arXiv subjects

George Jaroszkiewicz

Publications and source records attributed to George Jaroszkiewicz.

27 records · Page 2Linked to original sources

arXiv2001

Temporal discretisation of the Skyrme Model

Soliton models are used in elementary particle physics and nuclear physics to model extended objects such as nucleons, using effective field theories derived from more fundamental theories such as QCD. Computer simulation requires some sort of discretisation procedure, a notable example being lattice gauge theory applied in the imaginary time formulation. In this lecture we focus on simulation in real time and the problems which arise when invariants of the motion are monitored in a simulation. Ad hoc discretisations invariably introduce drift in numerically computed invariants, due not only to numerical accuracy (which can be negligible), but with the fact that the discretisation may not necessarily imply conservation. We discuss an approach developed which gives principles for the discretisation of such systems and for the construction of exact discrete invariants of the motion. This approach is applied to the Skyrme model. Talk at the International Workshop on Nuclear Theory, Rila, June 2001, to be published in the Proceedings.

hep-th↗

arXiv2001

The running of the Universe and the quantum structure of time

Some principles underpinning the running of the Universe are discussed. The most important, the machine principle, states that the Universe is a fully autonomous, self-organizing and self-testing quantum automaton. Continuous space and time, consciousness and the semi-classical observers of quantum mechanics are all emergent phenomena not operating at the fundamental level of the machine Universe. Quantum processes define the present, the interface between the future and the past, giving a time ordering to the running of the Universe which is non-integrable except on emergent scales. A diagrammatic approach is used to discuss the quantum topology of the EPR paradox, particle decays and scattering processes. A toy model of a self-referential universe is given.

quant-ph↗

arXiv2000

Causal Implication and the Origin of Time Dilation

We discuss the emergence of time dilation as a normal feature expected of any system where a central processor may have to wait one or more clock cycles before concluding a local calculation. We show how the process of causal implication in a typical Newtonian cellular automaton leads naturally to Lorentz transformations and invariant causal structure.

gr-qc↗

arXiv2000

Discrete spacetime: classical causality,prediction, retrodiction and the mathematical arrow of time

A mathematical definition of classical causality over discrete spacetime dynamics is formulated. The approach is background free and permits a definition of causality in a precise way whenever the spacetime dynamics permits. It gives a natural meaning to the concepts of cosmic time, spacelike hypersurfaces and timelike or lightlike flows without assuming the notion of a background metric. The concepts of causal propagators and the speed of causality are discussed. In this approach the concepts of spacetime and dynamics are linked in an essential and inseparable whole, with no meaning to either on its own.

gr-qc↗

arXiv1998

Principles of Discrete Time Mechanics: V. The Quantisation of Maxwell's Equations

Principles of discrete time mechanics are applied to the quantisation of Maxwell's equations. Following an analysis of temporal node and link variables, we review the classical discrete time equations in the Coulomb and Lorentz gauges and conclude that electro-magneto duality does not occur in pure discrete time electromagnetism. We discuss the role of boundary conditions in our mechanics and how temporal discretisation should influence very early universe dynamics. Quantisation of the Maxwell potentials is approached via the discrete time Schwinger action principle and the Faddeev-Popov path integral. We demonstrate complete agreement in the case of the Coulomb gauge, obtaining the vacuum functional and the discrete time field commutators in that gauge. Finally, we use the Faddeev-Popov method to construct the discrete time analogues of the photon propagator in the Landau and Feynman gauges, which casts light on the break with relativity and possible discrete time analogues of the metric tensor.

hep-th↗

arXiv1998

Principles of Discrete Time Mechanics: IV. The Dirac Equation, Particles and Oscillons

We apply the principles of discrete time mechanics discussed in earlier papers to the first and second quantised Dirac equation. We use the Schwinger action principle to find the anticommutation relations of the Dirac field and of the particle creation operators in the theory. We find new solutions to the discrete time Dirac equation, referred to as oscillons on account of their extraordinary behaviour. Their principal characteristic is that they oscillate with a period twice that of the fundamental time interval T of our theory. Although these solutions can be associated with definite charge, linear momentum and spin, such objects should not be observable as particles in the continuous time limit. We find that for non-zero T they correspond to states with negative squared norm in Hilbert space. However they are an integral part of the discrete time Dirac field and should play a role in particle interactions analogous to the role of longitudinal photons in conventional quantum electrodynamics.

hep-th↗

arXiv1998

Principles of Discrete Time Mechanics: III. Quantum Field Theory

We apply the principles discussed in earlier papers to the construction of discrete time quantum field theories. We use the Schwinger action principle to find the discrete time free field commutators for scalar fields, which allows us to set up the reduction formalism for discrete time scattering processes. Then we derive the discrete time analogue of the Feynman rules for a scalar field with a cubic self interaction and give examples of discrete time scattering amplitude calculations. We find overall conservation of total linear momentum and overall conservation of total theta parameters, which is the discrete time analogue of energy conservation and corresponds to the existence of a Logan invariant for the system. We find that temporal discretisation leads to softened vertex factors, modifies propagators and gives a natural cutoff for physical particle momenta.

hep-th↗

arXiv1997

Principles of Discrete Time Mechanics: I. Particle Systems

We discuss the principles to be used in the construction of discrete time classical and quantum mechanics as applied to point particle systems. In the classical theory this includes the concept of virtual path and the construction of system functions from classical Lagrangians, Cadzow's variational principle applied to the action sum, Maeda-Noether and Logan invariants of the motion, elliptic and hyperbolic harmonic oscillator behaviour, gauge invariant electrodynamics and charge conservation, and the Grassmannian oscillator. First quantised discrete time mechanics is discussed via the concept of system amplitude, which permits the construction of all quantities of interest such as commutators and scattering amplitudes. We discuss stroboscopic quantum mechanics, or the construction of discrete time quantum theory from continuous time quantum theory and show how this works in detail for the free Newtonian particle. We conclude with an application of the Schwinger action principle to the important case of the quantised discrete time inhomogeneous oscillator.

hep-th↗

arXiv1997

Principles of Discrete Time Mechanics: II. Classical field Theory

We apply the principles discussed in an earlier paper to the construction of discrete time field theories. We derive the discrete time field equations of motion and Noether's theorem and apply them to the Schrodinger equation to illustrate the methodology. Stationary solutions to the discrete time Schrodinger wave equation are found to be identical to standard energy eigenvalue solutions except for a fundamental limit on the energy. Then we apply the formalism to the free neutral Klein Gordon system, deriving the equations of motion and conserved quantities such as the linear momentum and angular momentum. We show that there is an upper bound on the magnitude of linear momentum for physical particle-like solutions. We extend the formalism to the charged scalar field coupled to Maxwell's electrodynamics in a gauge invariant way. We apply the formalism to include the Maxwell and Dirac fields, setting the scene for second quantisation of discrete time mechanics and discrete time Quantum Electrodynamics.

hep-th↗