In an ideal ferromagnet at temperatures below the critical temperature, the magnetization is proportional to the square root of T T c T T c. Second-order phase transitions (continuous). First-order phase transitions (discontinuous). Such a connection first appeared with the work of Gliner and the more elaborated considerations by Zeldovich in 1967, just fifty years after the \(\Lambda \)-term was first introduced by Einstein. Lecture 1: The Landau-Ginzburg theory of phase transitions. The general off-shell result yields a smooth function \(\rho _=\Lambda /(8\pi G_N)\), although accompanied with a peculiar association of \(\Lambda >0\) with a negative energy density of vacuum (sic), and still without hinting at any relationship with the quantum theory at this point. The on-shell renormalized result first appears at sixth adiabatic order, so the calculation is rather cumbersome. On this simple example we show how dynamics of correlation functions depends on the choice of initial Cauchy surface, basis of modes and on the choice of initial state build with the use of the corresponding creation and annihilation operators. On the other hand, in particle physics matter and radiation are described in terms of quantum field theory on Minkowski spacetime. Herein, we compute the zero-point energy (ZPE) for a nonminimally coupled (massive) scalar field in FLRW spacetime using the off-shell adiabatic renormalization technique employed in previous work. This is a model example of quantum field theory in curved space-time. In the standard model of cosmology, the universe is described by a Robertson-Walker spacetime, while its matter/energy content is modeled by a perfect fluid with three components corresponding to matter/dust, radiation, and a cosmological constant. We may however get over this adversity using a different perspective. As a consequence, one is bound to extreme fine-tuning of the parameters and so to sheer unnaturalness of the result and of the entire approach. In the standard model of cosmology, the universe is described by a Robertson-Walker spacetime, while its matter/energy content is modeled by a perfect fluid with three components corresponding to matter/dust, radiation, and a cosmological constant. The renormalization of the vacuum energy in quantum field theory (QFT) is usually plagued with theoretical conundrums related not only with the renormalization procedure itself, but also with the fact that the final result leads usually to very large (finite) contributions incompatible with the measured value of \(\Lambda \) in cosmology.
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