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Register a new userVortices in equilibrium scalar electrodynamics
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Scalar electrodynamics can be used to investigate the formation of cosmic strings in the early universe. We present the results of lattice Monte Carlo simulations of an effective three-dimensional U(1)+Higgs theory that describes the equilibrium properties of finite-temperature scalar electrodynamics near the transition. A gauge-invariant criterion for the existence of a vortex is used in measuring the properties of the vortex network in the equilibrium state both in the Coulomb and in the Higgs phase of the system. The naive definition of the vortex density becomes meaningless in the continuum limit and special care is needed in extracting physical quantities. Numerical evidence for a physical discontinuity in the vortex density is given.
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The phase diagram and critical behavior of scalar quantum electrodynamics are investigated using lattice gauge theory techniques. The lattice action fixes the length of the scalar (``Higgs) field and treats the gauge field as non-compact. The phase diagram is two dimensional. No fine tuning or extrapolations are needed to study the theorys critical behovior. Two lines of second order phase transitions are discovered and the scaling laws for each are studied by finite size scaling methods on lattices ranging from $6^4$ through $24^4$. One line corresponds to monopole percolation and the other to a transition between a ``Higgs and a ``Coulomb phase, labelled by divergent specific heats. The lines of transitions cross in the interior of the phase diagram and appear to be unrelated. The monopole percolation transition has critical indices which are compatible with ordinary four dimensional percolation uneffected by interactions. Finite size scaling and histogram methods reveal that the specific heats on the ``Higgs-Coulomb transition line are well-fit by the hypothesis that scalar quantum electrodynamics is logarithmically trivial. The logarithms are measured in both finite size scaling of the specific heat peaks as a function of volume as well as in the coupling constant dependence of the specific heats measured on fixed but large lattices. The theory is seen to be qualitatively similar to $lambdaphi^{4}$. The standard CRAY random number generator RANF proved to be inadequate
The Maxwell-Chern-Simons gauge theory with charged scalar fields is analyzed at two loop level. The effective potential for the scalar fields is derived in the closed form, and studied both analytically and numerically. It is shown that the U(1) symmetry is spontaneously broken in the massless scalar theory. Dimensional transmutation takes place in the Coleman-Weinberg limit in which the Maxwell term vanishes. We point out the subtlety in defining the pure Chern-Simons scalar electrodynamics and show that the Coleman-Weinberg limit must be taken after renormalization. Renormalization group analysis of the effective potential is also given at two loop.
The centre vortex structure of the vacuum is visualised through the use of novel 3D visualisation techniques. These visualisations allow for a hands-on examination of the centre-vortex matter present in the QCD vacuum, and highlights some of the key features of the centre-vortex model. The connection between topological charge and singular points is also explored. This work highlights the useful role visualisations play in the exploration of the QCD vacuum.
The main goal of this work is to study systematically the quantum aspects of the interaction between scalar particles in the framework of Generalized Scalar Duffin-Kemmer-Petiau Electrodynamics (GSDKP). For this purpose the theory is quantized after a constraint analysis following Diracs methodology by determining the Hamiltonian transition amplitude. In particular, the covariant transition amplitude is established in the generalized non-mixing Lorenz gauge. The complete Greens functions are obtained through functional methods and the theorys renormalizability is also detailed presented. Next, the radiative corrections for the Greens functions at $alpha $-order are computed; and, as it turns out, an unexpected $m_{P}$-dependent divergence on the DKP sector of the theory is found. Furthermore, in order to show the effectiveness of the renormalization procedure on the present theory, a diagrammatic discussion on the photon self-energy and vertex part at $alpha ^{2}$-order are presented, where it is possible to observe contributions from the DKP self-energy function, and then analyse whether or not this novel divergence propagates to higher-order contributions. Lastly, an energy range where the theory is well defined: $m^{2}ll k^{2}<m_{p}^{2}$ was also found by evaluating the effective coupling for the GSDKP.
In three dimensional Maxwell-Chern-Simons massless scalar electrodynamics with $ phi^6$ coupling, the $U(1)$ symmetry is spontaneously broken at two loop order regardless of the presence or absence of the Maxwell term. Dimensional transmutation takes place in pure Chern-Simons scalar electrodynamics. The beta function for the $phi^6$ coupling is independent of gauge couplings.
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