Propagation Of Scalar Fields Research Articles

Spontaneous symmetry breaking on the lattice generated by Yukawa interaction

We study by numerical simulation a lattice Yukawa model with naive fermions at intermediate values of the Yukawa coupling constant y when the nearest-neighbour coupling κ of the scalar field Φ is very weakly ferromagnetic ( κ ≈ 0) or even antiferromagnetic ( κ < 0) and the non-vanishing value of 〈Φ〉 is generated by the Yukawa interaction. The renormalized Yukawa coupling y R achieves here its maximal value and this y-region is thus of particular importance for lattice investigations of strong Yukawa interaction. However, here the scalar field propagators have a very complex structure caused by fermion loop corrections and by the proximity of phases with antiferromagnetic properties. We develop methods for analyzing these propagators and for extracting the physical observables. We find that going into the negative κ region, the scalar field renormalization constant becomes small and y R does not see, to exceed the unitarity bound, making the existence of a non-trivial fixed point in the investigated Yukawa model quite unlikely.

Path-integral representation for the relativistic particle propagators and BFV quantization.

The path-integral representations for the propagators of scalar and spinor fields in an external electromagnetic field are derived. The Hamiltonian form of such expressions can be interpreted in the sense of Batalin-Fradkin-Vilkovisky quantization of one-particle theory. The Lagrangian representation as derived allows one to extract in a natural way the expressions for the corresponding gauge-invariant (reparametrization- and supergauge-invariant) actions for pointlike scalar and spinning particles. At the same time, the measure and ranges of integrations, admissible gauge conditions, and boundary conditions can be exactly established.

The massive scalar field propagator on finite lattices

The propagator for the massive free scalar field is calculated for an arbitrary dimension on a finite lattice. The specific boundary conditions are shown, energy dispersion relation found, and applications to self-interacting fields are made. The weak and strong coupling expansions for self-interacting fields are discussed for the finite lattice. A few comments are made in regard to Monte Carlo simulations on finite lattices.

Scalar field propagators in the microcanonical ensemble

The real-time thermal propagator of the canonical ensemble is shown to be the Laplace transform of a propagator which is an ensemble average over states with fixed energy E. This microcanonical propagator is temperature independent. The Boltzmann factor exp( − βE) in the Laplace transform produces the temperature dependence of the canonical thermal propagator. The singularity structure of the microcanonical propagator is investigated and an explicit perturbation calculation is performed in order to elucidate the origin of temperature-dependent masses.

Scalar field propagators in the microcanonical ensemble: H. Arthur Weldon. Department of Physics, West Virginia University, Morgantown, West Virginia 26506

We present an argument reinterpreting the generalized uncertainty principle (GUP) and its associated minimal length as an effective variation of Planck constant (ħ), complementing Dirac's large number hypothesis of varying G. We argue that the charge radii (i.e. the minimal length of a scattering process) of hadrons/nuclei along with their corresponding masses support an existence of an effective variation of ħ. This suggests a universality of a minimal length in measurement of scattering process. Varying ħ and G explains the necessity of Von Neumann entropy correction in Bekenstein-Hawking entropy-area law. Lastly, we suggest that the effective value of ħ derived from various elements may be related to the epoch of their creation via nucleosynthesis.

Stability of the large-scale metric in fractal structures

Scalar-field propagation on fractal structures is used to select an effective metric from the symmetry properties of infrared fixed points. There are two fixed-point metrics, a minkowskian and a euclidean metric. It is ahown that both are locally stable, though only the euclidean metric is globally stable. This analysis suggests that minkowskian symmetry at large scales cannot be simply the outcome of random metrics at small scales, as was sometimes proposed.

Scalar field propagators in anti-de Sitter space-time

Simple expressions are found for the retarded, advanced, and Feynman propagators, as well as several other auxiliary invariant functions, for scalar fields of arbitrary mass in anti-de Sitter space-time.