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Register a new userConnection between GRW spontaneous collapse and Menskys restricted path integral models
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Roman Sverdlov
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In this paper we will show how Menskys model of restricted path integrals can be derived from GRW spontaneous collapse model.
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It is commonly assumed that zero and non-zero photon mass would lead to qualitatively different physics. For example, massless photon has two polarization degrees of freedom, while massive photon at least three. This feature seems counter-intuitive. In this paper we will show that if we change propagator by setting $i epsilon$ (needed to avoid poles) to a finite value, and also introduce it in a way that breaks Lawrentz symmetry, then we would obtain the continuous transition we desire once the speed of the photons is large enough with respect to preferred frame. The two transverse polarization degrees of freedom will be long lived, while longitudinal will be short lived. Their lifetime will be near-zero if $m ll sqrt{epsilon}$, which is where the properties of two circular polarizations arize. The $i epsilon$ corresponds to the intensity of Menskys continuous measurement and the short lifetime of the longitudinal photons can be understood as the conversion of quantum degrees of freedom (photons) into classical ones by the measurement device (thus getting rid of the former). While the classical trajectory of the longitudinal photons does arize, it plays no physical role due to quantum Zeno effect: intuitively, it is similar to an electron being kept at a ground state due to continuous measurement.
Quantum Monte Carlo belongs to the most accurate simulation techniques for quantum many-particle systems. However, for fermions, these simulations are hampered by the sign problem that prohibits simulations in the regime of strong degeneracy. The situation changed with the development of configuration path integral Monte Carlo (CPIMC) by Schoof textit{et al.} [T. Schoof textit{et al.}, Contrib. Plasma Phys. textbf{51}, 687 (2011)] that allowed for the first textit{ab initio} simulations for dense quantum plasmas. CPIMC also has a sign problem that occurs when the density is lowered, i.e. in a parameter range that is complementary to traditional QMC formulated in coordinate space. Thus, CPIMC simulations for the warm dense electron gas are limited to small values of the Brueckner parameter -- the ratio of the interparticle distance to the Bohr radius -- $r_s=bar{r}/a_B lesssim 1$. In order to reach the regime of stronger coupling (lower density) with CPIMC, here we investigate additional restrictions on the Monte Carlo procedure. In particular, we introduce two differe
Birefringence phenomena stemming from vacuum polarization are revisited in the framework of coherent scattering. Based on photon-photon scattering, our analysis brings out the direct connection between this process and vacuum birefringence. We show how this procedure can be extended to the Kerr and the Cotton-Mouton birefringences in vacuum, thus providing a unified treatment of various polarization schemes, including those involving static fields.
Through a very careful analysis of Diracs 1932 paper on the Lagrangian in Quantum Mechanics as well as the second and third editions of his classic book {it The Principles of Quantum Mechanics}, I show that Diracs contributions to the birth of the path-integral approach to quantum mechanics is not restricted to just his seminal demonstration of how Lagrangians appear naturally in quantum mechanics, but that Dirac should be credited for creating a path-integral which I call {it Dirac path-integral} which is far more general than Feynmans while possessing all its desirable features. On top of it, the Dirac path-integral is fully compatible with the inevitable quantisation ambiguities, while the Feynman path-integral can never have that full consistency. In particular, I show that the claim by Feynman that for infinitesimal time intervals, what Dirac thought were analogues were actually proportional can not be correct always. I have also shown the conection between Dirac path-integrals and the Schrodinger equation. In particular, it is shown that each choice of Dirac path-integral yields a {it quantum Hamiltonian} that is generically different from what the Feynman path-integral gives, and that all of them have the same {it classical analogue}. Diracs method of demonstrating the least action principle for classical mechanics generalizes in a most straightforward way to all the generalized path-integrals.
Recently we have reported the correct formulation of the hadron formation from the quarks and gluons by using the lattice QCD method at the zero temperature. Similarly we have also reported the correct formulation of the hadron formation from the thermalized quark-gluon plasma by using the lattice QCD method at the finite temperature. In this paper we extend this to non-equilibrium QCD and present the correct formulation of the hadron formation from the non-equilibrium quark-gluon plasma by using the closed time path integral formalism. Hadron formation from the non-equilibrium quark-gluon plasma is necessary to detect the quark-gluon plasma at RHIC and LHC.
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