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pycauset.spacetime.MinkowskiDiamond

class MinkowskiDiamond(dimension: int)

Inherits from: pycauset.spacetime.CausalSpacetime

Represents a causal diamond (Alexandrov interval) in flat Minkowski space.

Description

A causal diamond is the intersection of the future of a point \(p\) and the past of a point \(q\), where \(p \prec q\). In PyCauset, this is typically the standard unit diamond defined by the interval \([0, 1]^d\) in lightcone coordinates.

Parameters

  • dimension (int): The dimension of the spacetime. Currently, only \(d=2\) is fully supported for causal checks.

Methods

dimension

def dimension(self) -> int

Returns the dimension of the spacetime.

volume

def volume(self) -> float

Returns the volume of the diamond. For the standard unit diamond in lightcone coordinates, the volume is normalized to 1.0.

transform_coordinates

def transform_coordinates(self, coords: np.ndarray) -> np.ndarray

(Extension) Transforms raw lightcone coordinates to a visualization-friendly basis. For 2D, this rotates \((u, v)\) to Cartesian \((t, x)\).

get_boundary

def get_boundary(self) -> List[np.ndarray]

(Extension) Returns the boundary of the spacetime region in the transformed coordinate system. Used by visualization functions to draw the diamond edges.