出版社：SISSA, Scuola Internazionale Superiore di Studi Avanzati
摘要：We explore a new way to simulate quantum field theory, without introducing a spatial lattice. As
a pilot study we apply this method to the 3d lf 4 model. The regularisation consists of a fuzzy
sphere with radius R for the two spatial directions, plus a discrete Euclidean time. The fuzzy
sphere approximates the algebra of functions of the sphere with a matrix algebra, and the scalar
field is represented by a Hermitian N×N matrix at each time site. We evaluate the phase diagram,
where we find a disordered phase and an ordered regime, which splits into phases of uniform and
non-uniform order. We discuss the behaviour of the model in different limits of large N and R,
which lead to a commutative or to a non-commutative lf 4 model in flat space.
