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تسجيل مستخدم جديدLifting Spacetimes Poincare Symmetries
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In the following work, we pedagogically develop 5-vector theory, an evolution of scalar field theory that provides a stepping stone toward a Poincare-invariant lattice gauge theory. Defining a continuous flat background via the four-dimensional Cartesian coordinates ${x^a}$, we `lift the generators of the Poincare group so that they transform only the fields existing upon ${x^a}$, and do not transform the background ${x^a}$ itself. To facilitate this effort, we develop a non-unitary particle representation of the Poincare group, replacing the classical scalar field with a 5-vector matter field. We further augment the vierbein into a new $5times5$ funfbein, which `solders the 5-vector field to ${x^a}$. In so doing, we form a new intuition for the Poincare symmetries of scalar field theory. This effort recasts `spacetime data, stored in the derivatives of the scalar field, as `matter field data, stored in the 5-vector field itself. We discuss the physical implications of this `Poincare lift, including the readmittance of an absolute reference frame into relativistic field theory. In a companion paper, we demonstrate that this theoretical development, here construed in a continuous universe, enables the description of a discrete universe that preserves the 10 infinitesimal Poincare symmetries and their conservation laws.
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The following work demonstrates the viability of Poincare symmetry in a discrete universe. We develop the technology of the discrete principal Poincare bundle to describe the pairing of (1) a hypercubic lattice `base manifold labeled by integer verti
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