Conformal invariance in two-dimensional discrete field theory

Conformal invariance in 2-dimensional Discrete Field Theory

A discretized massless wave equation in two dimensions, on an appropriately chosen square lattice, exactly reproduces the solutions of the corresponding continuous equations. We show that the reason for this exact solution property is the discrete analog of conformal invariance present in the model, and find more general field theories on a two-dimensional lattice that exactly solve their conti...

Conformal Invariance in Two-dimensional Percolation

The word percolation, borrowed from the Latin, refers to the seeping or oozing of a liquid through a porous medium, usually to be strained. In this and related senses it has been in use since the seventeenth century. It was introduced more recently into mathematics by S. R. Broadbent and J. M. Hammersley ([BH]) and is a branch of probability theory that is especially close to statistical mechan...

Conformal Invariance for Non-Relativistic Field Theory

Momentum space Ward identities are derived for the amputated n-point Green’s functions in 3 + 1 dimensional non-relativistic conformal field theory. For n = 4 and 6 the implications for scattering amplitudes (i.e. on-shell amputated Green’s functions) are considered. Any scale invariant 2-to-2 scattering amplitude is also conformally invariant. However, conformal invariance imposes constraints ...

Twisted Conformal Symmetry in Noncommutative Two-Dimensional Quantum Field Theory

Turbulent Two Dimensional Magnetohydrodynamics and Conformal Field Theory

We show that an infinite number of non-unitary minimal models may describe two dimensional turbulent magnetohydrodynamics (MHD), both in the presence and absence of the Alf'ven effect. We argue that the existence of a critical dynamical index results in the Alf'ven effect or equivelently the equipartition of energy. We show that there are an infinite number of conserved quantities in 2D − M HD ...