Computational Physics

Exercises 463 To proceed, we must work out the tensors(^0 )and (^0 ). In order to do this, we note that, on the hexagonal grid, ...

464 The lattice Boltzmann method for fluid dynamics derivative) of the parabola is given by∇P/(νρ). Check also that the velocity ...

References 465 [15] M. R. Swift, E. Orlandini, W. R. Osborn, and J. M. Yeomans, ‘Lattice Boltzmann simulations of liquid–gas and ...

15 Computational methods for lattice field theories 15.1 Introduction Classical field theory enables us to calculate the behavio ...

15.2 Quantum field theory 467 describe what quantum field theory is and present several examples. In the follow- ing section, th ...

468 Computational methods for lattice field theories Ais a constant, and some special conditions are needed for the boundaries. ...

15.2 Quantum field theory 469 where we have assumed periodic boundary conditions in space and time (or van- ishing fields at the ...

470 Computational methods for lattice field theories with [ˆπn,φˆl]=−iδnl. (15.15) The hats are put aboveφandπto emphasise that ...

15.2 Quantum field theory 471 for arbitraryM, which denotes the number of particles present. It is possible to have the samekioc ...

472 Computational methods for lattice field theories and the Lagrangian describes the simplest interesting field theory for inte ...

15.3 Interacting fields and renormalisation 473 Thed-dimensional delta-function reflects the energy–momentum conservation of the ...

474 Computational methods for lattice field theories unacceptable. Another way to remove the divergences is by formulating the t ...

15.3 Interacting fields and renormalisation 475 theory is renormalisable is quite restrictive. For example, only theφ^4 potentia ...

476 Computational methods for lattice field theories values much larger than the lattice constant. This means that our parameter ...

15.4 Algorithms for lattice field theories 477 In the final sections of this chapter, simulation methods for gauge field theorie ...

478 Computational methods for lattice field theories where Knl=( 2 d+m^2 )δnl− ∑ μ δn,l+μ. (15.46) Defining Fourier-transformed ...

15.4 Algorithms for lattice field theories 479 function〈φnφl〉. The Fourier transform of this correlation function can be found q ...

480 Computational methods for lattice field theories straightforwardly in order to sample field configurations with Boltzmann we ...

15.4 Algorithms for lattice field theories 481 a Gaussian distributionρ(φn), according to the procedure just described. Then we ...

482 Computational methods for lattice field theories is equal to that of the corresponding Poisson solver algorithm, that is, th ...