick vector field as an extra degree of freedom in the theory. Thus gravity provides a natural mechanism for the emergence of this exotic particle.Comment: 8 pages, 1 figure, typos fixe

Spinodal Instabilities of Baryon-Rich Quark-gluon Plasma in the PNJL Model

Using the Polyakov-Nambu-Jona-Lasinia (PNJL) model, we study the spinodal instability of a baryon-rich quark-gluon plasma in the linear response theory. We find that the spinodal unstable region in the temperature and density plane shrinks with increasing wave number of the unstable mode and is also reduced if the effect of Polyakov loop is not included. In the small wave number or long wavelength limit, the spinodal boundaries in both cases of with and without the Polyakov loop coincide with those determined from the isothermal spinodal instability in the thermodynamic approach. Also, the vector interactions among quarks is found to suppress unstable modes of all wave numbers. Moreover, the growth rate of unstable modes initially increases with the wave number but is reduced when the wave number becomes large. Including the collisional effect from quark scattering via the linearized Boltzmann equation, we further find that it decreases the growth rate of unstable modes of all wave numbers. Relevance of these results to relativistic heavy ion collisions is discussed.Comment: 13 pages, 9 figure

Relationships Between Generalized Bernoulli Numbers and Polynomials and Generalized Euler Numbers and Polynomials

In this paper, concepts of the generalized Bernoulli and Euler numbers and polynomials are introduced, and some relationships between them are established

School Quality and Housing Prices: Empirical Evidence Based on a Natural Experiment in Shanghai, China

The extent to which the quantity and quality of education is capitalized into housing prices is a key issue in understanding the relationship between allocation of educational resources and the housing market. Using monthly panel data of 52 residential areas in Shanghai and employing a natural experiment of designating Shanghai Experimental Model Senior High Schools (EMSHS), we find that housing prices in Shanghai have capitalized the access to quality schools and other public goods. One quality school per square kilometer raises average housing prices by approximately 19%, and one best EMSHS per square kilometer increases housing prices by 21%. We also match the schools designated for EMSHS with schools of similar quality but not designated for EMSHS, and compare housing prices in the corresponding areas. We find that the designation increased the housing prices, showing that dissemination of information about school quality was significantly affected by the designation.education, housing market, capitalization, public goods, natural experiment